Evaluation of Failure Modes for Concrete Dams

Transkript

1 DEGREE PROJECT, IN CONCRETE STRUCTURES, SECOND LEVEL STOCKHOLM, SWEDEN 2015 Evaluation of Failure Modes for Concrete Dams LISA BROBERG & MALIN THORWID KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

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3 Evaluation of Failure Modes for Concrete Dams Lisa Broberg & Malin Thorwid June 2015 TRITA-BKN. Master Thesis 455, 2015 ISSN , ISRN KTH/BKN/EX 455 SE

4 c Lisa Broberg & Malin Thorwid 2015 Royal Institute of Technology (KTH) Department of Civil and Architectural Engineering Division of Concrete Structures Stockholm, Sweden, 2015

5 Abstract The safety of a concrete dam is ensured by designing according to failure criteria, for all combinations of loads using safety factors. Today in Sweden, RIDAS, the Swedish power companies guidelines for dam safety, is used for the design of dams and is based on BKR, the National Board of Housing, Building and Planning. Swedish dams are designed to resist two global failure modes; sliding and overturning. Combination of failure modes, that should be considered in the design of concrete dams, is however fairly unknown. Since 2009 the Eurocodes was adopted and came into force The Eurocodes have replaced BKR in the design of most structures in Sweden where the partial factor method is used to ensure safety in the design. The objective of this report was to examine if the design criteria for concrete dams in today s condition are enough to describe real failure modes. The other objective was to analyse if Eurocode is comparable to RIDAS in dam design. The stated questions were answered by performing a literature study of known dam failures and analytical calculations for different types of concrete gravity dams, with varying geometry and loading conditions. The programs CADAM and BRIGADE were also used as calculation tools to further analyse if failure occurred as expected. The results from the analytical calculations together with the performed FE analysis indicate that limit turning does occur and often generate lower safety factors compared to overturning. Limit turning is similar to overturning failure although it accounts for material failure in the rock. This design criterion is therefore, highly dependent on the quality of the rock and requires investigations of the foundation to be a good estimation of the real behaviour of the dam body. From the compilation of reported failures the conclusion was that the current design criteria are adequate. However, the real challenge lies in ensuring that the construction of dams is correctly performed to fulfil the stated criteria. A transition to Eurocode appears to be reasonable for the stability criterion. A modification of the partial factors is nevertheless necessary to obtain result corresponding to RIDAS, especially for the overturning criteria. Keywords: Gravity dams, concrete, design criteria, RIDAS, Eurocode, limit turning iii

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7 Sammanfattning För att uppnå säkra dammkonstruktioner, för alla lastkombinationer, dimensioneras dammar enligt bestämda brottvillkor som ska uppfylla en viss säkerhetsfaktor. Idag används RIDAS, för dimensionering av dammar i Sverige. RIDAS Kraftföretagens riktlinjer för dammsäkerhet, är baserat på BKR, Boverkets konstruktionsregler. I Sverige dimensioneras dammar för att motstå de två globala brottmoderna glidning och stjälpning. Frågan som behöver besvaras är om det finns eller kan finnas några kombinationer av brottmoder som borde beaktas vid dimensionering av dammar antogs Eurokoderna och trädde i kraft Eurokoderna har ersatt BKR vid dimensionering av de flesta konstruktioner i Sverige. I Eurokod används partialkoefficienter för att garantera säkra konstruktioner. Syftet med denna rapport var att undersöka om dagens brottkriterium är tillräckliga för att beskriva hur dammar går till brott. Rapporten behandlar även möjligheten att övergå från att dimensionera dammar enligt RIDAS till att dimensionera enligt Eurokod. För att besvara detta genomfördes en litteraturstudie av rapporterade dammbrott. Dessutom genomfördes analytiska beräkningar för flera olika typer av dammar med varierande geometri och lastfall. Programmen CADAM och BRIGADE användes som ytterligare verktyg för att analysera brottmoderna. Enligt resultat från de analytiska beräkningarna tillsammans med FE-beräkningarna ansågs limit turning inträffa och genererade i högre grad en lägre säkerhetsfaktorer i jämförelse med stjälpning. Limit turning kan förklars som delvis stjälpande och inkluderar brott av bergmassan. Brottmodet är dock beroende av kvalitéten hos berget och det krävs undersökningar av grunden för att kunna göra en god uppskattning av dammens verkliga beteende. Sammanställningen av tidigare brott visade att nu gällande brottkriterier är lämpliga och troligtvis tillräckliga. Utmaningen är istället att säkerställa att konstruktionerna är korrekt utförda och därmed uppfyller dessa brottkriterier. En övergång till Eurokod tycks vara möjlig för de globala brottmoderna, dock är det väsentligt att partialkoefficienterna justeras för att uppnå resultat som överensstämmer med RIDAS, särskilt för stjälpning. Keywords: Gravitationsdammar, betong, brottkriterium, RIDAS, Eurokod, limit turning v

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9 Preface This thesis was carried out from January to June 2015 at SWECO Energuide AB in collaboration with the Division of Concrete Structures, Department of civil and Architectural Engineering at the Royal Institute of Technology (KTH). The project was initiated by Dr. Richard Malm, who also supervised the project, together with Ph.D. candidate Daniel Eriksson and Adjunct Prof. Erik Nordström. We would especially like to thank Richard Malm for the continuous support which has been a great encouragement. We would also like to thank Daniel Eriksson for always finding time to help and guide us throughout this project. We also wish to thank Erik Nordstöm for his guidance and advice. We would like to thank the division at SWECO Eneriguide AB for their warm welcome and for an inspiring job environment. We would like to give special thanks to Johan Nilsson for the support and help during our work at SWECO. Stockholm, June 2015 Lisa Broberg & Malin Thorwid vii

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11 Contents Abstract Sammanfattning Preface iii v vii 1 Introduction Background Aim of report Limitations Structure of report Concrete gravity dams Gravity dams Massive dams Buttress dams Gate section Support methods Stability analyses Design loads Failure modes Methods for stability analyses RIDAS Design loads Failure modes Eurocode Design loads Failure modes Limit turning Crushing resistance Failure criteria Failure modes of concrete dams Documentation of failures Compiled failures Comparison of properties Failure type ix

12 4.2.3 Failure mode Description of failures Documentation regarding failures Results of the compiled failures Stability analyses Studied dams Input data Previously studied dams Stability Calculations Design approaches Parametric study CADAM Stability calculations Modelling FE-analysis Studied dams Model definition Results and discussion Analytical analyses Design approaches Parametric study Previously studied monoliths Analyses of limit turning Analytical analysis FE-analysis Conclusions Failure modes of concrete dams Analytical calculations Design guidelines Future studies Bibliography 95 A Compiled failures 101 B Results analytical analyses 103 C Output values for dams 105

13 Chapter 1 Introduction 1.1 Background Most dams in Sweden were built during 1950 to 1960 on solid good quality rock. The dams were built under different conditions and safety regulations compared to the demands stated today (Andersson, 2012). The knowledge of rock mechanics and material properties of concrete along with the building techniques have improved. Today the construction of new dams in Sweden is limited by regulations concerning the preservation of the environment. Therefore, the design of dams mostly involves maintenance and reparation of existing dams. Knowledge of why and how dam failure occurs, may help prevent or minimise the damage. The indication of how a dam behaves prior to failure is therefore of great importance in order to prevent failure. It is also important since it provides guidance on how to monitor and measure dams, what types of sensors and where these sensors should be placed to get early indications of possible failures. Risk and safety are essential in dam design due to the radical consequences a failure would cause to the surroundings, as seen in Figure 1.1. Figure 1.1: Baldwin Hills Reservoir after the disaster 1963 (Wilson, 1963). 1

14 CHAPTER 1. INTRODUCTION The consequences of failure could in the worst case scenario lead to lives lost and economic damage. Therefore, the government through the public utility Svenska Kraftnät, stated new requirements concerning higher safety demands for the existing dams (SFS 2014:114). The new requirements also concern the classification of the dams in Sweden; all dams must be classified, if a failure could result in severe consequences. In Sweden, the dam owner is responsible in the event of a failure or an accident. The Swedish power companies have issued the Swedish power companies guidelines for dam safety, RIDAS, based on the construction rules BKR (2010), the National Board of Housing, Building and Planning. Since 2011, the Eurocodes (the European construction standards) together with EKS 9 (2013), have replaced BKR in Sweden. However, Eurocode does not account for the design of dams (Andersson, 2014). Today Swedish dams are designed to withstand two global failure modes; sliding and overturning of the entire monolith. There are questions regarding if there are or can be any combinations of the failure modes, that should be considered in the design of concrete dams. 1.2 Aim of report The main focus of this report is to analyse the different types of failures that have occurred and can occur in concrete gravity dams, by examining the influence of different factors. The aim of this study is to answer the following questions: Is analytical calculations based on the global failure modes: sliding and overturning enough to describe the failure of the dam? Are there other potential failure modes not covered by these analytical calculations? Is a transition to Eurocode possible for dam design? Are the design guidelines according to Eurocode comparable to RIDAS? The stated questions will be answered by performing a literature study of reported dam failures and analytical calculations for several concrete gravity dams. In addition a FE-analysis will be performed for comparison. 1.3 Limitations This report only include concrete gravity dams and further limitations for the literature study are stated in Chapter 4. The analytical calculations only concern dams on rock foundation. The analyses are limited to Swedish conditions regarding material properties and design parameters. The influence from seismic loads is not included due to that it is not considered for design in Sweden, while it internationally may be of great importance for the design. 2

15 1.4. STRUCTURE OF REPORT 1.4 Structure of report Chapter 2 includes a presentation of theory behind the key concepts of concrete gravity dams. The main features for stability analyses of concrete gravity dams are presented. The different design loads for the stability analysis are stated and illustrated. A brief presentation of the causes of concrete gravity dam failure by explanation of the failure modes is presented. Stability analyses according to the guidelines RIDAS and Eurocode are presented in Chapter 3. How the guidelines account for the design loads and explanations of the analytical calculation methods for the failure modes described in Chapter 2 are given. A compilation of reported failures including causes and failure modes is presented in Chapter 4. Already known facts about the presented failures of concrete dams are compiled and the sources of failures that has occurred are detected. The analytical analyses in Chapter 5 describe the stability calculations for several different dams with varying geometry and loading conditions. A parameter study is used to determine the most influential parameter and to adapt the design of dams according to Eurocode with the stability calculations in agreement with RIDAS. The program CADAM and the software BRIGADE, are used as tools to enable a comparison to the analytical calculations. The key concepts on how to perform stability analyses with these tools are presented in this chapter. The results from the analyses described in Chapter 5, are presented in Chapter 6. In Chapter 7, the conclusions of the different concrete dam failure analyses are presented. Appendix A includes the full compilation about the failures of concrete dams presented in Chapter 4. Appendix B includes the results from the analytical calculations described in Chapter 5. The loads and level arms from the analytical calculations are presented in Appendix C. 3

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17 Chapter 2 Concrete gravity dams There are different types of concrete dams, which are distinguished by how the water pressure of the reservoir is transferred down to the ground. Descriptions of the different types of concrete gravity dams are included in this chapter. The two most common types are massive and buttress dams, presented in Section and Section respectively. Gate sections mainly consist of pillars and spillways, both are of gravity dam type and are described in Section Figure 2.1, shows the different dam types included in this report. Figure 2.1: The different types of dams included in this report, a) spillway and pillar, b) massive and c) buttress. For other types of dams, not included in this report, concrete can also be used in embankment dams, as a central or upstream membrane, as retaining walls for spillways or used for many secondary functions. Embankment dams are usually associated with at least one concrete dam part, either intake and/or discharge facilities. Concrete arch dams were introduced relatively late and therefore have a uniform, and somewhat higher quality. Arch dams are founded on rock and are of slender type with concaved arches (Kleivan et al., 1994). 5

18 CHAPTER 2. CONCRETE GRAVITY DAMS 2.1 Gravity dams Massive dams Massive or gravity dams are solid structures, designed to resist the external forces by its dead weight. Today, gravity dams are mainly constructed with concrete, compared to the previously used method of stone masonry. The development of new concrete gravity dams is ongoing and the Roller-Compacted Concrete dam (RCC) is an example of that. The RCC dam has a limited use of formwork, consists of a drier mix and is placed in a manner similar to paving, i.e. compacted with vibrating rollers. The benefits are cost beneficial with simple faster construction. The dams are built with no joints or reinforcement, with low cement content and the use of fly ash that enable less heat generation while curing (Kleivan et al., 1994). Solid concrete structures maintain stability against loads due to the geometric shape, mass and strength of the concrete (Ali, 2012). A gravity dam consists of either a continuous or a series of concrete monoliths separated by expansion joints (RIDAS, 2011). The monolith cross section is, in principle, triangular with a dam head, an inclination of the downstream face and a vertical upstream face, which also can have a small inclination, see Figure 2.2. The benefits of concrete gravity dams are that they are easily constructed on sites with a foundation of sufficient strength to carry the weight of the dam (Ali, 2012). Figure 2.2: Typical cross-section of a massive dam, reproduced from Bergh (2014). The monoliths are mainly placed in a straight line or sometimes slightly curved, see Figure 2.3 and are usually of a width between 5 m to 10 m (Bergh, 2014). 6

