Soil slope stability analysis combining shear strength reduction and slip line method

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Soil slope stability analysis combining shear strength reduction and slip line method

Supervisor: Yongchang Cai

Ph.D. candidate: Jie Wu

School of Civil Engineering

Tongji University, China

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Research background

Predicting the stability of soil slopes is a classical problem for

both of practicing engineers and academics.

Picture from: http://www.ccma.vic.gov.au/soilhealth/photos.htm

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Two main challenges need to be confronted when

dealing with soil slope

Research background

1. The Determination of potential slip lines of the soil slope

2. The calculation of corresponding safety factors

Picture from: http://ceae.colorado.edu/~regueiro/images/slope.jpg

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Research background

When the limit equilibrium method is applied

1

3

The stress strain behavior of soil are often neglected

The calculation models are often overly simplified

Arbitrary assumptions are usually introduced to ensure static determinacy

1

22

3

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Research background

In the past several decades, there have been growing interests

in Numerical slip line theory, which is developed from the

classical slip line theory. As a particular method for soil slope

stability analysis, the potential slip line surfaces can be tracked

in an efficient way.

Slip line

Start points of the search

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Content

Slip line method for evaluating slope stability

Application in soil slope stability analysis

Combination of Shear strength reduction and slip line method

Conclusion

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Slip line method for evaluating slope stability

7

For plane problem, when failure occurs, it has two failure planes(lines) and the angle μ between the failure plane(line) and the principal stress orientation is specific. As shown in figure below, 1 and 2 represents the maximum principal stress orientation(θ) and the minimum principal stress orientation, respectively. And α and β represent two failure planes(lines).

Traditional Slip line theory

tan( )

tan( )

dyu

dxdy

udx

：

：

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Slip line method for evaluating slope stability

Traditional Slip line theory

M-C material Tresca material 

For M-C material:

For Tresca material:

However, Traditional Slip line theory is based on rigid-plastic assumption and it can only solve some simple problems.

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Slip line method for evaluating slope stability

Numerical Slip line theory

2 2

2 2

cos sin 2 sin cos( )sin cos (cos sin )

n y x xy

n y x xy

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Slip line method for evaluating slope stability

0n

1

1

21   = arctan

2

21   = arctan +90

2

xyx y

x y

xyy x

x y

when

when

，

，

2 23 1

3 1

cos sin( )sin cos

n

n

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Slip line method for evaluating slope stability

2 21 3

3 1

( sin cos ) tan

( )sin cos

cK

So, the slope safety can be defined as below:

For the minimum of K, solve the equation 0K

3 1

3 1

(45 arcsin( ))2 *cotc

Thus, the two surfaces of the smallest anti-shear safety factor can be expressed as:

  3 1

3 1

(45 arcsin( ))2 *cotc

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Slip line method for evaluating slope stability

By linking the critical slip surface of each point, the slip surface group of slopes can be obtained. The safety factors of the slip surfaces can be calculated by the formula below. The slip surface corresponding to the minimum safety factor is the critical slip surface of slopes stability.

1

1

tann

ij ij ij ijj

n

ij ijj

c l

Fl

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Application in soil slope stability analysis

The following is the procedure of slip line theory to analyze soil slopes stability, that is, the stress distribution and its value in soil slopes is calculated by Ansys and then the slip line theory is applied to find the potential slip surface based on the stress status of the slopes.

1

Modeling in Ansys

2 3

Stress distribution in slopes

4critical slip

surface and safety

factor

Searching the

potential slip line surfaces

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Example 1

This example was provided by Australian Computer Aided Design Society (Donald and Giam, 1992).

Safety factor=1

Geometric model

Finite element mesh

γ（ KN/

m3）E（ Kp

a）μ c（ KPa

）Ψ(°)

25 1e7 0.2 1e3 38

Reference calculation result:

In Limit Equilibrium State

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Example 1 (cont.)

Contours of maximum principal stress (Elasticity)

Critical slip surfaces (Elastoplastic)

Contours of maximum principal stress (Elastoplastic)

Critical slip surfaces (Elasticity)

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Orientation of slip line (Elastoplastic)

Example 1 (cont.)

Orientation of slip line (Elasticity)

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Plastic range indicated in red color

material γ/KN m-3 c/KPa Ψ/° E/KPa v

Layer 1 19.5 0 38.0 1.0*104 0.25

Layer 2 19.5 5.3 23.0 1.0*104 0.25

Layer 3 19.5 7.2 20.0 1.0*104 0.25Layer 1

Layer 2

Layer 3 Reference safety factor is 1.400

Example 2

Another benchmark from Australian Computer Aided Design Society

The orientation of slip line

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Example 2 (cont.)

Shear strength reduction method, Fs=1.450

Limit equilibrium method, Fs=1.400

Critical slip surface, Fs=1.487

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Application in soil slope stability analysis

Based on the calculation results of the 2 examples, some conclusions can be drawn as follows:

When the soil slope, especially its top area, is not in the plastic state, there is a dramatic change of the orientation of the slip line and the slip surface tracked is singular at corresponding area, and the factor of safety is also not minimum.

1. The shear strength reduction method can be employed to reduce the material parameters until materials of the slope approaching the plastic state. Then the slip surface calculated maybe not singular and would be more like the real one.

2. the defect that the slip surface cannot be easily obtained by the conventional shear strength reduction method can also be corrected.

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Combination of shear strength reduction and slip line method

The central concept of the SSR method is very simple. Successively reduce some factors in the shear strengths of slope materials until the finite element model does not converge to a solution, which means the failure occurs. The critical factor at which failure occurs is taken to be the factor of safety.

The following is the combination of the shear strength reduction and slip line method.

1

Modeling in Ansys

3 4

Stress distribution in slopes

5Comparing the shape

of different slip

surfaces

Searching the critical

slip surfaces

2Set a range of different

strength reduction

factors

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Combination of shear strength reduction and slip line method

Plastic range indicated in red color, strength reduction factor is 1.3

The critical slip line, safety factor is 1.073

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Combination of shear strength reduction and slip line method

Plastic range indicated in red color, strength reduction factor is 1.4

The critical slip line, safety factor is 1.008

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Combination of shear strength reduction and slip line method

Plastic range indicated in red color, strength reduction factor is 1.45

The critical slip line, safety factor is 0.997

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Conclusions

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· The slip surface is singular and not as smooth as the real one if

the material, particularly in the top of the slope, is in elastic

state rather than plastic state.

· The slip line method is time efficient and no priori assumptions have

to be made when it is employed to the stability analyze of the soil

slope.

· The combination of strength reduction and slip line method can

correct the defect that the slip surface can not be directly get by the

strength reduction method, and is an effective way to track the slip

surfaces and to evaluate soil slopes stability.

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Thank you very much for your

attention !

AcknowledgementsThe authors gratefully acknowledge the support of national science and technology support program (2011BAB08B01), and program for new century excellent talents of ministry of education of China (NCET-12-0415).