This book focuses on the unified solutions and analysis for the problems in soil mechanics based on the unified strength theory, which is a new theory on the yield and failure of materials under multi-axial stresses. Then, it provides a system of yield and failure criteria adopted for most materials, from metallic materials to rocks, concretes, soils, polymers, etc. It includes the Tresca criterion, Mohr–Coulomb theory, and Mises criterion as well, which are special cases or linear approximation of the UST.
Author(s): Mao-Hong Yu
Publisher: Springer-ZUP
Year: 2023
Language: English
Pages: 222
City: Hangzhou
Preface
Contents
1 Introduction
1.1 Backgrounds
1.2 Discussions of the Mohr–Coulomb Strength Theory
1.2.1 On the Intermediate Principal Stress
1.2.2 On the Stress Circle
1.2.3 On the Frication Angle
1.2.4 Comparison Between Strength and Deformation Obtained by Plane Strain and Triaxial Tests
1.2.5 Strength Index of Soils: Friction Angle φ (True Triaxial Test)
1.2.6 Shear Strength Index C
1.2.7 Peak Strength σ01 of Soils
1.2.8 On the Analysis Results of Structural
1.2.9 On Axisymmetric Triaxial Tests Method
1.3 New Theoretical Basis of Soil Strength
1.4 Soil Mechanics Based on Unified Strength Theory
References
2 Stress State and Element
2.1 Introduction
2.2 Stresses on the Oblique Plane
2.2.1 Stresses on the Oblique Plane
2.2.2 Principal Shear Stresses
2.2.3 Octahedral Shear Stress
2.3 Hexahedron, Octahedron, and Dodecahedron
2.3.1 Principal Stress Element
2.3.2 Isoclinal Octahedron Element
2.3.3 Single-Shear Element
2.3.4 Twin-Shear Element
2.3.5 Dodecahedral Principal Shear Stress Element
2.3.6 Twin-Shear Stress State and Twin-Shear Element
2.4 Stress Space
2.4.1 Relation Between ( σ1 ,σ2 ,σ3 ) and (x, y, z)
2.4.2 Relation Between ( σ1 ,σ2 ,σ3 ) and (ξ, r, θ) or
2.5 Summary
Reference
3 Stresses in Soil Masses
3.1 Introduction
3.2 Effective Stress of Soils
3.3 Self-weight Stress
3.4 Contact Pressure
3.4.1 Vertical Centric Load
3.4.2 Vertical Eccentric Load
3.5 Additional Stress in Soils
3.5.1 Additional Stress Due to Vertical Concentrated Load
3.5.2 Additional Stress Due to Distributed Load
3.5.3 Stress Analysis in Spatial Problems
3.6 Additional Stresses in Plane Strain State
3.6.1 Vertical Line Load
3.6.2 Vertical Uniform Strip Load
3.7 Stresses Induced by Uniform Circular Load
3.8 A Brief Introduction of Soil Elasto-plastic Stress Analysis
References
4 Strength Characteristics of Soil
4.1 Introduction
4.2 Strength Different Effect (SD Effect)
4.3 Shear Strength and Effect of Normal Stress
4.4 Normal Stress Effect of Twin-Shear Strength
4.5 Effect of Hydrostatic Stress
4.6 Effect of Intermediate Principal Stress
4.7 Effect of Stress Angle
4.8 Convexity and Inter- and Outer Boundary of the Failure Limit Surface of Soils
References
5 Yu Unified Strength Theory
5.1 Introduction
5.2 Voigt-Timoshenko Conundrum
5.3 Mechanical Model of the Yu Unified Strength Theory
5.4 Mathematical Modeling of the Yu Unified Strength Theory
5.5 Experimental Determination of Material Parameters
5.6 Mathematical Expression of the Yu Unified Strength Theory
5.7 Other Formulations of the Yu Unified Strength Theory
5.7.1 Yu Unified Strength Theory Cohesion C and Friction Angle Φ Expression
5.7.2 Unified Theoretical Expression of Strength with Positive Compressive Stress
5.8 Relation Among the Parameters of the UST
5.9 Special Cases of the UST for Different Parameter b
5.10 Special Cases of the UST by Varying Parameter a