19 2.1. GRAVITY DAMS Figure 2.3: Stadsforsen, massive dam in Sweden (Malm, 2015) Buttress dams Over time, there has been a strong effort towards improving concrete quality. There has been a shift from the previously dominant gravity type dam such as massive dams, towards a more slender type of dam with reinforcement, known as a buttress dam (Kleivan et al., 1994). Buttress dams consist of two rigidly connected elements, the upstream water barrier (frontplate) and the supporting buttress on the downstream side, which together form a monolith, see Figure 2.4. The upstream water barrier transfers the hydrostatic pressure over to the buttress, which in turn transfers it down to the foundation. The water barrier is inclined so the vertical water loads, together with the weight of the concrete, act in favour for the stability of the monolith (DOI, 2009). Figure 2.4: Cross-section of a buttress dam (Left), Section of a buttress dam (Right), reproduced from RIDAS (2011). A buttress dam consists of a series of monoliths, connected by horizontal struts acting as contraction joints, connecting the adjacent monoliths, see Figure 2.5. The casting arrangements and the construction are somewhat more demanding compared to most other types of dams. However, buttress dams are more suitable on 7

20 CHAPTER 2. CONCRETE GRAVITY DAMS weak foundations compared to gravity dams, due to the reduced volume of concrete (Bergh, 2014), while the contact pressure between the buttress and the foundation is considerably higher. Figure 2.5: Rätan, buttress dam in Sweden (Vattenkraft.info, 2009) Gate section Concrete gravity dams also consist of gate sections to transport water in specific directions and release water pressure on the dam structure. Concrete functions as a fastener for many different types of gate installations, with variable functions. The gate type could be sliding, roller or radial gates, with the function of either an outlet gate, intake or daft tube (Kleivan et al., 1994). An example of a gate section in Sweden is shown in Figure 2.6 Figure 2.6: Lima, Spillway dam with two river type gates (Norconsult, 2012). 8

21 2.1. GRAVITY DAMS For a spillway section see Figure 2.7, where the overflow is designed with a vertical upstream face. The water is able to flow over the crest along the inclined downstream side with training walls, keeping the water in place and finally the water reaches the energy dissipating structure, forming a hydraulic jump to avoid erosion of the riverbed. Pillars, non-overflowing blocks function as enclosures of a number of overflow sections, see Figure 2.7. Usually spillway sections have gates and typically, radial gates see Figure 2.7. Figure 2.7: Spillway section (Left), plane view of spillway (Right), reproduced from RIDAS (2011). For hydropower structures, the intake is the connection between the reservoir and the waterway connected to the turbine of the hydroelectric power plant. Intake gates are normally designed with a trash rack preventing debris, ice, fish, etc. from entering the intake. In addition, it also consists of a gate of river or tunnel type, to close of the conduit, see Figure 2.8. Figure 2.8: Section of a typical inlet and power station, reproduced from RIDAS (2011). The behaviour of a spillway, discharge part, and intake part of the dam is similar to concrete gravity dams, thus the geometry and loading conditions may be more complicated (Westberg and Hassanzadeh, 2007). The surface of the concrete is subjected to very high water velocities as well as abrasion, and therefore must be steel plated. 9

22 CHAPTER 2. CONCRETE GRAVITY DAMS Support methods There are different support methods for concrete gravity dams. Common methods are to secure the dam body to the foundation by rock bolts or tendons. Rock bolts are non-pre-stressed reinforcement bars installed in the interface between the foundation and the dam body. There are different types of fastners for the rock bolts and they can be secured to the foundation through anchors, cables, dowles or by grouting. The bolts are anchored in the dam body by adhesion. Rock tendons consist of pre-stressed cables or rods, anchorage and corrosion-inhibiting coating. The tendons can be unbonded or bonded to the surrounding concrete. The tendon is inserted into a casing and grouted after the tendon is stressed (PTI, 2000). Another common method used to support concrete dams is earth support fill on the downstream side of the dam, giving rise to stabilising forces. A grout curtain helps to stabilise the dam by decreasing the uplift pressure. The grout curtain is achieved by inserting cement into pores and cavities in the ground. The grout curtain might deteriorate over time and therefore the decreased uplift is usually not accounted for in the design of dams (Ferc Engineering Guidelines, 2002). The uplift pressure could also be decreased by inserting drainage pipes. 2.2 Stability analyses Concrete dams are massive large structures since they are designed to fulfil the requirements for stability. The design should also fulfil requirements for long life spans and water tightness to withstand the permanent water pressure (Bond, 2014). The safety of the concrete dam is assured by designing according to failure criteria, for all combinations of loads using safety factors. The safety criterion is the definition of the stress level when failure occurs. The safety factors are chosen to provide for all underlying uncertainties. Their magnitude should reflect the probability of the occurrence for the particular load, the accuracy of conditions and the method of analysis. The factor of safety is thereby higher for foundation studies, because of the greater amount of uncertainty in assessing the load-resistance capacity of the foundation Design loads The loads included in the stability analysis should represent the actual loads acting on the concrete dam during operation. Many of the loads are unable to be exactly determined, the engineer is then responsible for estimating these loads based on available measurements, judgement and experience (Ferc Engineering Guidelines, 2002). The required loads acting on a dam for a stability analysis are shown in Figure

23 2.2. STABILITY ANALYSES Figure 2.9: Loads acting on a dam, reproduced from (Bergh, 2014). 1. Hydrostatic pressure (P1-P2) depends on the water level in the dam 2. Tailwater pressure (P3-P4) depends on the tailwater level 3. Uplift pressure (P5) hydrostatic pressure acting vertically, assumed to vary linearly from hydrostatic pressure at the heel to the tailwater pressure at the toe 4. Dead weight (P6) the weight of the concrete 5. Ice pressure (P7) load acting on the face of the dam due to an ice cover 6. Silt pressure (P8) settled sediments exerting active pressure towards the dam 7. Seismic loads (P9-P11) horizontal and vertical accelerations caused by earth quakes Failure modes The definition of dam failure can differ between individuals, the general definition could be expressed as: "Collapse or movement of part of a dam or its foundation, so that the dam cannot retain water (ICOLD, 1995). Concrete dams have various failure behaviour. Sliding or shear failure is the most common failure for dams constructed on rock. The dam may fail due to crushing, i.e. the failure of its materials when the compressive stresses exceed the acceptable stresses. Concrete cannot withstand sustained tensile stress and if the tension that develops in the concrete exceed its tensile strength, it could lead to ultimate failure. The dam may also fail due to overturning where it rotates about the toe (Ali, 2012). 11

24 CHAPTER 2. CONCRETE GRAVITY DAMS Overturning Overturning occurs when the forces acting on the dam causes rotation of the dam, see Figure Overturning is analysed by calculating a factor of safety, which is defined as the ratio of stabilising and overturning moment. These moments are calculated around its toe or another weak point in the structure or foundation. For the overturning failure, it is also important that the resultant is located in the mid third of the base area since this will assure that the whole base of the dam is under compression. If tensile stress can be avoided it will reduce crack propagation in the concrete. The criterion is verified by application of the Navier equation for a cantilever action under combined axial and bending load (Bergh, 2014). Figure 2.10: Overturning failure around the dam toe. Sliding Sliding occurs when the horizontal forces exceed the frictional resistance. Sliding can be divided in to three different kinds of failures (Gustafsson et al., 2008): 1. Failure in the interface between the concrete and the foundation (Figure 2.11 a). 2. Failure in weak planes of the foundation, such as cracks (Figure 2.11 b). 3. Failure in the solid foundation (Figure 2.11 c). Figure 2.11: Different types of sliding failures, reproduced from Gustafsson et al. (2008). 12

25 2.2. STABILITY ANALYSES There are different views on whether cohesion between the concrete and the foundation can be accounted for in the sliding stability. The reason is that it is difficult to quantify through borings and testing. Higher allowable safety factors may be applied, if cohesion is included in the calculations for sliding stability (Ferc Engineering Guidelines, 2002). If cohesion is not accounted for, the concrete-rock interface is treated as unbonded giving a conservative method that may result in expensive and over-strong structures (Krounis, 2013). Failure in the interface between the foundation and the dam body is normally accounted for in the design of dams. Though failure more often occurs in weak planes of the foundation, see Figure 2.11 (DOI, 2012). Sliding can also occur in the dam body at weak planes such as lift joints or along cracks, this failure is seldom analysed except for high dams (Ali, 2012). Limit turning According to Fishman (2007), the classical failure modes sliding and overturning, do not account for material failure. Classical overturning failure is unrealistic as it requires infinitely strong rock and concrete. Fishman infers that the one failure mode, either limit turning or sliding, giving the lowest stability factor should be used for the design of the structure and decisions regarding interface preparation (Fishman, 2009). Fishman states that the stresses developing below the upstream side will result in a tensile crack along the rock, see Figure A compressive zone will be formed in the rock, underneath the toe, due to the applied forces on the dam. When the stresses exceed the crushing resistance of the rock, a crushing zone is formed. The size of the crushing zone depends on the strength of the rock, for a weaker rock the crushing zone will extend further to the upstream side. The turn axis appears where the tensile crack and the compressive crack meet. The concrete and rock will act as a single body and failure will occur when they rotate about the new rotation point. This failure mechanism is called limit turning, which is similar to the overturning method although it also accounts for the strength of the rock. The result gives a more reliable and conservative safety factor (Fishman, 2009). Figure 2.12: Limit turning failure. 13

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27 Chapter 3 Methods for stability analyses In this chapter, the design methods for stability analyses are presented. There are different methods for analysing failure of dams, varying between countries or methods. In Sweden, RIDAS (2011), is used for the design of dams and is based on BKR BKR was replaced with EKS 9 (2013). Today, Eurocode is used and function as guidelines providing a common structural design in European countries. A revision of RIDAS, to incorporate Eurocode instead of BKR has begun. The transition work is led by Svensk Energi, responsible for RIDAS. The research company, Energiforsk, previously known as Elforsk until January 2015, has also started to work with the transition from BKR to Eurocode. The investigations has so far mostly been focused on cross-section design (Andersson, 2014). For the stability analyses, there is an ongoing project financed by Energiforsk, where a structural reliability based method is under development. In this report, the focus will be on RIDAS, using the deterministic method, compared to Eurocodes semi-probabilistic method, resulting in the use of partial factors, for calculations of stability (Westberg, 2014). The denotations from RIDAS and Eurocode were used in Section 3.1 and Section 3.2, respectively. 3.1 RIDAS RIDAS (2011), is based on BKR, with adjustments for specific requirements for concrete dams. BKR, as mentioned before, is not valid today however it may still be used if the contents do not conflict with the Eurocodes (Andersson, 2014). Guidelines are given for the design of dams together with control and reconstruction of existing dams. RIDAS states requirements for stability, strength and durability of the dam and what criteria to fulfil. The requirements and criteria concern gravity dams, where RIDAS have included the most common types; massive and buttress dams, including spillway, inlet dams and pillars. 15

28 CHAPTER 3. METHODS FOR STABILITY ANALYSES Design loads RIDAS (2011) includes guidelines to determine design loads acting on concrete dams. It states how to account for the loads presented below. RIDAS also gives guidance how to account for rock anchors (described below), temperature effects, creep and shrinkage, and traffic loads (included if unfavourable), which are not described in this report. Dead weight For design of new concrete dams, the dead weight for reinforced concrete is assumed to be 23 kn/m 3 if no material tests are available. For existing dams, the dead weight should be determined from material tests or from information about the design. Hydrostatic pressure Both the water pressure on the up- and downstream side should be accounted for. The most unfavourable combinations of up- and downstream water levels applied to the dam determine the water pressure to be used in the calculations. Uplift pressure The uplift pressure distribution varies for different dam types and designs with or without drain pipes. For massive dam structures without drainage where the whole foundation area is under compression, the uplift pressure distribution varies linearly from the upstream to the downstream side. For massive dams the uplift pressure can be reduced by the use of drain pipes as shown in Figure 3.1 and Figure

29 3.1. RIDAS Figure 3.1: Uplift distribution for a dam with a drainage pipe in the rock and a drainage tunnel by the rock surface, reproduced from RIDAS (2011). The uplift distribution in Figure 3.1 will vary from H to 0.3 (H h) + h closest to the drainage tunnel and varies linearly to h at the toe of the monolith, with no uplift beneath the drainage tunnel. H is the headwater level and h is the tailwater level. Figure 3.2: Uplift distribution for a dam with a drainage pipe in the rock and drainage tunnel in the concrete, reproduced from RIDAS (2011). The uplift distribution in Figure 3.2 will vary from H to 0.5 (H h) + h closest to the drainage tunnel and varies linearly to h at the toe of the monolith. H is the headwater level and h is the tailwater level. 17

30 CHAPTER 3. METHODS FOR STABILITY ANALYSES For buttress dams, the uplift distribution is assumed to vary linearly over the thickness of the frontplate. If the buttress is thicker than 2 m, the uplift pressure underneath the buttress should be included as shown in Figure 3.3. Figure 3.3: Distribution of uplift pressure for a buttress dam with a buttress thicker than 2 m, reproduced from RIDAS (2011). For spillways, the uplift distribution is assumed similar to massive dams. The uplift distribution in Figure 3.4 is assumed for pillars, where w is the width of the pillar. The uplift varies from full uplift pressure to zero at the distance w from the spillway. Figure 3.4: Uplift distribution for pillars, reproduced from RIDAS (2011). The effect from cement grouting is not considered in the uplift pressure distribution, due to the strength of the cement decrease with time due to deterioration. The grout curtain is only considered as extra safety and should not be accounted for unless re-grouting is possible. This is seldom the case due to difficulties incorporating re-grouting tunnels in the dam body design. 18

