Reliability-Based Design in Soil and Rock Engineering: Enhancing Partial Factor Design Approaches

Description

This book contains probabilistic analyses and reliability-based designs (RBDs) for the enhancement of Eurocode 7 (EC7) and load and resistance factor design (LRFD) methods. An intuitive perspective and efficient computational procedure for the first-order reliability method (FORM, which includes the Hasofer–Lind reliability index) is explained, together with discussions on the similarities and differences between the design point of EC7/LRFD and RBD-via-FORM. Probability-based designs with respect to the ultimate and serviceability limit states are demonstrated for soil and rock engineering, including shallow and deep foundations, earth-retaining structures, soil slopes, 2D rock slopes with discontinuities, 3D rock slopes with wedge mechanisms, and underground rock excavations. Renowned cases in soil and rock engineering are analyzed both deterministically and probabilistically, and comparisons are made with other probabilistic methods. This book is ideal for practitioners, graduate students and researchers and all who want to deepen their understanding of geotechnical RBD accounting for uncertainty and overcome some limitations and potential pitfalls of the evolving LRFD and EC7. Solutions for the book’s examples are available online and are helpful to acquire a hands-on appreciation: https://www.routledge.com/9780367631390. Cover Half Title Title Page Copyright Page Table of Contents Abbreviations and symbols Author Chapter 1: Introduction 1.1 Intended audience 1.2 Overview of chapters Part I: Background chapters on probabilistic methods, LRFD and EC7 Chapter 2: Hasofer–lind index, FORM, reliability-based design and SORM 2.1 Suggested books and internet resources for understanding basic statistical terms 2.2 A simple hands-on Hasofer–Lind method in spreadsheet 2.3 Intuitive grasp of the Hasofer–Lind index via expanding dispersion ellipsoid perspective 2.4 FORM for correlated non-gaussian variables 2.5 A simple example of RBD-via-FORM and correlated sensitivities 2.6 How mean-value point determines the sign of reliability index 2.7 Probabilistic consolidation settlement analysis 2.7.1 Method 1: Efficient Spreadsheet Method 2.7.2 Method 2: Traditional Iterative Algorithm 2.8 Probabilistic analysis of earthquake-induced cyclic shear stress in saturated sand 2.9 Second-order reliability method (SORM) in spreadsheet 2.10 Correlation matrix must be positive definite 2.11 System FORM, response surface method, and importance sampling Chapter 3: Civil and environmental applications of reliability analysis and design 3.1 Introduction 3.2 Example 1: Probability of traffic congestion 3.2.1 Solution based on mean and standard deviation of safety margin 3.2.2 Alternative solution procedure based on Hasofer–Lind index 3.3 Example 2: Design of traffic capacity for a target reliability index 3.4 Example 3: Probabilities of arriving late and arriving in time 3.4.1 Alternative solution using spreadsheet function for the single random variable case of T 3 3.5 Example 4: Required travel time from RBD-via-FORM 3.6 Example 5: Supply and demand of irrigation water 3.7 Example 6: Thermal pollution in a river 3.8 Example 7: Reliability of a storm sewer system 3.9 Example 8: Reliability of a breakwater at LA Spezia Harbour in Northern Italy 3.10 Example 9: Spillway capacity 3.11 Example 10: Two ways of increasing spillway capacity, and rbd with cost considerations 3.12 Example 11: Column subjected to biaxial bending moments and axial force 3.13 Example 12: Moment capacity of a reinforced concrete beam 3.14 Example 13: Reliability analysis of an asymmetrically loaded beam on Winkler medium 3.15 Example 14: A strut with complex supports and implicit performance function Chapter 4: Eurocode 7, LRFD and links with the first-order reliability method 4.1 Introduction 4.2 Load and resistance factor design approach, and links with form design point 4.3 Eurocode 7 approach, and links with the design point oF RBD-via-FORM 4.4 Example RBD of foundation settlement with back-calculated partial factors 4.5 Probabilistic settlement analysis of Hong Kong land reclamation test fill 4.5.1 Sensitivity considerations 4.5.2 Limit state surfaces and performance functions pertaining to magnitude and rate of soft clay settlement 4.5.3 Distinguishing positive and negative reliability indices 4.5.4 Reliability analysis for different limiting state surfaces 4.5.5 Obtaining probability of failure (P f) and CDF from β indices 4.5.6 Obtaining PDF curves from β indices 4.6 Conduct Monte Carlo simulations wisely 4.6.1 Distortions caused by