5.11 Limit Loci of the UST by Varying Parameter b in the π-Plane
5.12 Limit Loci of the Yu Unified Strength Theory in Plane Stress State
5.13 Limit Surface of the Yu Unified Strength Theory
5.14 Limit Surfaces of the Yu Unified Strength Theory Drawed by Kolupave-Altenbach
5.15 Comparison Between the UST and Experimental Results
5.16 Significance of the Yu Unified Strength Theory
5.17 Summary
References
6 Compression and Settl
6.1 Introduction
6.2 Compression Test and Compression Index
6.2.1 Compression Test and Compression Curve
6.2.2 Compressibility Index
6.2.3 Rebound Curve and Recompression Curve
6.3 Influence of Stress History on Settlement
6.3.1 Stress History of Natural Soil Layers
6.3.2 Determination of Pre-consolidation Pressure
6.3.3 Final Settlement of Foundation Considering the Effect of Stress History
6.4 Relationship Between Deformation and Time
6.4.1 Seepage Deformation of Saturated Soils
6.4.2 Terzaghi’s One-Dimensional Consolidation Theory
6.4.3 One-Dimensional Consolidation Differential Equation
6.4.4 Calculation of Consolidation Degree
6.4.5 In Late-Stage Settlement Calculated by Settlement Observation Data
6.5 Settlement Analysis for the City Wall of East Gate in Xi’an
6.6 Analysis of Unidirectional Compression Consolidation in Saturated Soft-Soil
6.7 Analysis of Shear Consolidation in Saturated Soft-Soil
6.8 Consolidation Analysis of in Saturated Soft-Soil Foundation Under Uniform Load
6.9 Settlement Analysis of the Foundation of Big Goose Pagoda
References
7 Earth Pressure Theory
7.1 Introduction
7.2 Theoretical Solution of Rankine’s Earth Pressure
7.2.1 Theoretical Analysis Model
7.2.2 Formula Derivation When the Intermediate Principal Stress Is Larger
7.2.3 Formula Derivation When the Intermediate Principal Stress Is Smaller
7.3 Expression of UST with Shear Strength
7.4 Unified Solution of Theory on Sliding Wedge for Earth Pressure
7.5 Examples for Unified Solution of Rankine's Earth Pressure
7.5.1 Example 1 (Zhang J, Hu RL, et al.)
7.5.2 Example 2 (Zhang J, Hu RL, Yu WL, et al.)
7.5.3 Example 3 (Fan W, Shen ZJ, et al.)
7.5.4 Example 4 (Yuan JL)
7.5.5 Example 5
7.5.6 Example 6 (Ying J, Liao HJ, et al.)
7.6 Study on J. Karstedt Space Earth Pressure of Reinforced Retaining Wall Based on the UST
7.7 Unified Solution of Space Earth Pressure Computing Theory
7.8 Summary
References
8 Ultimate Bearing Capacity of Strip Footings
8.1 Introduction
8.2 Bearing Capacity of Strip Footings
8.2.1 Formula of Ultimate Bearing Capacity
8.2.2 The Influence of Various Parameters on Ultimate Bearing Capacity
8.3 Ultimate Bearing Capacity of Footings Caused by Cohesion and Overloading
8.3.1 Formula Deduction of Ultimate Bearing Capacity of Foundation
8.3.2 The Influence of Parameters on the Ultimate Bearing Capacity
8.4 Examples
8.4.1 Compared with the Calculated Results of Terzaghi Formula
8.4.2 Comparison Between Unified Strength Formula and Meyerhof Formula
8.5 Slip Line Unified Solution of Ultimate Bearing Capacity for Strip Footings
8.6 Summary
References
9 Slope Stability
9.1 Introduction
9.2 Theoretical Derivation of Bearing Capacity
9.3 Examples
9.4 Unified Solution of Bearing Capacity of a Trapezoid Structure When It Is Subjected to Uniform Load
9.5 Slip Line Unified Solution of Trapezoidal Structures
9.6 Unified Solution of Slope Bearing Capacity When It Is Subjected to Uniformly Distributed Load
9.7 Slip Line Unified Solution of Slope
References