31 3.1. RIDAS Ice load The intensity of the horizontal ice pressure depends on the geographic location, altitude and local conditions for the dam. RIDAS suggest the horizontal ice pressure 50 kn/m with an ice thickness of 0.6 m, for dams located in the southern part of Sweden. Dams located in the middle part, should be designed for an ice load of 100 kn/m with an ice thickness of 0.6 m. An ice load of 200 kn/m with an ice thickness of 1 m, is suggested for the rest of Sweden. The resultant of the ice pressure is assumed to be located at one third of the ice thickness, calculated from the top surface of the ice. Rock anchors For lower dams, it can be hard to achieve stability, and according to RIDAS in these cases it is allowed to assign a load capacity of 140 MPa to the rock bolts. This is applied for dams that have a headwater level less than 5 m and do not belong to any of the two highest safety classes. For all other dams, rock anchors should not be considered in the stability calculations, due to the complications of verifying their strength. However, it is stated that the installation of rock anchors of the dimension φ25 32 is a good preventive measure. Earth pressure Soil may be added as downstream support fill to increase stability. The earth pressure should be determined as a at-rest pressure and it should be calculated as the lowest theoretical pressure that may occur. The soil density and earth pressure coefficient should be obtained from in-situ tests. If testing is not possible, the values in Table 3.1 may be used. Table 3.1: Example values for unit weight and coefficients for earth pressure RIDAS (2011). Material Unit weight density [ kn/m 3 ] Friction angle [ ] Coefficient for earth pressure [-] Un-saturated Saturated φ At-rest K 0 Active K a Rockfill Gravel Sand Moraine

32 CHAPTER 3. METHODS FOR STABILITY ANALYSES Failure modes According to RIDAS (2011) there are three failure modes that need to be analysed for stability; sliding, overturning and the bearing capacity of the concrete and the foundation. Dam stability analyses are performed using safety factors for overturning and allowable friction coefficients for sliding, to achieve a safe design. RIDAS has listed different load combinations to be analysed, these are divided in to; normal load combinations, exceptional load combinations and accidental load combinations. The loads are calculated without partial factors and are analysed for individual monoliths. Overturning For overturning the requirement of the safety factor s is defined according to Table 3.2. Table 3.2: Saftey factor for overturning. Load case Safety factor (s) Normal 1.50 Exceptional 1.35 Accidental 1.10 The safety factor defines the relation between stabilising and overturning moment, see Equation (3.1), and should not be lower than the safety factor in Table 3.2. s = M stab M over (3.1) Sliding RIDAS states that sliding should be analysed between the interface of the concrete and in the foundation, along potential weak planes and in weak points in the dam body. Stability against sliding is achieved if the sum of the horizontal forces divided by the vertical forces, see Equation (3.2), does not exceed the maximum allowed friction coefficient, see Table 3.3. µ = R H R V µ max = tan δ g s g (3.2) 20

33 3.2. EUROCODE where R H R v tan δ g s g is the resultant of the horizontal forces. is the resultant of the vertical forces. is the friction angle. is the safety factor. Table 3.3: Maximum friction coefficient, µ max Foundation Normal load case Exceptional load case Accidental load case Rock Gravel, sand and moraine Silt The maximum friction coefficient can be calculated according to Equation (3.2) where the values for the safety factor s g are presented in Table 3.4. Table 3.4: Saftey factors s g for calculations of µ max. Foundation Normal load case Exceptional load case Accidental load case Rock Gravel, sand and moraine Silt Cohesion between the dam and the foundation should not be considered in the calculations for the resistance against sliding according to RIDAS. When calculating stability against sliding, the value for the maximum allowed friction coefficient (µ max ) is calculated according to Equation (3.2), with values of the safety factor from Table 3.4 and the friction angle from geotechnical investigations. The values in Table 3.3 can be used for dams constructed on a foundation of good quality, when calculating stability against sliding. 3.2 Eurocode Eurocode is the European standard for technical rules in construction work, providing a common structural design tool in European countries. Eurocode clearly states that their guidelines do not cover the design of dams. This is due to the high safety required for dams and that other aspects than for usual design need to be considered. This section is therefore solely based on the authors assumptions on how to apply Eurocode to dam design. Therefore, in this report a compilation of information from the listed Eurocodes below was performed in order to obtain a method applicable for stability analyses of dams. 21

34 CHAPTER 3. METHODS FOR STABILITY ANALYSES EN 1990 Basis for structural design. EN 1991 Actions on structures. EN 1992 Design of concrete structures. EN 1997 Geotechnical design. The same failure modes as described in Section were analysed. The values and equations in the following sections were based on the assumption that dams can be considered as comparable with retaining wall structures Design loads The safety is applied on the loads by partial factors. The load acting on the structure is multiplied with the partial factor γ to define the design load. The loads are classified according to variation in time: permanent or variable loads and whether the load is favourable or unfavourable, which would result in different partial factors. When designing geotechnical structures, different approaches are used. In accordance with retaining wall structures, the concrete dams were assigned the design approach 3 (DA 3). The different approaches give different values for the partial factors; for load and load effects, soil parameters and the strength (EC 7, 2011). Design approach 3 states that different partial factors should be used for geotechnical actions and structural actions. Geotechnical actions are defined as actions transmitted to the structure by the ground, fill, standing water or groundwater. For structural actions the strength of the material is significant. For the structural actions Equation (3.3) and (3.4) are used. For geotechnical actions, Equation (3.5) is used (EC 0, 2002). The partial factors for the equations are listed below in Table 3.5. E d = Σγ d γ G G k + Σγ d γ Q ψ 0,i Q k,i (3.3) E d = Σγ d ξ γ G G k + γ d γ Q,1 Q k,1 + Σγ d γ Q,i ψ 0,i Q k,i (3.4) E d = Σγ d γ G G k + γ d γ Q,1 Q k,1 + Σγ d γ Q,i ψ 0,i Q k,i (3.5) where γ G γ d G kg γ Q,i ψ 0,i Q k,i ξ is the partial factor for permanent actions. is the partial factor depending on safety class. is the characteristic value of a permanent action. is the partial factor for variable action. is the factor for combination value of a variable action. is the characteristic value of a single variable action. is the reduction factor. 22

35 3.2. EUROCODE Table 3.5: Partial factors according to Eurocode (EC 7, 2011). Load combination equation 3.3/ For an unfavourable permanent load γ G = 1.35 γ G = 1.1 For a favourable permanent load γ G = 1.0 γ G = 1.0 For an unfavourable variable load γ Q = 1.5 γ Q = 1.4 For a favourable variable load γ Q = 0 γ Q = 0 Reduction factor ξ = 0.89/- - Structures are classified into different safety classes depending on the harm a failure would cause, the definitions are stated in Table 3.6. For calculations of stability, according to the partial factor method in EC 0 (2002), the partial factor γ d is applied and this value depends on the safety class of the structure. The partial factor for the different safety classes is shown in Table 3.7. Table 3.6: Consequence classes (EC 0, 2002). Consequences class CC3 CC2 CC1 Description High consequence for loss of human life, or economic, social or environmental consequences very great. Medium consequence for loss of human life, economic, social or environmental consequences considerable. Low consequence for loss of human life, and economic, social or environmental consequences small or negligible. Table 3.7: Partial factors γ d according to safety class (EC 0, 2002). Safety class Partial factor, γ d Dead weight The dead weight stabilises the dam and therefore acts as a favourable, permanent load and is a structural action. For reinforced concrete with normal weight, the density γ c = 24 kn/m 3 should be used for calculations of the dead weight (EC 1, 2013). 23

36 CHAPTER 3. METHODS FOR STABILITY ANALYSES Hydrostatic pressure The horizontal water load (HW) acting on the upstream face, shown in Figure 3.5, is a permanent and unfavourable load while horizontal tailwater load (TW) on the downstream side and the vertical load (VW) are permanent and favourable loads. The water loads are categorised as geotechnical actions. For analyses where the hydrostatic pressure is increased above the headwater level, the hydrostatic pressure can be classified as a variable load. Figure 3.5: Hydrostatic pressure. According to EC 1 (2013) the density for fresh water is set to γ w = 10 kn/m 3 and the loads caused by water should be determined with respect to the water level. No combination factor is given for the water load; therefore, in this report, a value in the interval between the value for the highest snow load and the value for imposed loads on buildings was assumed. The combination factor ψ 0,w = 0.75 can therefore be used for variable water loads. Uplift pressure The vertical uplift pressure is considered as an unfavourable permanent load and geotechnical action. The density of water and the partial factor can be set according to the hydrostatic pressure. An additional horizontal uplift pressure will be present for monoliths without horizontal bottom surfaces. The horizontal uplift pressure can act as both an favourable and an unfavourable load, depending which direction the monolith is inclined. The horizontal uplift pressure resultant can also, depending on the location, vary between unfavourable and favourable for sliding and overturning. Ice load The ice load is an unfavourable variable load and is a structural action. In this report, the combination factor ψ 0,ice = 0.8 was chosen for the load combinations, based upon the highest value for snow loads. 24

37 3.2. EUROCODE Rock anchors Rock anchors are considered as permanent favourable loads and geotechnical actions. The design strength of the reinforcing rock anchors may be calculated according to Equation (3.6). where f yd = f yk γ s (3.6) f yk γ s is the characteristic strength of the reinforcement. is the partial factor for the reinforcement. The partial factor applied to untensioned and tensioned reinforcement bars is in this report assumed to be γ s = 1.15 based on EC 2 (2011). Earth pressure Earth pressure is both a favourable and an unfavourable permanent load and is in this report considered as a geotechnical action. Eurocode states that the soil properties should be chosen from investigations or by theoretical or empirical correlation or from other relevant documentation. If standard values from tables are used, the characteristic values should be chosen with great care. According to the design of retaining wall structures, the determination of the earth pressure should be taken as at-rest pressure, if no movement of the wall relative the ground takes place. The lateral earth pressure coefficient, K O is calculated according to Equation (3.7) for a horizontal backfill and according to Equation (3.8) for an inclined backfill and depend on the friction angle (EC 7, 2011). Horizontal backfill: Inclined backfill: K O = (1 sin ϕ ) OCR (3.7) K O;β = K O (1 + sin β) (3.8) where ϕ is the effective friction angle. OCR is the overconsolidation ratio. β is the slope of the soil. Values for the unit weight density and friction angle in Table 3.8, was obtained from Trafikverket (2011). 25

38 CHAPTER 3. METHODS FOR STABILITY ANALYSES Table 3.8: Material properties for ground materials. Material Unit weight density [ kn/m 3 ] Friction angle [ ] Un-saturated Saturated ϕ Rockfill Gravel Sand Gravelly moraine Sandy moraine Silty moraine Eurocode also states that the earth pressure should be calculated according to the chosen design approach, as shown in Equation (3.9). The design value of the earth pressure is: where X d = X k γ M (3.9) X k γ M is the characteristic value of the material property. is the partial factor of the material property. The partial factor for material properties was chosen in accordance with design approach (DA3) to γ M = 1.3. In most cases the earth pressure acts as a stabilising force, leading to a decreased force, resulting in a more conservative value for the earth pressure. If the earth pressure is active, the diagram in Figure 3.6 can be used to obtain the active earth pressure coefficient, K a. 26

39 3.2. EUROCODE Figur C.1.1 Aktiva, effektiva jordtryckskoefficienter K a (den horisontella delen): stöttad horisontell markyta ( = 0) Failure modes 128 Figure 3.6: Active earth pressure (EC 7, 2011). EC 7 (2011) defines how to perform the design of geotechnical structures. The calculation model should describe the behaviour of the foundation and be reliable and give an error on the safe side. It should be verified that ultimate limit state is not exceeded for: Internal failure or excessive deformation of the structure or structural elements, in which the strength of the structural material is significant in providing resistance (STR). Tillägg och kommentarer i detta dokument har gjorts av Emma Persson. Teknikområde Grundläggning. Senaste revidering Uppdatering enligt EKS9 har gjorts av Anette Sjölund och Elizaveta Pronina. Senaste revidering Failure or excessive deformation of the ground, in which the strength of soil or rock is significant in providing resistance (GEO). Overturning The failure criterion presented in Equation (3.10) for ultimate limit state from EC 0 (2002), defines the safety against overturning as: M d,dst M d,stb + T d (3.10) 27

40 CHAPTER 3. METHODS FOR STABILITY ANALYSES where M dst M stb T d is the overturning moments. is the stabilising moments. is the shearing resistance. If the shearing resistance, T d, is included, it should not have a considerable effect on the result. Sliding The failure criterion presented in Equation (3.11) for ultimate limit state according to EC 7 (2011), defines the safety against sliding as: H d R d + R p;d (3.11) where H d R p;d R d is the design value of unfavourable horizontal forces. is the design value of favourable horizontal forces is the design shear resistance. The design shear resistance is calculated by Equation (3.12). where V d tan δ d R d = V d tan δ d γ M (3.12) is the design value of the effective vertical load. is the design friction angle. According to Eurocode, the friction angle tan δ d, should be determined based on geotechnical investigations. 3.3 Limit turning Crushing resistance An important parameter in the limit turning calculations is the crushing resistance of the rock mass, R cr. This is a better estimation of the resistance to shear loading compared to the shear strength parameters friction angle and cohesion. The crushing resistance of the rock mass should be obtained from geotechnical investigations and depends on the peak shear and normal stresses acting on the rock. When the crushing resistance is exceeded and the crushing zone is formed, a limit turning 28