negative values of random numbers 4.6.2 Distortions caused by physically incompatible random numbers in Monte Carlo simulations Part II: Reliability-based design applied to soil engineering Chapter 5: Spread foundations 5.1 Introduction 5.2 Hasofer–Lind index applied to the RBD of a spread foundation with two random variables 5.3 Hasofer–Lind index reinterpreted via expanding ellipsoid perspective 5.4 Effect of parametric correlations on failure probability 5.5 First-order reliability method (FORM) 5.6 An EC7 design of strip footing width based on characteristic values and partial factors 5.7 FORM analysis of EC7 design to estimate its reliability and probability of failure 5.8 RBD-via-FORM for target reliability index, to compare with EC7 footing width design 5.9 RBD-via-FORM resolves load-resistance duality of a retaining wall foundation 5.9.1 Information and insights at the design point of RBD-via-FORM 5.9.2 Comparison of RBD-via-FORM with Monte Carlo simulation and MVFOSM 5.10 RBD-via-FORM insights for LRFD 5.10.1 Back-calculations of LF and RF from the design point of RBD-via-FORM 5.10.2 Load-resistance duality revealed in load factors back-calculated from RBD-via-FORM 5.11 Reliability analysis of serviceability limit state involving the Burland and Burbidge method 5.11.1 Deliberations by Tomlinson (2001) on the ULS and SLS of a spread foundation 5.11.2 Statistical properties of compressibility m v in Burland and Burbidge data 5.11.3 FORM analysis for probability of settlement exceedance 5.11.4 From normally distributed log(m v) to lognormally distributed m v for FORM analysis 5.12 Distinguishing positive FROM negative reliability indices Chapter 6: Pile foundations 6.1 Introduction 6.2 A driven pile in stiff clay below a jetty 6.2.1 Deterministic design of the length of a jetty pile 6.2.2 Statistical inputs, and RBD-via-FORM 6.2.2.1 Quantifying the scatter/uncertainty in c u 6.2.2.2 Quantifying the scatter/uncertainty in adhesion factor α 6.2.2.3 Reliability-based design of pile length in soil 6.2.2.4 Discretized random field 6.3 A driven pile in sand 6.3.1 Maximum allowable design load based on EC7-DA1b 6.3.2 RBD of design load for the driven pile in sand 6.3.2.1 Refined formulation prior to RBD 6.3.2.2 RBD involving discretized random field 6.4 Randolph and Wroth method of estimating pile settlement, extended probabilistically 6.4.1 Deterministic estimation of pile settlement using the Randolph and Wroth method 6.4.2 Extending the Randolph and Wroth method to reliability analysis of pile settlement 6.5 A laterally loaded pile in soil with strain-softening and depth-dependent P-Y curves 6.5.1 Deterministic numerical procedure for a laterally loaded pile involving strain-softening p-y curves 6.5.2 From deterministic numerical procedure to probabilistic analysis of laterally loaded piles 6.5.3 Pile with 26 m cantilever length 6.5.4 Fully embedded pile with no cantilever length 6.6 Laterally loaded pile: verification of spreadsheet numerical procedure with Hetenyi solution for linear p-y model Chapter 7: Earth retaining structures 7.1 Introduction 7.2 Rotational ultimate limit state of a semi-gravity wall 7.3 Reliability-based design of a semi-gravity retaining wall 7.3.1 Limit state functions with respect to rotation and sliding 7.3.2 Hasofer–Lind reliability index for correlated normal variates 7.4 Comparison with EC7 DA1B design of base width b for rotation ULS 7.5 Vector Components of active earth thrust are allied, not adversarial 7.6 RBD-via-FORM for an anchored sheet pile wall 7.6.1 Possible multiple outcomes in EC7 ( 2004) DA1b design of anchored sheet pile involving stabilizing–destabilizing unit weight 7.7 Positive reliability index only if the mean-value point is in the safe domain 7.8 RBD-via-FORM for an example modified from Terzaghi et al. (1996) 7.8.1 Deterministic analysis with search for the critical quadrilateral wedge 7.8.2 Design resistance from the perspective of LRFD and EC7-DA2 7.8.3 Extending the modified Terzaghi et al. (1996) deterministic example to RBD-via-FORM 7.8.4 RBD-via-FORM of tie rod force to resist lateral thrust 7.8.5 Another failure mode involving surface rolling along the slope of the stockpiled iron ore 7.9 Retaining walls with steady-state seepage towards a vertical drainage layer behind the wall 7.9.1 Deterministic example from Clayton et al. (2013), extended into probability-based design 7.9.2 Extending the Clayton et al. example to probability-based design 7.9.3 Deterministic example from Lambe and Whitman (1979), extended probabilistically Chapter 8: Soil slope stability 8.1 Introduction 8.2 A deterministic example from Terzaghi et al. (1996), extended