Geotechnical Analysis: Definition of a theoretical framework to classify currently available analysis methods Flashcards
What are the first two design requirements for any geotechnical structure?
- Basic geometry of the structure
- Loading conditions
What ground conditions must be known for design?
Soil stratigraphy
Soil strength
Soil stiffness
Groundwater conditions
What service locations must be identified in a site investigation?
Gas, water, electricity, sewers, tunnels
Why must the type and depth of adjacent building foundations be known?
To assess potential interactions and influence from new construction.
What performance restriction is needed for crane operations on overhead rails?
Limited differential settlement between support columns
Why must interaction with existing structures be considered in geotechnical design?
Because soil-structure interaction is continuous between the new and existing elements.
What four aspects must analysis assess to ensure a SAFE & STABLE structure?
Local stability
Overall stability
Magnitudes of structural forces
Magnitudes of movements
What is an example of a local stability issue?
A foundation or retaining wall deforming while soil remains stable
If a wall fails but houses behind remain intact, what design aspect failed?
Local stability
What is an example of overall stability failure despite a stable wall?
A slope failure behind the wall with a visible slip surface
Name three structural elements that can experience internal forces in soil.
Retaining walls, props, tunnel linings
What types of forces must be calculated under both working and ultimate conditions?
Bending moments
Shear forces
Axial forces
What is the formula for factor of safety in structural design?
Fs = Qu / Qw
Where:
Fs = Factor of safety
Qu = Ultimate load
Qw = Working load
Requirement: Fs > 1.0
Why must the magnitude of ground and structure movements be analysed?
To ensure serviceability and avoid damaging existing infrastructure.
Why was movement analysis crucial near the Big Ben clock tower?
To prevent damage to the sensitive clock mechanism and nearby structures
What are the two limit states in geotechnical design?
Ultimate Limit State (ULS)
Serviceability Limit State (SLS)
What four conditions must an analysis satisfy to be considered exact?
Equilibrium
Compatibility
Constitutive behaviour
Boundary conditions
In geotechnical analysis, what is the general equilibrium condition?
Σ External forces = Σ Internal forces
What is the differential form of equilibrium in the x-direction with stress terms?
∂σx/∂x + ∂τyx/∂y + ∂τzx/∂z + γ = 0
What are the 6 stress components in a 3D system?
σx, σy, σz, τxy, τyz, τxz
What does compatibility ensure in geotechnical analysis?
That strains result in a continuous, non-overlapping deformation
What does non-compatible deformation look like in analysis?
Discontinuous or unrealistic geometry post-deformation
What are the displacement–strain relationships for direct strain?
εx = ∂u/∂x
εy = ∂v/∂y
εz = ∂w/∂z
What are the shear strain expressions?
γxy = ∂v/∂x + ∂u/∂y
γyz = ∂w/∂y + ∂v/∂z
γxz = ∂w/∂x + ∂u/∂z
What component of the framework provides the additional 6 equations needed for a full solution?
Constitutive behaviour (stress–strain relationship)
What does the constitutive relationship describe in geotechnical materials?
The relationship between stress and strain under loading
What are the three typical stress-strain behaviours of soil?
Ductile
Strain softening
Strain hardening
What is the general matrix form of the constitutive law?
{Δσ} = [D]{Δε}
Where [D] is the stiffness matrix, {Δσ} = stress increment vector, {Δε} = strain increment vector.
Why might we reduce the number of parameters in the D-matrix?
To simplify the geometry and boundary conditions for efficient modelling
What assumption does a plane strain idealisation make?
That all cross-sections in the z-direction are the same (no strain along z)
What are the two plane strain assumptions regarding displacements?
w = 0 (no displacement in z-direction)
u and v are independent of z
In plane strain, which stress components are non-zero?
σx, σy, and τxy (out-of-plane components are zero)
Which method of geotechnical analysis satisfies all four theoretical requirements: Equilibrium, Compatibility, Constitutive Behaviour, and Boundary Conditions?
A. Limit Equilibrium
B. Stress Field
C. Full Numerical
D. Limit Analysis (UB/LB)
C. Full Numerical
The Limit Equilibrium method satisfies equilibrium, but fails to satisfy ___ and ___, and only partially satisfies ___.
Compatibility, Constitutive Behaviour, Boundary Conditions