41 3.3. LIMIT TURNING failure will occur (Fishman, 2007). From experiments performed by Fishman the relationship between the crushing resistance and uniaxial stress was obtained, shown in Equation (3.13). R cr = 1.47 σ c (3.13) If no investigations are available, values from Table 3.9 may be used in the calculations (Fishman, 2009). Table 3.9: Crushing resistance R cr for different categories of rock mass (Fishman, 2009). Category of rock Type of foundation Parameter R cr (MPa) I II III IV Massive, large fragmental, laminated, platy, very low and low jointed, unweathered rock characterised by uniaxial compression strength in a sample σ c > 50 [MPa] Medium jointed, inconsiderably weathered rock characterised by σ c > 50MP a Intensively jointed rock with σ c = 15 50MP a and inconsiderably weathered and low jointed rock with σ c = 5 15Mpa Semi-rock, platy, thin-platy, medium, high and very high jointed with σ c = 5MP a

42 CHAPTER 3. METHODS FOR STABILITY ANALYSES Failure criteria The stability factor is the ratio between the sum of resisting moments and the sum of turning moments. Including the moment from the force of the peak crushing resistance S. The moments are calculated relative to the turning axis O, as sown in Figure 3.7. Figure 3.7: Principles of limit turning, reproduced from Fishman (2007). The position of O axis is determined as follows: N O = (a, d) = (, [(h a e a 2 ) 1/2 h]) (3.14) t R cr The force of peak crushing resistance is defined in Equation (3.15). S = (a 2 + d 2 ) 0.5 t R cr (3.15) The moment of the peak crushing resistance will be calculated about the O axis and added to the resisting moment: M p.c = S b cr 0.5 (3.16) Limit turning stability factor, relative to the O axis: F s = ΣM r ΣM t (3.17) 30

43 3.3. LIMIT TURNING where a d N T t R cr is the x-distance from the downstream toe B to the position of the turning axis O. is the y-distance from the downstream toe B to the position of the turning axis O. is the resultant of the vertical forces. is the resultant of horizontal forces. is the width of the structural section along a projected center-line or the thickness of the buttress. is the crushing resistance of the rock. h is the lever arm of the horizontal forces T relative the downstream toe B. e is the lever arm of the vertical forces N relative the downstream toe B. b cr Mr Mt is the length of crushing plane OB. is the sum of resisting moments. is the sum of turning moments. 31

44

45 Chapter 4 Failure modes of concrete dams The aim of this chapter was to detect the factors that might cause concrete massive and buttress dams to fail. Especially to consider if other than the currently used design criteria could be relevant. Dams are designed against failure criteria based on sliding and overturning. By going back and studying failures it is possible to detect if the failure criteria are sufficient or if other failure modes may have to be accounted for in the design process. This chapter includes a compilation of reported concrete dam failures across the world; how and what have caused them to fail. This study excludes China since the documentation there is incomplete. Many failures occurred decades ago, and therefore the documentation and important information regarding these failures might be inadequate. Greater incidents of concrete dams were also included. Known dam failures without information about either the foundation or the failure cause were excluded. 4.1 Documentation of failures The aim of the engineering industry today is to take responsibility of establishing a global collaboration as well as openness to share and increase the general knowledge of the industry by creating formalised channels such as registers and organisations. The Committee on Dam Safety (CODS) in particular is working with this. However, it is difficult to obtain information about particular failures, especially in cases where failure took place long ago. Other reasons could be that some dam owners are not willing to admit failure and do not make the records public, or due to a legal policy preventing publication of records. This has slowed down the technical development of the industry, limiting possibilities of understanding earlier generations thoughts behind their solutions and designs. The sharing of information and the ability to talk about dam failures could help increase our knowledge of the field as well as provide the opportunity to learn from the experience of others, which would greatly increase the knowledge of the industry (Isander, 2013). 33

46 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS 4.2 Compiled failures The study includes failures of 19 concrete dams. These are divided into 12 massive dams, one gravity spillway dam and six buttress dams, presented in Table 4.1. The included failures have, to varying degrees, documented information about the failure and the dam. For a full compilation of the studied dams, see appendix A. Table 4.1: Concrete massive and buttress dams included in the study. Dam name Country Dam type Height over lowest foundation Year commissioned Year of failure Bayless 1 USA Massive (1911) Camara 2 Brazil Massive Eigiau 3 GB Massive Elwha river 1 USA Massive (hydro-power) High Falls 6 USA Massive Marquette no 3 6 USA Massive Shih-Kang dam 5 Taiwan Massive (gravity spillway) St Francis 1 USA Massive Torrejon-Tajo 1 Spain Massive Upriver dam 6 USA Massive Warrensburg 6 USA Massive Xuriguera 1 Spain Massive Zerbino 4 Italy Massive Ashley 1 USA Buttress Cascade lake dam 8 USA Buttress Komoro 1 Japan Buttress Morris Sheppard 7 USA Buttress Overholser 1 USA Buttress Stony creek 1 USA Buttress (Douglas, 2002) 2 (Shaffner and Scott, 2013) 3 (J Andrew et al., 2011) 4 (Luino et al., 2014) 5 (Kung et al., 2001) 6 (Reegan, 2015) 7 (Anderson et al., 1998) 8 (Jarrett, 1986) 34

47 4.2. COMPILED FAILURES Comparison of properties In Section 4.2, Table 4.1 show the variation in year commissioned, age at failure and height, these properties are compared in Figure 4.1 and Figure 4.2. The majority of the studied dams were commissioned before 1940 according to Figure Massive dams Buttress dams 1 0 Figure 4.1: Year studied dams were commissioned. After five years During first five years During first filling * Buttress dams Massive dams During construction Figure 4.2: Variation in age at failure of the analysed buttress and massive dams. The buttress dams had according to Figure 4.2 slightly a higher tendency to fail during the first five years while the massive dams generally failed after five years. The majority of the failures did however occur within the first years. Failure is less feasible for older dams, where the possibility of failures per year decrease with the age of the dam. First filling is the first time the dam was filled 35

48 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS Failure type Information about foundation material and geology of the foundation is presented in Table 4.2. In some cases information is missing, and this is denoted with the symbol "-". The failure of each dam is referred to a certain failure type, the used failure codes are defined below. F f, F b, F a, F m, Dam name failure due to dam foundation. failure due to the structural behaviour of the dam body. failure due to appurtenant works. failure due to dam materials. Table 4.2: Failure types for massive dams. Foundation material Geology Failure code Bayless Rock Sandstone horizontal layers with shale and Ff clay between Camara Rock Plane of micaceous silty clay Ff Eigiau Clay Hard blue clay containing boulders of granite Ff/Fm overlain by a layer of peat Elwha river Soil/rock Fluvioglacial and conglomerate Ff High Falls Rock - Fm Marquette no 3 Rock - Fa Shih-Kang dam Rock Top deposition layer: unconsolidated gravel, Ffb sands, silts and clay. On Soft bedrock: slate-gray, sandy-shale and silty-sandstones St francis Rock Conglomerate and schist Ff Torrejon-Tajo - - Fa/Fm Upriver dam Soil - Fa Warrensburg - - Fa Xuriguera Rock - Ff Zerbino Rock Schist and hornfeld Faf Ashley Soil Fluvioglacial Ff Cascade lake dam Soil Glacial terminal-moraine sediments Ffa Komoro Rock Tuff Ff Morris Sheppard Rock Shale Ff Overholser Rock - Ffa Stony creek Soil - Ff 36

49 4.2. COMPILED FAILURES Failure mode Table 4.3 contain information about the failure type by either information about the failure mode of the foundation marked with the symbol "x", or the failure mode of the dam, as listed below. The failure mode is the parameter affecting the incident mode. The following definitions have been used: P, piping; water and material passing through the foundation. SC, scour; when sediment surrounding the dam abutment is removed. S, sliding. SH, EQ, shear sliding within dam. earthquake damage. T/C, tensile and compressive failure within dam. ST, structural damage to appurtenant equipment, such as spillway gates. Dam name Table 4.3: Failure mode for massive dams. Failure mode foundation (P) (SC) (S) Failure mode dam Failure type code Failed due to overtopping Bayless x Ff Overtopping due to unknown cause Camara x Ff Not at highest water level Eigiau x Ff/Fm Not at highest water level Elwha river x Ff Filled High Falls (ST) Fm Overtopping due to unknown cause Marquette no 3 Fa Overtopping due to unknown cause Shih-Kang dam (EQ) Ffb No information St Francis x x Ff Gradual during first fill Torrejon-Tajo (SH) Fa/Fm Flood during construction Upriver dam x Fa Overtopping due to unknown cause Warrensburg (T/C) Fa No information Xuriguera x Ff No information Zerbino x x Faf Overtopping due to unknown cause Ashley x Ff J ust spilling when pipe failed Cascade lake x Ffa Overtopping due to unknown cause dam Komoro x x Ff No suggestions of high water level Morris Sheppard x Ff Releases kept within channel capacity Overholser x Ffa Overtopping due to unknown cause Stony creek x Ff Not clear if failed at top level or overtopping 37

50 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS 4.3 Description of failures Descriptions about the failures for those dams which are not further discussed in Section are given in Table 4.4 and Table 4.5. Dam name Table 4.4: Failure description for massive dams. Failure description High Falls Overtopping led to breach of 23 meter long portion of concrete crest cap, left half the spillway. Repairs completed. Marquette no 3 Overtopping and failure of abutment, due to an failure of upstream dam. Torrejon-Tajo Shear sliding within the dam. Failure cause was traced to organic material present in the aggregate and filling of the dam by a flood during construction before the concrete had fully hardened. Upriver dam Washout of the abutment and the power canal embankments due to overtopping. Not a complete failure and reparation of the dam was possible. Warrensburg Breach of north abutment. Reconstructed in Xuriguera Failed by foundation sliding, shear strength and poor design. Table 4.5: Failure description for buttress dams. Dam name Ashley Stony creek Cascade lake dam Komoro Overholser Failure description Piping failure in fine sand with clay and gravel, 6m deep below cut-off. Piping in foundation followed by settling of dam, cracking and collapse of dam. The dam was overtopped before tipping over and failing. The cause of failure was the hydrostatic water pressure on the dam and erosion of the abutments. Stored water was released rapidly due to short time of breach development and the width of the breach was large. Failure due to softening of volcanic ash in foundation. Unclear cause, either piping, sliding or both. Overtopping leading to scour of abutment. 38

51 4.3. DESCRIPTION OF FAILURES Documentation regarding failures Bayless Dam, USA Flaws in the Design of the Dam A cut-off wall (shear key) was installed to suitable bedrock and steel rods were built into the wall and secured in the rock (The Engineering News Publishing company, 1910). Against the upstream face, an embankment dam was placed, composed of compacted disintegrated shale, clay and some loam. The intention of the embankment was to prevent water percolating down to the porous strata beneath the dam. The engineer desired a deep cut-off wall that was to be constructed down through the rock strata, but was overruled due to its cost. When the dam was completed one small vertical crack followed by more cracks, appeared on one side of the spillway. This was due to contraction since there was no water in the dam. The Bayless dam prior to failure is shown in Figure 4.3. Figure 4.3: Bayless Dam prior to failure (The Engineering News Publishing company, 1910). First failure One year after the dam was completed, rapid melting of large amount of snow occurred and within three days, the dam was filled to maximum capacity. The next day, a large slice of earth below the dam dropped down 1.2 m and partially slid into the valley. The water retained within the dam eroded a path beneath where the earth had slid. Eventually the water began flowing up through the ground in large quantities, 5-15 m downstream from the dam toe. The result was that the water flowed under the dam in the embankment through the rock strata (The Engineering News Publishing company, 1910). During the third day, the flowing water resulted in that a portion of the dam, at the overflow spillway section, slided 0.4 m at the top and 8 m at the base, causing the crack widths to increase at the downstream face which unloaded the cracks at the upstream face. The movement lasted for eight 39

52 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS hours resulting in overflowing of the dam. It took 16 hours to completely empty the reservoir. The total failure time of the dam was approximately two days. The reservoir was lowered and no repairs were made before the dam was put back into service (DOI, 2012). The initial cause of failure was piping, which caused softening of the clay and shale, lying between two layers of rock, causing the top layer of rock to slip forward onto the lower layer. The results from the failure were leaks under the dam, transverse cracks in the main section and movement of the central part downstream (The Engineering News Publishing company, 1910). Second failure At the end of summer, in 1911, the dam failed for the second time, due to high headwater level, nearly as great as what caused the first slip failure. The dam failed in 30 minutes with no indications of a gradual failure. Four-fifths of the length of the dam broke into several large fragments, see Figure 4.4; most of them remained nearly vertical. The two largest fragments near the centre (spillway section), fragment E & D in Figure 4.4 shifted downstream and rotated slightly from its original alignment and, on both sides of these, large gaps were formed. At the west end, 38 m of the dam was still intact, fragment G in Figure 4.4 and to the east, fragment B & C the entire dam was broken and displaced. The failure was so extensive that no conclusion of the initial point of failure could be drawn. The appearance of the failed dam, however, indicates a sliding failure. Observations from the wreckage may suggest that the westerly gap with its sections, slit and sheared out at levels above the foundation, as a secondary effect (The Engineering News Publishing company, 1911). Figure 4.4: Bayless Dam, resulting fragments and positions after failure (The Engineering News Publishing company, 1911). 40