probabilistically 8.2.1 Analytical ϕ u = 0 procedure 8.2.2 From deterministic analysis to reliability-based design of the Terzaghi et al. problem 8.2.3 Perspectives, insights and information provided by RBD-via-FORM 8.3 An excavated slope in London Clay that failed despite a high computed factor 8.3.1 Deterministic ϕ u = 0 slip circle analysis, with summation of moments from horizontal strips 8.3.2 Probabilistic analysis incorporating discretized random field for London Clay 8.4 Probabilistic analyses of a slope failure in San Francisco Bay mud 8.4.1 Reliability analysis with correlated lognormals and statistical inputs based on in situ and lab tests 8.4.2 Reliability-based design of slope angle and excavation depth 8.5 Reliability analysis of a Norwegian slope accounting for spatial autocorrelation 8.6 System reliability analysis for multiple failure modes 8.7 Lambe and Whitman sloping core dam example, refined deterministically and extended probabilistically 8.7.1 Deterministic analysis for a specific slip surface of θ 1 = 10° 8.7.2 Search for the deterministic critical slip surface by varying the inclination angle θ 1 8.7.3 From deterministic critical slip surface to reliability analysis 8.8 Spencer method reformulated for spreadsheet, for non-circular slip surface 8.8.1 Deterministic reformulations and example analyses 8.8.2 Same template for Spencer, Bishop Simplified and force equilibrium methods but different constraints 8.8.3 Reformulated Spencer method extended probabilistically 8.8.4 Effect of closer discretization of random field 8.9 Finite element reliability analysis via response surface methodology Part III: Reliability-based design applied to rock engineering Chapter 9: Plane sliding in rock slopes 9.1 Introduction 9.2 Plane sliding stability analysis, an example from Goodman (1989) 9.2.1 Deterministic analysis using an alternative procedure 9.2.2 RBD-via-FORM of potential plane sliding 9.3 An example of two-block stability analysis in rock slopes 9.3.1 Goodman (1989) closed form equation for limiting equilibrium of a two-block mechanism 9.3.2 An alternative deterministic procedure for two-block stability analysis 9.3.3 Reliability-based design of support force for a two-block mechanism in rock slope 9.3.3.1 Comparison with Monte Carlo simulation 9.3.3.2 Information and insights at the FORM design point, and implications for Eurocode 7 and LRFD 9.4 Deterministic formulations and reliability-based design of SAU MAU ping slope in Hong Kong 9.4.1 LRFD considerations: Non-uniqueness of inferred LF and RF from RBD-via-FORM 9.4.2 Combined methods of drainage, slope reprofiling and reinforcement to improve slope reliability 9.5 Reliability analysis of a failed slope in a limestone quarry Chapter 10: Rock slopes with three-dimensional tetrahedral wedges 10.1 Introduction 10.2 Obtaining β 1, δ 1, β 2 and δ 2 angles from dip directions and dips 10.3 Kinematic requirement for formation of wedge mechanism in rock slopes 10.4 Limit equilibrium equations for the factor of safety of wedge in rock slope 10.4.1 Sliding along both planes, that is, along the line of intersection 10.4.2 Sliding along plane 1 only 10.4.3 Sliding along plane 2 only 10.4.4 Contact is lost on both planes 10.4.5 Water pressure coefficients G w1 and G w2, and relationship with water pressures u 1 and u 2 10.5 Comparison with stereographic method 10.6 Verification using the vectorial method described in Hoek and Bray 10.6.1 Verification of an example with BiPlane failure mode 10.6.2 Verification of an example with sliding failure along a single plane 10.6.3 Verification for all four failure modes of wedge mechanism in rock slope 10.7 Reliability analysis and RBD of a tetrahedral rock wedge with a dominant failure mode 10.8 Reliability-based design of drainage to enhance stability of wedge in rock slope 10.9 Reliability analysis reveals a more critical plane1 mode behind the mean-value biplane mode 10.10 Sensitivity computation in the ellipsoid approach 10.11 Chapter summary Chapter 11: Underground excavations in rock 11.1 Introduction 11.2 Deterministic ground–support interaction analysis of a shaft excavated in sandstone 11.3 Reliability analysis involving ground–support interaction of a shaft excavated in sandstone 11.4 Roof wedge in tunnel, a tale of two factors of safety 11.5 Reliability analysis of tunnel roof wedge reveals context-dependent sensitivities 11.6 Deterministic verification using Bobet and Einstein (2011) formulation of reinforced tunnel 11.7 Reliability-based design of the length and spacing of rockbolts for a target β value Appendix: An efficient spreadsheet algorithm for FORM References Further reading Index