Complex geology slope stability analysis by shear strength reduction

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Complex geology slope stability analysis by shear

strength reduction

Marek Cala, Jerzy Flisiak

Department of Geomechanics, Civil Engineering & Geotechnics AGH University of Science & Technology

Slope stability

Shear strength reduction technique (SSR)

The stability of slopes may be estimated using 2D limit equilibrium methods (LEM) or numerical methods.

Due to the rapid development of computing efficiency, several numerical methods are gaining increasing popularity in slope stability engineering.

The factor of safety (FS) of a soil slope is defined as the number by which the original shear strength parameters must be divided in order to bring the slope to the point of failure.

 



 

= 

=

trial trial

FS arctg tg FS

c c ϕ ϕ

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• It’s well known fact that for simple slopes FS obtained from SSR is usually the same as FS obtained from LEM (Griffiths & Lane, 1999; Cala & Flisiak, 2001).

• However, for complex geology slopes considerable differences between FS values from LEM and SSR may be expected (Cala

& Flisiak, 2001).

Department of Geomechanics, Civil Engineering & Geotechnics 19

Shear strength reduction technique (SSR)

25 m25 m

hg

45^o

Several analyses for the slope with weak stratum were performed to study the differences between LEM and SSR.

Weak layer 1m thick SSR versus LEM

0 10 20 30 40

Distance of weak layer from slope crest

1.4 1.5 1.6 1.7 1.8 1.9 2

FS

Weak layer 1 m thick FLAC Fellenius Bishop Janbu

25 m25 m

hg

45^o

Hard soil c=75 kPa, φφφφ=30^o Soft soil c=25 kPa, φφφφ=10^o

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Weak layer 5m thick

SSR versus LEM

25 m25 m

hg

45^o

0 10 20 30 40 50

Distance of weak layer from slope crest

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

FS

Weak layer 5 m thick FLAC Fellenius Bishop Janbu

Hard soil c=75 kPa, φφφφ=30^o Soft soil c=25 kPa, φφφφ=10^o

Bishop FS = 1.731 FLAC

FS = 1.54

20 m 1 m

SSR versus LEM

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15

15 m10 m10 m

20.918 m 15 m

15 m

45^o

40^o

γφ=20 kN/m = 20 c = 10 kPa

3 o

Department of Geomechanics, Civil Engineering & Geotechnics

SSR versus LEM benched slope case

FLAC/SLOPE (Version 4.00) LEGEND 16-Jul-02 18:17

Factor of Safety 0.90

Shear Strain Rate Contours 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 Contour interval= 5.00E-07 (zero contour om itted) Boundary plot

0 2E 1

-1.50 0 -0.50 0 0.50 0 1.50 0 2.50 0 3.50 0 4.50 0 5.50 0 (*10^1 )

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000

(*10^1) JOB TITLE : bench

Itasca Consulting Group, Inc.

Minneapolis, Minnesota USA

SSR versus LEM

benched slope case

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Modified shear strength reduction technique

1. Apply classic SSR technique to calculate FS₁(FLAC/Slope).

2. Export *.dat file to FLAC. Calculate the initial, stable situation by increasing c and φ. φ. φ. φ.

3. Find the representative number of steps (N_r) which

characterises the response time of the system. Use 1.1N_rfor further calculations.

4. Calculate situation for FS₁(check out for communication between FLAC and FLAC/Slope and elimination of any mistakes).

5. Reduce c and φ φ φ to find further FSφ _i( prepare *.dat file manually or using Excel; each time start from the initial, stable *.sav file).

Modified shear strength reduction technique

Velocity vectors Displacement vectors

Plasticity indicators FS₂= 1.00 Shear strain rate

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Modified shear strength reduction technique

Velocity vectors Displacement vectors

Plasticity indicators FS₂= 1.24 Shear strain rate

FS =0.90₁ Bishop FS=0.921

FS =1.002

Bishop FS=1.008

FS =1.243

Bishop FS=1.228

MSSR versus LEM

benched slope case

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9

FLAC/SLOPE (Version 4.00)

LEGEND 30-Jun-02 8:24

User-defined Groups bedrock zwietrzelina_wet ily_podweglowe kontakt_spag_wI_wet I_poklad_wegla ily_miedzyweg_dolne kontakt_spag_wII_wet II_poklad_wegla stary_zwal_wew Boundary plot

0 2E 2

-2.500 -1.500 -0.500 0.500 1.500 2.500 3.500 4.500 (*10^2)

0.500 1.500 2.500 3.500 4.500 5.500 6.500 7.500

(*10^2) JOB TITLE : 5_layer_wet

Department of Geomechanics, Civil Engineering & Geotechnics

Shear strength reduction technique Large, complex geology slope case

FLAC/SLOPE (Version 4.00) LEGEND 30-Jun-02 8:24

Shear Strain Rate Contours 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 3.50E-06

Contour interval= 5.00E-07 (zero contour omitted) Boundary plot

0 2E 2

-2.500 -1.500 -0.500 0.500 1.500 2.500 3.500 4.500 (*10^2)

0.500 1.500 2.500 3.500 4.500 5.500 6.500 7.500

(*10^2) JOB TITLE : 5_layer_wet

Shear strength reduction technique

Large, complex geology slope case

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Modified shear strength reduction technique

Displacement vectors

Shear strain rate FS₂= 0.87

Modified shear strength reduction technique

Plasticity indicators

Shear strain rate FS₃= 1.02

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Modified shear strength reduction technique

Shear strain rate FS₄= 1.17

Modified shear strength reduction technique

Displacement vectors

Velocity vectors FS₅= 1.29

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Modified shear strength reduction technique

Shear strain rate FS₅= 1.29

FS =0.67₁ FS =0.872

FS =1.023 FS =1.174

Bishop FS=1.351 FS =1.295

Bishop FS=1.255

MSSR versus LEM

large, complex geology slope case

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Conclusions

• For a simple, homogeneous slope, FS calculated with SSR are usually the same as FS obtained from LEM.

• In the case of a simple geometry slope consisting of two geological units, FS calculated with SSR may be considerably different than FS from LEM.

• In the case of complex geometry and geology slopes SSR technique is much more “sensitive” than LEM.

• Another step forward is the modified shear strength reduction technique – MSSR.

• Application of SSR/MSSR with FLAC may be recommended for the large-scale slopes of complex geometry.

• Such a powerful tool as MSSR with FLAC gives the opportunity for the complete stability analysis for any slope.

• Limitations: visibility, interpretation.

• Verification !!!