53 4.3. DESCRIPTION OF FAILURES Camara Dam, Brazil Flaws in the Design of the Dam The dam failed due to lack of information regarding the foundation. The smooth foliation surfaces were left untreated leading to failure during the first filling. Indications from material in the drains, leakage through the concrete and clogging of drain holes, etc. suggests that failure was about to occur. The designer recommended emptying the reservoir however due to political reasons it was not implemented (Shaffner and Scott, 2013). Figure 4.5: Camara Dam, failure at foundation of left abutment (Risk Assessment International, 2013). Failure The reservoir was filled rapidly in about two weeks, due to heavy rains, and the retained volume gradually increased thereafter. After about five months when the reservoir was about 3/4 full, it failed at the foundation of the left abutment, due to erosion from soil-filled discontinues. High pressure gradients developed under the dam. As the flow rate of the reservoirs retained water increased the erosion and driving forces on the low-shear strength rock slabs, the dam and the abutment started to slide until a hole was piped beneath the dam causing a flood. The remains are shown in Figure 4.5. The remaining rock in the left abutment is essentially free from fractures indicating that piping occurred along the entire length of fracture (Ferc Engineering Guidelines, 2014). 41

54 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS Eigiau Dam, United Kingdom Flaws in the Design of the Dam Different contractors were involved in the construction of the dam. The footings should have been founded 1.8 m below the clay surface, but at the point of failure, only 0.5 m was embedded into the clay layer. From investigations, it was suggested that poor quality concrete contributed to the failure. The concrete lacked the correct volumes of sand and cement, resulting in the aggregates not cementing together. The stone aggregates were larger than desirable and were placed carelessly; in several cases with voids under their bed surfaces (J Andrew et al., 2011). Figure 4.6: Eigiau Dam, remaining breach (Geograph, 2010). Failure A 10 m long breach occurred in the concrete at the side leg of the dam, see Figure 4.6. The breach scoured a 20 m wide channel three meters below the ground surface. Large portions, 1.5 million cubic meters, of water were released in the first hour and caused Coedty dam 2.5 miles downstream to overtop and the concrete wall to collapse. In itself, the soft, porous condition of the boulder clay was aggravated by cracking due to dehydration in the preceding summer when the lake bed was exposed (J Andrew et al., 2011). 42

55 4.3. DESCRIPTION OF FAILURES Elwha Dam, USA Flaws in the Design of the Dam The dam, seen in Figure 4.7, was founded on a deep gravel deposit and water therefore blew out the foundation (Oakes, 2001). The contractors ignored specifications from the engineers, resulting in the dam not being secured to the bedrock. Figure 4.7: Elwha Dam prior to failure (KPLU 88.5, 2011). Failure The dam failed during the first fill due to piping failure of the alluvium under the dam. Lower sections of the dam were removed by the flowing water and large portions of material eroded under the dam in about two hours resulting in a hole. Various reparation methods were attempted and finally the hole was filled with debris. The Elwha dam failure started serious environmental investigations, regarding removal of the dam to restore the river to its natural self-regulating state. The dam was finally removed

56 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS Morris Sheppard Dam, USA Flaws in the Design of the Dam The stability of the foundation was based on peak shear strengths and did not consider uplift pressures (Anderson et al., 1998). Failure Sliding of the spillway section, see Figure 4.8, on the shale foundation, most probably occurred over a period of several years and was discovered during a routine inspection 45 years after construction. Figure 4.8: Morris Sheppard dam prior to failure, spillway section (Anderson et al., 1998). Floatation of the lower portion of the hollow spillway section, together with the low resistance to sliding, added to the tendency, of the hollow spillway to move downstream. The reservoirs water level was quickly lowered to avoid complete failure. The metal survey points, that were installed along a line, had formed a bow, which indicated that the hollow spillway section had moved downstream on a slippage zone in the foundation, and from observations, cracks in the footings were found. Core borings were made, which indicated that the hydrostatic uplift pressure, under the spillway slab, was 65 % of the retention level. From the borings a longitudinal crack along the top of the upstream cut-off was located. This may have allowed for water to enter the foundation causing significant pressure beneath the shale layer. Drainage wells were installed to reduce the uplift pressures. A network of measuring equipment was installed as to keep track of any movement or change in uplift pressure. 44

57 4.3. DESCRIPTION OF FAILURES Shih-Kang Dam, Taiwan Flaws in the Design of the Dam The Shih-Kang dam was designed according to the traditional design concept of a pseudo static earthquake acceleration (Kung et al., 2001). The effect from the vertical motion was, however, neglected. The original pseudo static horizontal acceleration was less than the real peak horizontal acceleration of the Chi-Chi earthquake, which, in turn, caused sliding failure. Failure The dam was damaged by surface ruptures caused by; an active fault, the large displacement of ground surface and great ground motion induced by the Chi-Chi earthquake. The dam moved in a north-west direction, 10 m vertically and 11 m horizontally. The ground deformation caused the dam body to crack and separate from the foundation. The stiffness of the structures affected the deformation of the dam body. The left side rock gradually rose towards the upper end of the fault-created scarp. The north part, between the spillway and the abutment, was cracked along the construction joints into several huge blocks, see Figure 4.9. Water then leaked through the cracks. The entire dam body seemed to have bent towards the downstream side. Figure 4.9: Shih-Kang Dam post failure (HSS, 2013). The water level was decreased to reduce pressure on the dam and complete failure was avoided. 45

58 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS St. Francis Dam, USA Flaws in the Design of the Dam The dam, see Figure 4.10 was not designed with the correct uplift theory; uplift pressure acting to destabilise the sloping abutments. The cross section contained limited seepage relief, only a few uplift relief wells beneath the central core and no overlapping for expansion joints. To increase reservoir storage the dam height was increased 6 m without any substantive widening of the dam base width. The dam was arched upstream but arch action was neglected in the design. During initial filling several transverse cracks appeared which were filled in and sealed. The engineers did not understand the concepts of effective stress and uplift. If the foundations had been deeper, a cut-off wall and a grout curtain, with seepage relief wells would have been installed, the failure may had been avoided (Rogers, 1995). Figure 4.10: St:Francis Dam prior to failure (Water and power, 2015). Failure The reservoir had been held within 7 mm from the spillway for five days and the dam became unstable. At the west abutment a new larger leak and soiled discharge were detected on the morning of the failure, caused by hydraulic piping. The dams west abutment, built up on a fault contact, was unknowingly founded upon massive paleo mega-slides, causing cracking between the rock in the mid valley and the abutment (Rogers, 1995). Eventually the entire left hand side failed, inducing a domino effect of block failure at the right abutment (Veale and Davison, 2011). The blocks cut off along the transverse crack resulted in large leaks at the toe of the east abutment slide and 12 hours later, the dam collapsed. Forty minutes prior to the failure, the water level was rapidly decreasing. During final filling, a massive land slide occurred along the dams left abutment, carrying blocks and cutting off parts of the dam as the reservoir rose to full pool. The slide material initially plugged the outflow until the slide material was eroded by 46

59 4.3. DESCRIPTION OF FAILURES the increasing flood wave. Full hydrostatic pressures entered the transverse cracks causing hydraulic uplift to eliminate the dams stabilising dead load. A sudden and dangerous overstressing of the dams cantilevered load capacity lead to excessive tilt and overturning, causing the upstream heel to go into tension, full hydrostatic head pressure was introduced within the dam structure which then finally cracked. The central core of the dam was tilted towards the east abutment and tension developed in pre-existing cracks. Finally the west abutment was scoured away causing the central core to rotate (Rogers, 1995). The dam appeared normal shortly before the failure; it failed 7.5 minutes later and emptied within an hour. All that was left was a single monolith standing in the middle of the valley, see Figure Figure 4.11: St:Francis, resulting blocks from the abutment failure (Los Angeles Times, 2013). Zerbino Dam, Italy Flaws in the Design of the Dam The dam was constructed 300 m west of the Main Dam of Bric Zerbino, where a saddle, formed by two ridges, was at a lower elevation which could have been overflowed and poured out into the riverbed (Luino et al., 2014). The dam, shown in Figure 4.12 was built rather hastily and without sufficient geologic investigations. It was assumed that the saddle consisted of sound rock. The dam stood on highly jointed schist s making up a particularly weak zone within the rock mass. Water leaks were noticed across the rock diaphragm. Attempts to make the rock mass impervious were made with no satisfactory results. Miscalculation of precipitation in the area caused the water levels in the dam to differ from the values used in the design. 47

60 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS Figure 4.12: Zerbino Dam prior to failure (Molare.net, 2010). Failure Heavy rains caused the level of the reservoir to rise quickly and therefore the bottom discharge valves were opened to handle these large volumes. The large amount of mud and debris accumulating at the bottom of the dam caused the valves to stop working after only a few minutes. The reservoir could then only be discharged at the surface spillway and the siphons. Water then started to overflow, see figure 4.13 into both the main and the secondary dam, Zerbino. This caused repercussion on the jointed rocks that made up the saddle. After just one hour, the large water pressure, of the overflowing reservoir, displaced large rock blocks causing destabilisation of the dam which lead to the collapse. The Zerbino dam failed due to scour and sliding during overtopping. The level of the reservoir went down by some 25 m within a few minutes. Figure 4.13: Zerbino Dam, flooded reservoir (Molare.net, 2010). 48

61 4.4. RESULTS OF THE COMPILED FAILURES 4.4 Results of the compiled failures The comparison of the properties for the documented failures in Section indicate that majority of the massive dams failed after five years, in fact in a wide range of years after the dam was commissioned. This corresponds well with the fact that the majority of the failed dams were built The majority of the dams stood for many years, which could indicate ageing of concrete as a contributing factor. All but one of these dams failed due to overtopping, showing that the massive dams were sensitive to additional loading. The massive dams could have been designed against lower loads than they were subjected to at the time of failure. The majority of the buttress dams failed during the first five years, due to foundation failure. The failure types described in Section are compared in Figure The used failure codes are listed below. F f, F b, F a, F m, failure due to dam foundation. failure due to the structural behaviour of the dam body. failure due to appurtenant works. failure due to dam materials Massive dams Buttress dams 1 0 Ff Ffa Ffb Ff/Fm Fa/Fm Fa Fm Figure 4.14: Failure types of the studied massive and buttress dams. Of the studied failures, the majority failed due to, or partly due to, the dam foundation. This indicate the importance of a good foundation, meaning that information about the material and properties of the foundation play a crucial part in dam design i.e. dam stability. This could be achieved by geological studies, core samples, material testing, site visits, etc. 49

62 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS Figure 4.14 indicates that the failure type for massive dams are mainly due to different combinations of foundation and dam failure. Massive dams are heavy structures with a large amount of concrete volume, which requires a strong enough foundation and correct casting arrangements. For buttress dams, foundation failure is the dominant failure mode. The reason could be that buttress dams are light structures. The casting sequence and construction of buttress dams are complicated where faults are more prone to occur. The failure modes descried in Section are compared in Figure 4.15, with the definitions listed below. P, piping failure. SC, scour failure. S, sliding failure. SH, EQ, shear sliding within dam. earthquake damage. T/C, tensile and compressive failure within dam. ST, N o, structural damage to appurtenant such as spillway gates. no information was available Massive dams Buttres dams 1 0 P S/SC S S/P SH EQ No T/C ST SC info Figure 4.15: Failure modes of the studied massive and buttress dams. The majority of the failures occurred in the foundation, seen in Figure 4.15, which in some cases could have been avoided if improved geotechnical investigations were performed. Figure 4.15 also shows that failures in buttress dams are mainly caused by piping, sliding or both. Since not so many cases of failed buttress dams are included in this study, it is hard to conclude if there is a coincidence or if sliding and piping is what mainly causes the buttress dams to fail. From the results, piping affect buttress dams more than massive dams, not surprising considering that the water 50

63 4.4. RESULTS OF THE COMPILED FAILURES only have to travel underneath the frontplate of the buttress. For a massive dam there is a much longer distance for the water to erode before it causes failure. Sliding is more common for buttress dams, also not surprising since the less use of concrete volume, and therefore also the vertical component acting on the sliding surface is smaller. This is not always the case for the buttress dams since the inclination of the frontplate results in an additional vertical water load. The initial, or the main cause of failure is shown in Figure 4.15, although when the failure starts to propagate it will proceed to fail due to other failure modes or combinations of failure modes. The dam failures described in Section above, give a clear indication that there is a combination of failure modes leading to the final failure of the dam. Out of all the studied cases, none failed due to global overturning; this indicates that it is mostly a theoretical failure or that this failure mode is designed with high safety margin. The only indications of overturning were found after the initial failure, as a local failure of parts of the whole structure. This might create questions regarding the importance of this design criterion, however it is still an adequate and accurate indicator of the dams stability. As shown in Figure 4.15, only one dam failed within the dam body, which occurred during construction before the concrete had cured properly, which therefore does not suggest that the global stability is insufficient, but rather that special considerations should be made also during construction. Figure 4.16 shows a summation of failures caused by faults in the dam design or during construction of the dam. Inadequate ground investigations Poor construction Number of failures Unknown Figure 4.16: Faults in dam design or construction for the studied dams. From the failures described in Section above it is clear that, to some extent, the neglect of vital information, or requirements, occurred in all cases. It is hard 51

