Geotechnical Analysis: Stress fields Flashcards

1
Q

What theoretical requirements does the Stress Field method satisfy and not satisfy?

A

Satisfies: Equilibrium only.
Does not satisfy: Compatibility, Constitutive Behaviour, Boundary Conditions

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2
Q

In Limit Equilibrium, where is equilibrium applied?

A

Only to the failing soil block between the failure surface and boundary.

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3
Q

What are the main assumptions of the Stress Field method?

A
  • Soil is at failure everywhere
  • Combine failure criterion with equilibrium equations
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4
Q

What are the stress components for a soil element in plane strain?

A

σx, σy, τxy, γ

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5
Q

What are the plane strain equilibrium equations?

A

∂σx/∂x + ∂τxy/∂y = 0 (1)
∂σy/∂y + ∂τxy/∂x + γ = 0 (2)

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6
Q

What do σ₁′ and σ₃′ represent in a Mohr circle?

A

Major and minor principal effective stresses.

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7
Q

What is the Mohr-Coulomb failure criterion in component stresses?

A

(σx′ - σy′)/2 = τxy
τ = c’ + ((σx′ + σy′)/2) * sin(φ′)

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8
Q

What is the final combined failure criterion used in Stress Field method?

A

[(σx′ - σy′)/2]² + τxy² = [c′ + ((σx′ + σy′)/2) * sin(φ′)]²

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9
Q

How many unknowns and equations are present in the Stress Field method?

A

3 unknowns: σx, σy, τxy; 3 equations (2 equilibrium + 1 failure criterion)

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10
Q

What type of equations arise in Stress Field analysis?

A

Two hyperbolic partial differential equations (PDEs)

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11
Q

What are the characteristic direction equations?

A

dy/dx = tan(θ - π/4 - φ′/2)
dy/dx = tan(θ + π/4 + φ′/2)

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12
Q

Do Stress Field solutions apply to the whole continuum?

A

No, only to a partial zone of interest.

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13
Q

What do characteristic lines represent in Stress Field analysis?

A

Directions along which stresses vary.

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14
Q

Why is the solution near a retaining wall called a “partial stress field”?

A

Because it does not extend through the full soil mass.

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15
Q

What does σT represent in tunnel analysis using stress fields?

A

The tunnel support pressure

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16
Q

What does the characteristic mesh represent in tunnel analysis?

A

The network of stress propagation paths from the tunnel wall.

17
Q

What is the initial stress state in Rankine theory?

A

σx′ = K₀ * σy′

18
Q

When does the active stress state develop?

A

When lateral extension reduces σx′ until failure occurs.

19
Q

What is the Rankine active earth pressure expression?

A

σx′ = Ka * σy′

20
Q

When does the passive stress state develop?

A

When lateral compression increases σx′ until failure occurs.

21
Q

What is the Rankine passive earth pressure expression?

A

σx′ = Kp * σy′

22
Q

In Rankine theory, what is always true about τxy?

A

τxy = 0
Therefore, σx′ and σy′ are principal stresses.

23
Q

What is the equation for σxa′ in the Rankine active case?

A

σxa′ = σy′ - 2 * a * A

24
Q

What is the final expression for active pressure from Mohr circle?

A

σxa′ = σy′ - 2 * c′ * cot(φ′)

25
Q

What are two key applications of the Stress Field method?

A
  1. Rankine active/passive earth pressures
  2. Bearing capacity problems
26
Q

What is the difference in obliquity angles for active vs passive stress states?

A

Active: α = π/4 + φ′/2
Passive: β = π/4 - φ′/2

27
Q

What is the final expression for passive pressure from Mohr circle?

A

σxp′ = σy′ + 2 * c′ * cot(φ′)