64 CHAPTER 4. FAILURE MODES OF CONCRETE DAMS to know if there were any relevant reasons for these assumptions, especially in the cases of poor construction. Failure due to overtopping is shown in Figure 4.17, where it is detected that extreme floods affect the behaviour of the dam. Even though the height of the water level is not the decisive factor for the failure, high water levels result in higher water pressures affecting the concrete. No information Not at highest water level Before first fill Buttress dams Massive dams Overtopping No suggestions of high water level Figure 4.17: Failure due to overtopping for the studied buttress and massive dams. 52

65 Chapter 5 Stability analyses In the analytical analyses, several different dams were studied with varying geometry and loading conditions. Stability calculations were performed with Matlab R2013a according to both RIDAS and Eurocode as defined in Section 3.1 and Section 3.2. Some of the analysed dams do not fulfil today s failure criteria, due to that the dams were designed according to different presumptions. Improvements have in many cases been performed to fulfil the more recent criteria. The structural rehabilitation were for some cases included, depending on the obtained drawings and information. The dams were subjected to the first normal load case according to RIDAS, with the headwater level of the dam, full ice load and all gates closed. For the calculations according to Eurocode, the loads were combined according to design approach 3, see Section In addition the stability analysis tool, CADAM was used for the massive dams for comparison. The failure criteria were calculated and compared to the analytical calculations. The analytical calculations according to Eurocode were further investigated through a parametric study. The aim was to establish the most influential parameter, modify the design loads by adjusting the partial factor and finally obtain results in agreement with the results from the stability calculations according to RIDAS. The dams were also analysed analytically for the failure mode limit turning. The dam with the largest difference in safety factor for overturning and limit turning, in addition to a dam with a minimal difference in the safety factor for overturning and limit turning, was analysed with the FEM software BRIGADE Plus Studied dams The calculations were performed for a variation of dam types subjected to different loads. The geometry of the different types of studied dams is shown in Figure 5.1 and Figure 5.2. These figures show the headwater level, the rotation point and the 53

66 CHAPTER 5. STABILITY ANALYSES characteristic loads applied to the different dam types, i.e. tailwater level and soil level. Figure 5.1: Geometry of the spillway Dam 9 (Left) and pillar Dam 11 (Right) Figure 5.2: Geometry of the buttress Dam 14 (Left) and massive Dam 2 (Right) Input data The required information about the input data for the different dams was collected from Section for calculations according to RIDAS and Section for calculations according to Eurocode. Recommended material values, characteristic values and partial factors were chosen according to Eurocode to the extent it was possible. Standard values from RIDAS were used if the required information was not found in Eurocode, which was the case for both the uplift pressure and the ice load. Usually, the uplift pressure for pillars is calculated with a distribution for massive dams to account for uncertainties regarding the uplift pressure. This was applied to the analysed pillars in this report, instead of the distribution suggested in Section according to RIDAS. For the calculations performed according to RIDAS, the density of water ρ = 1000 kg/m 3 and the gravitational force g = 9.81 m/s 2 was used. 54

67 5.1. STUDIED DAMS In this report dams were classified as safety class 3, since dam failures could result in the loss of human life and are likely to have great economic consequences. The partial coefficient γ d = 1.0 was applied to the loads according to Eurocode, see Table 3.7. Eurocode does not mention when rock bolts should be accounted for and therefore the guidelines from RIDAS were applied. For calculations according to Eurocode, the common reinforcement steel Ks40 was used, with a characteristic strength f yk = 370 MPa for φ = 25 mm and f yk = 350 MPa for φ = 32 mm (Ljungkrantz et al., 1994). For the calculations according to RIDAS, the load capacity of 140 MPa was used for the rock bolts. In the calculations according to Eurocode, the lateral earth pressure K O was calculated according to Equation (3.7) from Section with OCR = 1. The knowledge of the shear resistance T d for the studied dams was limited and hence it was excluded from the calculations. In Eurocode, the geotechnical design is more based on investigations compared to RIDAS. Since the value of the friction angle is not defined in Eurocode, a standard value of δ d = 45 for rock foundations was used for the calculations of the sliding criterion. For calculations according to RIDAS, values from Table 3.3 in Section was used for µ max to calculate the stability against sliding. 55

68 CHAPTER 5. STABILITY ANALYSES Geometry Table 5.1 provides an overview of the geometry of the studied dams. In some cases there is no value assigned to the geometric parameter, and this is denoted with the symbol "-". Under the column for drainage "x" is placed if the dam has a drainage system. The following abbreviations are used in Table 5.1 and Table 5.2: Dam M, massive dam. B, buttress dam. S, spillway. P, pillar. S + P, spillway and pillar. GW, width of massive/pillar/spillway. Table 5.1: Input data for the geometry used in the stability calculations. Type HeightGW Buttress width Frontplate width Inclination upstream face Inclination Inclination downstream sliding plane face [m] [m] [m] [m] [ ] Dam 1 M :1 10: Dam 2 M :1 10: Dam 3 B Varies 35: Dam 4 B :10 14: Dam 5 M :1 2: Dam 6 B :10 14: Dam 7 M :1 32: x Dam 8 S :1 Varies Dam 9 S :1 Varies 0 - Dam 10 P :1 Varies Dam 11 P :1 8.5:1 0 - Dam 12 S :1 Varies 0 - Dam 13 P :1 35: Dam 14 B Varies 35: Dam 15 P :1 25:10 0 x (S+P) S Varies Varies 0 x Dam 16 P :1 Varies 0 - Dam 17 P :1 Varies 0 - Dam 18 P :1 Varies 0 - Drainage Loads Table 5.2 provides an overview of the applied loads acting on the dams. When a load was not applied to a dam it is denoted with the symbol "-". 56

69 5.1. STUDIED DAMS Table 5.2: Input data for the loads used in the stability calculations. Dam Type Ice Load Soil material Rock bolts Strength tendons Head water Soil level Tailwater level Rotation point φ level [kn] [mm] [kn] [m.a.s.l] 1 [m.a.s.l] [m.a.s.l] [m.a.s.l] Dam 1 2 M 200 Moraine Dam 2 M 200 Moraine Dam 3 B Dam 4 B 200 Rockfill Dam 5 M 100 Moraine Dam 6 B Dam 7 M 100 Moraine Dam 8 S Dam 9 S Dam 10 P 100 Rockfill Dam 11 P Dam 12 S - Gravel Dam 13 3 P Dam 14 B Dam 15 P (S+P) S Dam 16 P Dam 17 P Dam 18 P meter above sea level. 2 Rock bolts accounted for according to RIDAS. 3 Additional loads from a gate, including the dead weight as well as the hydrostatic load acting on the gate. Limit turning The safety factor for limit turning was calculated with the crushing resistance R cr = 20 MPa for all the studied dams, from Table 3.9. From the results of the analytical calculations, the dam with the largest difference in the safety factor for overturning and limit turning and the dam with the small difference in the safety factor for overturning and limit turning, was analysed with the FEM software BRIGADE. Additionally parametric analyses of the crushing resistance R cr was performed to obtain the relationship between the crushing resistance and the safety factor for limit turning for the dams analysed with BRIGADE. 57

70 CHAPTER 5. STABILITY ANALYSES Previously studied dams In the report by Fouhy and Rios Bayona (2014), Dam 4, Dam 6 and Dam in Table 5.1 and Table 5.2, was studied. Their study contains a probabilitybased analysis for evaluation of the stability of dams to account for the omission of uncertainties. The aim of their study was to find a reliability index, β-target value, applicable to the stability analyses for sliding and overturning of concrete dams. Fouhy and Rios (2014) also performed a deterministic analysis to enable an interpretation of the results from the probability-based analysis. They performed their analysis with three different load combinations, Load Combination 1 which corresponds to the first normal load case in RIDAS was off interest for this report. The differences compared to this report is presented below. The sliding criterion was based on the Mohr-Coulomb equation which includes cohesion. Different values for concrete density. The ice load was based on a report by Adolfi and Eriksson (2013), which in turn is based on collected values for the annual maximum. A higher value for the characteristic yield strength of steel was used. The results from Fouhy and Rios for load combination 1 are presented in Table 5.3. A brief comparison of the β-target values with the values stated in Eurocode, see Table 5.4, was included in the report. The β-target values have a reference period of one year, which correspond to the probability of dam failure evaluated over a period of one year (Westberg, 2010). The highlighted values in Table 5.3 are those who do not pass the criteria, either according to RIDAS for the deterministic calculations or according to Eurocode, RC3, for the probabilistic calculations. This enable us to easily note how high β-values that were obtained and the difficulties in comparing these to Eurocode. There is a bad correlation between the β-value and the safety factor. For the sliding criterion only one dam fail according to the deterministic calculations while all but one fail in the probabilistic calculations. For the overturning criterion all values obtained from the probabilistic calculations are well above the limit according to Eurocode. 58

71 5.2. STABILITY CALCULATIONS Table 5.3: Results from Fouhy and Rios Bayona (2014). Dam Probabilistic Deterministic β for overturning β for sliding Overturning Sliding Dam Dam Dam Dam Dam Dam Table 5.4: Recommended minimum reliability values according to Eurocode Safety class Minimum values for β Probability of failure/year RC RC RC Stability Calculations Design approaches Overturning The failure criterion for overturning was calculated according to Equation (3.1) from Section The safety factor s should satisfy Equation (5.1). s = M stab M over > 1.5 (5.1) In the calculations according to Eurocode, the failure criterion for overturning Equation (3.10) from Section 3.2.2, should satisfy Equation (5.2). s = M d,stb M d,dst 1.0 (5.2) 59

72 CHAPTER 5. STABILITY ANALYSES Sliding The failure criterion for sliding according to RIDAS, was calculated according to Equation (3.2) from Section The friction coefficient µ should satisfy Equation (5.3), with µ max for the rock foundation, from Table 3.3. µ = R H R V µ max = 0.75 (5.3) The failure criterion for sliding Equation (3.11) from Section 3.2.2, according to Eurocode, should satisfy Equation (5.4). H d R p;d R d 1.0 (5.4) Limit turning The safety factor was set to fulfil the value for overturning according to RIDAS, from Table 3.2, and should satisfy Equation (5.5). The safety factor for limit turning, about the O axis: F s = ΣM r ΣM t > 1.5 (5.5) Calculation method The calculations were executed in Matlab where a numerical analysis tool was developed for the stability analyses. These analyses were performed according to Figure

73 5.2. STABILITY CALCULATIONS SPILLWAY MASSIVE BUTTRESS PILLAR Define attributes Frontplate Hole Gate Plot dam Calculate geometry Calculate Loads Water pressure Horizontal water pressure Vertical water pressure if inclined upstream face Vertical water pressure if spillway Tail water pressure Vertical tailwater pressure Horizontal tailwater pressure if inclined downstream face Earth Pressure Vertical and horizontal earth pressure: Soil same density Soil diff. density Uplift Horizontal and vertical uplift: If tailwater If hole If inclined foundation else Vertical uplift Rock bolts /tendons Horizontal force Vertical force Ice load Horizontal force: If not buttress else Stability If not Buttress Partial factors Load combinations SLIDING CRITERION Partial factors Load combinations If Buttress Input: Rotation points coordinates Loads Horizontal Vertical SLIDING CRITERION RIDAS Loads Horizontal Vertical Input: Rotation points coordinates Level arms Rotating moment Stabilising moment OVERTURNING RIDAS Rotating moment Stabilising moment Level arms Input: R cr Input: R cr Position of O axis Foundation crushing resistance Partial factors OVERTURNING EUROCODE LIMIT TURNING Partial factors Position of O axis Foundation crushing resistance Figure 5.3: Stability calculations in Matlab. 61

74 CHAPTER 5. STABILITY ANALYSES Parametric study In the calculations according to Eurocode, the safety is defined on the loads by a partial factor. Since these calculations were performed according to design approach DA 3 for retaining walls, the values for the partial factors may not be adequate for concrete dams, therefore a parametric study was performed. The aim was to define the parameter with the greatest influence on the stability by calculation of the weighting factor, see Equation (5.6). The design load could then be modified by varying the partial factor to obtain a safety factor in agreement with the results from RIDAS. The parametric study was performed for the loads acting on the dams, i.e. the parameters for the sliding and the overturning criterion were analysed. The importance of each load was calculated in relation to the total loads affecting the structure, according to Equation (5.6). α i = x i x 2 i x 2 n (5.6) where x i α is the value for the load studied. is the weighting factor. Equation (5.7) should then be fulfilled for all the included parameters. α 2 i α 2 n = 1 (5.7) 5.3 CADAM The computer program CADAM is a tool used to analyse structural behaviour and safety for concrete massive dams. The program can be used to perform 2D analyses of a single monolith, assuming a unit thickness of 1 meter (Leclerc et al., 2001). CADAM was used to analyse the stability for the massive dams included in the analytical calculations. The intention was to investigate if the program is a usable tool and equivalent to the analytical calculations. CADAM enables analyses of the crack length, which was utilised to examine the contact between the dam body 62

75 5.3. CADAM and foundation, known from the literature study in Chapter 4 to have a significant influence on failure Stability calculations In CADAM the gravity method is used to perform the stress analyses to determine the crack lengths and the compressive stresses. Along with the stability analyses to obtain the safety margin against sliding and the placement of the resultant for all forces acting on the structure. This makes it possible to evaluate stability against sliding and overturning of the dam (Leclerc et al., 2003). The method is based on rigid body equilibrium to determine the internal forces acting upon the joints in the dam and the rock-concrete interface and beam theory to determine the stresses (Leclerc et al., 2001). In CADAM sliding is defined as: SSF = (ΣV + U) tan φ + ca c ΣH (5.8) where ΣV U φ c A c ΣH is the sum of vertical forces excluding uplift pressure. is the uplift pressure force resultant. is the friction angle. is the cohesion. is the area under compression. is the sum of horizontal forces. Overturning is defined as: OSF = ΣM S ΣM O (5.9) where ΣM S ΣM O is the sum of the stabilising moments. is the sum of the destabilising moments. 63

76 CHAPTER 5. STABILITY ANALYSES Modelling Input data The massive dams presented in Section 5.1.1; Dam 1, Dam 2, Dam 5 and Dam 7 were analysed. The density of the concrete was set to 2300 kg/m 3. The friction angle was defined as 45 and the cohesion was assumed to be zero for all dams. The loads presented in Table 5.2 were applied to the dams. Model definition The geometry was defined as for the analytical calculations and the masses and materials were defined. The geometry of Dam 2 and the applied loads; water pressure, ice load and resultants of the earth support fill are shown in Figure 5.4. Dam 7 have a complicated geometry of the crest and was therefore simplified due to limitations in CADAM, which only allows solid geometries with straight lines. Figure 5.4: Section of Dam 2, showing geometry and loading in CADAM. Load combinations For dams with earth support fill the force resultants for earth pressure from the analytical calculations were applied, using the user defined loads as point loads. The loads where combined according to normal load combination. 64

77 5.4. FE-ANALYSIS For Dam 1 with rock bolts, the resultant force of the bolts was applied as two point loads and positioned where the rock bolts intersect the interface of concrete and the rock. The force was applied with an elevation of 0.1 m in order for the program to apply the force on the structure. Cracking and uplift options Specification of the cracking option was defined as tensile strengths for crack initiation and propagation. The calculations were performed with constant uplift pressure and with modified uplift pressure after cracking of the dam initiated. The drainage system for Dam 7 was calculated with the option USACE 1995, which enables the reduction of the uplift pressure as stated in RIDAS. In addition the option to reduce the effectiveness of the drainage after cracking beyond the drain, was used. Output variables CADAM may generate different output reports where the stability drawings were of interest. The studied output variables were the safety factors for sliding and overturning, calculated in CADAM according to Equation (5.8) and Equation (5.9), with and without modified uplift pressure. The program also provides information about the extent of cracking in the concrete and rock interface. 5.4 FE-analysis A 2D linear elastic finite element analysis, was performed to evaluate if Fishmans assumption that the failure mode limit turning is more likely to occur compared to an overturning failure. One additional analysis was performed, where the rock was provided with plastic properties to study the impact of limit turning. The analysis was performed in BRIGADE. To prevent that sliding occurred in the FE analysis, a high value for the friction coefficient was defined between the rock foundation and the concrete dam body. Thereby the monolith was forced to overturn. The destabilising loads were successively increased in the analysis to capture the load capacity of the dam. 65

78 CHAPTER 5. STABILITY ANALYSES Studied dams A massive monolith, Dam 2, was analysed since the overturning criterion was not fulfilled and the difference in the safety factor for overturning and limit turning was small, later shown in Section The second studied monolith was the buttress monolith, Dam 3, due to the relatively large difference in the safety factor for limit turning and overturning, later shown in Section The magnitudes of the applied loads were taken from the analytical analyses in Section 5.1.1, presented in Table 5.2. The material properties are presented below. Massive monolith, Dam 2 The concrete is of type K300 with similar properties to C25/30, used today. The used values are presented in Table 5.5. Table 5.5: Material properties of C25/30 (EC 2, 2011). Density 2300 kg/m 3 Young s Modulus 31 GPa Poisson s ratio 0.2 The rock foundation was assumed to be granite and the material properties are presented in Table 5.6. Table 5.6: Material properties of granite (Björnström et al., 2006). Density 2300 kg/m 3 Young s Modulus 60 GPa Poisson s ratio 0.2 The crushing resistance was set to R cr = 20 MPa. Equation (3.13) was used to obtain the compressive stress at which the crushing zone would form. Buttress monolith, Dam 3 The material values for the rock foundation are assumed equal to those presented in Table 5.6. The concrete strength is assumed to correspond to C20/25 as shown in Table

79 5.4. FE-ANALYSIS Table 5.7: Material properties of C20/25 (EC 2, 2011). Density 2300 kg/m 3 Young s Modulus 30 GPa Poission s ratio 0.2 For the buttress monolith, the crushing resistance was set to R cr = 20 MPa. The yield stress of the rock was defined as 13.6 MPa according to Equation (3.13) and was assigned to plot a graph showing the stress and strain relationship Model definition Model The geometry of the monoliths and the foundations was defined by creating parts, and modelled as solid 2D deformable bodies. Plane stress elements with different thickness was used to enable the parts to have different widths. For the massive monolith, the parts were assigned a thickness of 1 m. For the buttress monolith, the foundation as well as the monolith was divided into two parts. The foundation part connected to the frontplate was defined with the same width as the frontplate. The foundation part connected to the buttress was defined with the same width as the buttress. Interaction For both monoliths the interaction between the surfaces of the dam body and the foundation was achieved using a frictional contact definition. The normal behaviour was described by a penalty formulation to allow for elastic slip. The penalty formulation approximates hard interaction, hard pressure-overclosure (Dassault Systèmes, 2007). The friction coefficient was chosen to 10 to disable sliding. The reason for this is that that otherwise the monolith would fail due to sliding. For the buttress monolith, the surface connection between the two foundation parts and the interaction between the frontplate and the buttress was defined with tie constraints. 67

80 CHAPTER 5. STABILITY ANALYSES Load procedure The analysis was defined in different load steps. In the initial step, the initial interactions regarding contact behaviour between the different parts and the boundary condition was applied. The boundary condition for the foundation was set to constrain the bottom of the foundation. The dead weight of the materials was applied in the second step to allow the normal force and friction force to stabilise. The gravity loads were defined with a uniform acceleration in the vertical direction. For the massive monolith, earth pressure was applied to the monolith in an additional step before the design loads were applied. To simulate the failure of the monoliths, the method of overload was used where the design loads were applied in the first stage and in the second stage the destabilising loads were increased until failure was reached. The horizontal water pressure and the uplift pressure were increased by increasing the density of the water. The method resulted in that the monolith was subjected to an increased load while the lever arm did not change (Nordström et al., 2015). For the massive monolith, the destabilising loads were increased by applying amplitude to the loads in the same step as the design loads were applied. For the buttress monolith, the loads were increased by applying additional destabilising loads in a separate step after the design loads had been applied, shown in Figure 5.5. The design loads and constrains applied to the massive monolith are seen in Figure 5.6. The hydrostatic loads and earth pressure were defined as pressure loads and the ice load was defined as a pressure load but with a uniform distribution. 68

81 5.4. FE-ANALYSIS Figure 5.5: Design loads applied to the buttress monolith (Left) and the increased destabilising loads (Right). Figure 5.6: Design loads applied to the massive monolith. Mesh The buttress monolith was assigned a free mesh, built up out of pre-defined mesh patterns, due to the complex geometries, see Figure 5.7. The foundations and the massive monolith, with a simpler geometry, were assigned a structural mesh see Figure 5.7. Plane stress and plane strain elements were chosen where each node has two degrees of freedom. The strain components perpendicular to the element faces are zero and the loading acts in the plane of the element (Patzák, 2014). 69

82 CHAPTER 5. STABILITY ANALYSES Plane stress elements of type CPS4, were used for the buttress monolith where the thickness of the elements is small in relation to the width. An convergence test was performed, resulting in a mesh size of 0.5 m for the whole buttress monolith model. The number of degrees of freedom was Plain strain elements were used for the massive monolith where the thickness is equal to unity, by using the element type CPE4R. A mesh size of 0.1 m was used for the whole massive monolith model, where convergence test was performed. The number of degrees of freedom was Figure 5.7: Mesh of the massive monolith (Left) and the buttress monolith (Right). 70

83 Chapter 6 Results and discussion In this chapter the results from the analytical calculations are presented. A comparison of the stability calculations between RIDAS (2011), Eurocode and CADAM is performed. The results from the parametric study for the stability calculations according to Eurocode are presented. The results from the analytical calculations and the FE-analysis of limit turning are presented. 6.1 Analytical analyses Design approaches A compilation of the analytical results is presented in this section. Overturning According to RIDAS, the safety factor s should satisfy Equation (5.1), from Section where s > 1.5 According to Eurocode, stability against overturning should satisfy Equation (5.2), from Section where M d,stb M d,dst 1.0 The safety factor for overturning according to CADAM, Equation (5.9) from Section 5.3.1, should satisfy Equation (5.1) according to RIDAS. 71

84 CHAPTER 6. RESULTS AND DISCUSSION The number of analysed dams that satisfied stability against overturning according to RIDAS, Eurocode and CADAM are shown in Figure Massive Buttress Spillway Pillar Spillway + Pillar Total monoliths Overturning RIDAS Overturning Eurocode Overturning CADAM Overturning modified uplift CADAM Figure 6.1: Total dams that satisfy the failure criterion for overturning according to the different methods. As seen in Figure 6.1, there are four dams that satisfied the overturning criterion according to Eurocode but could not fulfil the criterion according to RIDAS. The pillars represent the biggest difference in meeting the criterion according to Eurocode compared to RIDAS. According to the analysis performed in CADAM there is no difference in the number of massive dams that satisfy the failure criterion. The essential part of the results was if RIDAS and Eurocode account for stability against overturning with comparable safety factors. However, the majority of the dams gave the same results for the two criteria, the numerical values according to Eurocode always overestimate the safety of the dams compared to RIDAS. The results gave a clear indication that a parameter study was of interest for the overturning criterion. A compilation of how well the results from RIDAS compare with the results according to Eurocode is presented in Figure 6.2. This was done by normalising the safety factors obtained from the two methods. It is clearly shown that the results from Eurocode overestimate the safety and that the safety factor most comparable to RIDAS still differ more than 10 %. 72

85 6.1. ANALYTICAL ANALYSES 1.6 ± 10% RIDAS EC SRIDAS/SRIDAS.lim S EC /S EC.lim Figure 6.2: The relationship between safety factors for overturning calculated according RIDAS and Eurocode, presented with normalised safety factors. The obtained numerical values for the safety factors are presented in Appendix B, Table B.1 and CADAM in Table 6.1. Sliding To achieve stability against sliding according to RIDAS, the friction coefficient µ should satisfy Equation (5.3), from Section 5.2.1: µ µ max = 0.75 Stability against sliding, according to Eurocode, is fulfilled if Equation (5.4) from Section is satisfied, i.e. H d R p;d R d 1.0 The safety factor for sliding is defined according to Equation (5.8) from Section in CADAM. Equation (6.1) was used to enable the results from CADAM to be comparable with the other analytical results. s = 1 SSF (6.1) Figure 6.3 shows the number of analysed dams, that satisfy stability against sliding according to RIDAS, Eurocode and CADAM. 73

86 CHAPTER 6. RESULTS AND DISCUSSION Massive Buttress Spillway Pillar Spillway + Pillar Total monoliths Sliding RIDAS Sliding Eurocode Sliding CADAM Sliding modified uplift CADAM Figure 6.3: Total dams that satisfy the failure criterion for sliding according to the different methods. Sliding according to CADAM resulted in no difference for unchanged uplift pressure. There was a difference when the uplift pressure was modified after cracking initiated, due to the increase in uplift pressure resulting in the dams more prone to fail. From Figure 6.3 only one more dam failed according to Eurocode, this indicates that the sliding criterion from Eurocode is comparable to the sliding criterion from RIDAS. The results do however indicate that the safety criterion is slightly harder to satisfy according to Eurocode. A compilation of how well the results from RIDAS compare with the results according to Eurocode is presented in Figure 6.4. This was done by normalising the safety factors obtained from both RIDAS and Eurocode. The figure shows that there is a big difference in the correlation between the safety factors from Eurocode and RIDAS. 74

87 6.1. ANALYTICAL ANALYSES 1.6 ± 10% RIDAS EC SRIDAS/SRIDAS.lim S EC /S EC.lim Figure 6.4: The relationship between safety factors for sliding calculated according RIDAS and Eurocode, presented with normalised safety factors. Overturning and sliding The analysed dams which satisfy stability against both overturning and sliding failure are presented in Figure 6.5. The results show that there is no greater difference between the two methods, even though more dams satisfy the criterion according to Eurocode for overturning. The reason for the good compliance seen in Figure 6.5 is that the failure criteria are more consistent for sliding according to the two methods. 75

88 CHAPTER 6. RESULTS AND DISCUSSION Total monoliths RIDAS Eurocode CADAM Modified uplift CADAM 0 Massive Buttress Spillway Pillar Spillway + Pillar Figure 6.5: Total dams that satisfy both failure criteria according to the different methods. The results in Figure 6.5 motivate the performance of a parameter study to obtain failure criteria applicable to dams. CADAM The safety factors from CADAM are presented in Table 6.1, showing the results for the unchanged uplift pressure and the modified uplift pressure after cracking, including the analytical safety factors from Section according to RIDAS. Table 6.1: Results from analytical calculations and CADAM. Dam Height [m] Analytical (RIDAS) CADAM CADAM-modified uplift Sliding Overturning Sliding Overturning Sliding Overturning Dam Dam Dam Dam For overturning, the safety factors in Table 6.1 with modified uplift pressure after cracking are a bit lower than the safety factors for the unchanged uplift pressure as well as the analytical safety factors. The results from the analyses gave a lower stability with modified uplift pressure after cracking, which was expected. Sliding 76

89 6.1. ANALYTICAL ANALYSES resulted in higher safety factors for the modified uplift, i.e. increase the chance for a sliding failure to occur. The result was that only Dam 1 did not fulfil the safety criterion and Dam 2 was just on the limit, compared to the unchanged uplift where all the studied dams fulfilled the safety criterion. The safety factors calculated in CADAM were comparable to the analytical calculations according to RIDAS. Showing that CADAM is a suitable design tool for massive dams when analysing the stability. In addition to calculating the safety factors, the crack length in the contact surface between the rock and concrete was calculated. The analyses were performed to obtain additional information about the stability. The percentage of how much of the joint that cracked is presented in Table 6.2. Table 6.2: Resulting crack length, presented as crack percentage of the contact surface from CADAM. Dam Height [m] Crack percentage of the contact surface [%] CADAM CADAM - modified uplift Dam Dam Dam Dam For Dam 1, Dam 2 and Dam 5, that did not fulfil the failure criterion for overturning according to RIDAS, seen in Figure 6.1, the cracking in the concrete and rock interface was significant. In most of the cases the crack length was 100 %, seen in Table 6.2, for both the unchanged and modified uplift. From the analyses of the crack length only Dam 7 resulted in percentages that are reasonable for a dam that has not failed. For the other dams the percentage of 100 % definitely serve as indications of insufficient stability. Since these dams have not failed in reality, there is a possibility that the dams are subjected to lower loads than the required loads in RIDAS. The stability criterion for overturning is known to be difficult to fulfil for low dams, confirmed by the results from the analyses in CADAM. There could also have been faults done in the simplifications or that the program presents an inaccurate estimation. 77

90 CHAPTER 6. RESULTS AND DISCUSSION Effect of rock bolts Only Dam 1 can according to RIDAS account for rock bolts in the stability criteria. The steel strength accounted for in the two methods differ significantly. The difference between the two methods was determined by performing additional stability calculations for all the dams with rock bolts, presented in Table 5.2. The results did not show any difference for sliding, it did not affect which dams that fulfilled the sliding criterion. A difference could be detected for the overturning criterion presented in Figure 6.6. The safety factors for RIDAS and Eurocode were calculated according to Section and Section 3.2.1, with rock bolts included in the stability calculations. It was easily detected that more dams satisfied the overturning criteria according to Eurocode. Figure 6.6 shows how well the safety factors calculated with the two methods compare. As previously stated it was clear that the calculations according to Eurocode result in much higher safety factors. 1.6 ± 10% RIDAS EC SRIDAS/SRIDAS.lim S EC /S EC.lim Figure 6.6: The relationship between safety factors for overturning with rock bolts calculated according RIDAS and Eurocode, presented with normalised safety factor. It was difficult to determine if the steel strength according to RIDAS is reduced more than necessary or if Eurocode overestimates the strength. In this report the design criteria according to RIDAS were followed for the calculations including rock bolts and the corresponding calculations according to Eurocode were modified to give similar results. 78

91 6.1. ANALYTICAL ANALYSES Parametric study By performing a parametric study it was possible to detect which partial factor to modify to gain results that coincided with RIDAS. The results are presented in Figure 6.7 and Figure 6.8. Uplift pressure 50% Horizontal water pressure 22% Ice pressure 28% Figure 6.7: The most influential destabilising parameters for overturning. The destabilising parameters with the most influence for the overturning criterion were the vertical uplift pressure (50 %), followed by the ice pressure (28 %) and the horizontal water pressure (22 %). Uplift pressure 18% Ice pressure 12% Horizontal water pressure 70% Figure 6.8: The most influential destabilising parameters for sliding. The most influential destabilising load parameters for the sliding criterion were determined. The calculations resulted in that the horizontal water load had the 79

92 CHAPTER 6. RESULTS AND DISCUSSION greatest influence (70 %), followed by the vertical uplift pressure (18 %) and the ice load (12 %). Overturning Due to four more dams satisfy the overturning criterion according to Eurocode compared to RIDAS, one additional analytical calculation was performed, with new partial factors to obtain results corresponding to RIDAS. Since the uplift is the most influential parameter for stability against overturning, the partial factor was modified. Due to uplift being a geotechnical action, the partial factor was changed to the value for an unfavourable variable load, γ Q = 1.4. This resulted in that one additional dam failed, i.e. in agreement with RIDAS. Further analytical calculations were then performed where γ Q was increased to 1.5 for the uplift pressure. While the partial factors for permanent favourable loads was changed to γ G = 0.9 due to that the stabilising loads had a great influence in the parameter study. With these modifications of the partial factors for the overturning criterion, the results from Eurocode were more comparable to RIDAS. The numerical values for the calculations with the modifications are presented in Table

93 6.1. ANALYTICAL ANALYSES Table 6.3: Result from parametric study of the overturning criterion according to Eurocode and RIDAS. Dam Eurocode from Eurocode RIDAS from number Section modified Section Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam In Figure 6.9 it is possible to see how the modified partial factors result in safety factors that correspond better to RIDAS. An improvement of the previous results was obtained and the majority of the results do not differ more than ± 10 % from the safety factor from RIDAS. 81

94 CHAPTER 6. RESULTS AND DISCUSSION 1.6 ± 10% RIDAS EC modified RIDAS EC SRIDAS/SRIDAS.lim S EC /S EC.lim Figure 6.9: The relationship between safety factors for overturning calculated according RIDAS, Eurocode and Eurocode with modified partial factors, presented with normalised safety factors. Sliding RIDAS and Eurocode were quite consistent for the sliding criterion, but since some difference between the safety factors was obtained, an attempt to achieve results equivalent to RIDAS was made. The horizontal water pressure was the most influential parameter. The partial factor for the horizontal water pressure was modified to γ Q = 1.0, which did not affect the results for the stability criterion. If γ Q for the horizontal water pressure was further decreased or further modifications of the partial factors for the loads were made, it resulted in dams already in agreement with RIDAS to change, i.e. an unwanted result. The results gave that the partial factor for the horizontal water load could only be modified to γ Q = 1.0. As shown in Figure 6.10 the modified partial factors give a slightly better correspondence to RIDAS. The result is however, still not satisfying and therefore more studies need to be performed to find partial factors that would result in a acceptable correspondence to RIDAS. 82

95 6.1. ANALYTICAL ANALYSES 1.6 ± 10% RIDAS EC modified RIDAS EC SRIDAS/SRIDAS.lim S EC /S EC.lim Figure 6.10: The relationship between safety factors for sliding calculated according RIDAS, Eurocode and Eurocode with modified partial factors, presented with normalised safety factors. Rock bolts Including rock bolts gave no difference in the result regarding the sliding criterion and therefore only the partial factors for overturning are discussed in this section. The modified partial factors used for the results presented above, γ Q = 1.5 and γ G = 0.9, were used to determine if the results from Eurocode and RIDAS would be more similar. The outcome was not as desired and an additional calculation was performed where, in addition to the previous adjustments, the partial factor γ s was changed to The adjustment of γ s affected the strength of the rock bolts. The modifications resulted in more comparable safety factors to RIDAS, shown in Figure

96 CHAPTER 6. RESULTS AND DISCUSSION 1.6 ± 10% RIDAS EC modified RIDAS EC SRIDAS/SRIDAS.lim S EC /S EC.lim Figure 6.11: The relationship between safety factors for overturning with rock bolts calculated according RIDAS, Eurocode and Eurocode with modified partial factors, presented with normalised safety factors Previously studied monoliths From the report by Fouhy and Rios Bayona (2014), the results was interpreted as a big scatter, where the performed comparison with the acceptable values according to Eurocode was limited. From the probabilistic analyses in their report, no conclusions could be drawn about if the failure criterion was fulfilled or not. Fouhy and Rios Bayona (2014) showed that their probabilistic method gave the same β-value for a dam that fulfil the deterministic failure criterion as for a dam that fails to fulfil the criterion. By observation and comparison to Eurocode, the probabilistic method did not result in comparable safety limits. The use of partial factors in this report shows better correspondence with RIDAS. 6.2 Analyses of limit turning Analytical analysis The safety factors from the analytical calculations for limit turning and overturning according to RIDAS, calculated with R cr = 20 MPa, are presented in Table 6.4. The table also includes the difference between the safety factors for the two criteria. 84

97 6.2. ANALYSES OF LIMIT TURNING Table 6.4: Results from analytical calculations of stability against limit turning and overturning. Dam Height [m] Limit turning Overturning from Section Difference[%] Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam Dam The dam with the greatest difference between the safety factors was Dam 3 where the difference between the two criteria was 11 %. For the majority of the dams the difference between the safety factors was insignificant. For all dams under 10 m the impact of limit turning on the safety factor was negligible. For Dam 9 the safety factor for limit turning increased, showing that limit turning not always result in lower safety factors. This is presumed to be due to that the sum of the stabilising forces are either increased more or decreased less than the sum of destabilising forces. A high contributed stabilising force from the rock might be an other reason why the safety factor increased. From the assumption that limit turning should fulfil the same criterion as overturning, only one dam, Dam 14, failed due to limit turning while fulfilling the criteria for overturning. By the comparison of Dam 5 and Dam 6 as well as for Dam 4 and Dam 7, the difference between the safety factors is greater for buttress dams compared to massive dams of the same height, highlighted in the results presented in Table 6.4. The impact of the crushing resistance on the safety factor for limit turning can be seen in Figure 6.12 and Figure For Dam 2 in Figure 6.12, the relationship 85

98 CHAPTER 6. RESULTS AND DISCUSSION between the safety factor for limit turning and the crushing resistance show that the limit turning criterion is of importance for rock with poor quality, typically a crushing resistance less than 5 MPa. However, for Dam 3, in Figure 6.13, the safety factor for limit turning does not approach the value of the safety factor for overturning in the same way as for Dam 2, therefore in this case the rock quality becomes more important. The possibility of a limit turning failure may be worth to consider for high dams. 1.2 Limit turning Overturning Safety factor [-] Crushing resistance of rock [MPa] Figure 6.12: The relationship between the safety factor for limit turning and the crushing resistance for Dam Limit turning Overturning Safety factor [-] Crushing resistance of rock [MPa] Figure 6.13: The relationship between the safety factor for limit turning and the crushing resistance for Dam 3 A significant influence of the crushing resistance can clearly be seen which also show the need for geotechnical investigations in order for limit turning design criteria to be 86

99 6.2. ANALYSES OF LIMIT TURNING useful. In dam design today approximated material values are often used. The use of approximated values for the crushing resistance may lead to inadequate design FE-analysis For both the massive and the buttress monolith, the ultimate loading for the destabilising loads was defined as two times the design load. The ultimate loading was chosen to ensure the model to reach failure. Dividing the load at which the monolith goes to failure with the design load made it possible to extract the safety factor to examine if it corresponded with the analytical calculations from RIDAS. By analysing if the compressive stresses that corresponds to the crushing resistance were reached, it was possible to determine if limit turning failure would occur before overturning failure. Based on Equation (3.13) a compressive strength of 13.6 MPa (corresponding to the crushing resistance 20 MPa) was used to detect failure. For Dam 3, the compressive stresses corresponded to the crushing resistance when the ratio of total loads/design loads = The parts of the rock underneath the toe started to plasticise, i.e. formation of the crushing zone, indicating that limit turning would occur before overturning. In Figure 6.14, when the ratio of total loads/design loads = 1.89, a greater part of the rock beneath the toe had reached stresses equal to the crushing resistance and the crushing zone was easily detected. This gives that the analytical safety factor for limit turning 1.74 from Section appears reasonable. By extracting the stresses distributed over one element in the rock crushing zone, plastic deformation of the rock could also be seen, shown in the stress-strain curve in Figure Showing that the stresses in the rock lead to the formation of a crushing zone before the overturning failure occurred, at a safety factor corresponding to 1.94, i.e. similar to the analytical safety factor for overturning. 87

100 CHAPTER 6. RESULTS AND DISCUSSION Figure 6.14: Compressive stress in Dam Stress [MPa] Strain [ ] Figure 6.15: Stress-strain relationship for Dam 3. 88

101 6.2. ANALYSES OF LIMIT TURNING The analysis of Dam 2 did not display any signs of limit turning failure, which was not surprising considering the results from Section where Dam 2 only had 0.4 % lower safety factor for limit turning compared to overturning. The model failed when the safety factor was 1.09, which corresponds to the analytical safety factor for overturning. The rock did not reach the compressive stresses required for the crushing zone to develop, as seen in Figure This indicates that the dam is more prone to fail according to overturning compared to limit turning. Figure 6.16: Compressive stresses in Dam 2. 89