Slope Stability in Unsaturated Soils

By: Behnam Shadravan Professor: Sai Vanapalli ,

Photo by D. Noe http://geosurvey.state.co.us/Default.aspx?tabid=113

Outline z Introduction z Method

of Slices z Infinite Method z FEM z Dynamic Programming z Conclusion

http://www.em.gov.bc.ca/Mining/Geolsu rv/Surficial/landslid/default.htm

Importance z Globally

(Annual) 1000 Deaths, Billion US $4 damage(Westen, 2004) z In Canada and the United States , US $2.2 billion a year. (Singroy, 2004)

Photo: The Hope slide, 18 kilometres east of Hope,BC http://www.em.gov.bc.ca/Mining/Geolsurv/Surficial/landslid/default.htm

Landslide Types

Photo Ref. http://www.em.gov.bc.ca/Mining/Geolsurv/Surficial/landslid/default.htm

Conventional Slope Analysis (Abramson et al 1996) Limit Equilibrium

Fs

A

Su required

FS about Force W C R

FS about Moment x R W

Su Su

Su

Fs f

Resisting Moment Overturning Moment

R

Su ds Wx

Analysis Methods Deterministic- Probabilistic, 2D- 3D One Section Method of Slices Infinite Slope FEM Dynamic Programming

Which methods are applicable for unsaturated soils?

Photo Ref.http://www.em.gov.bc.ca/Mining/Geolsurv/Surficial/landslid/default.htm

Method of Slices b XL EL

W ER

Slip Surface Sm

XR

Ground Surface

N Redrawn from Fredlund, 1987

Dam Model Ref: J.Graham, (2005) , Seminar in Carleton University

Regular Method of Slices Limit Equilibrium Method c'

n

u a tan

'

u a u w tan

b

Assume in discrete layers in unsaturated zone: b c c ' u a u w tan Shear force at the base of a slice Sm

B c F

n

u w tan '

Method of Slices (Fredlund et al, 1987)

General Limit Equilibrium Priority: z Satisfy both Force and Moment Equilibrium. z Shear Strength is variable

Method of Slices

Infinite Method z z z z z z z

Long distance Consistent subsoil Failure plane Limit Equilibrium Method Especially vegetated hill slopes infiltration Considering root effect Critical Depth based on properties variations

Photo: J. Graham (2005) , Seminar in Carleton University

Infinite Method Slope Surface

Slope Surface W

dcr

Failure Surface T N

Infinite Method Collins and Znidarcic, 2004

d cr

c'

w

. hc . tan 2

b

.cos . tan

w

.hp .tan '

tan '

Finite Element Method z Slope

modeling z Seepage, Combination of nonlinearity of flow and the use of steep permeability

Finite Element Mesh Finite Element Mesh used for slope , (NG, Pand, 2000)

Finite Element Mesh used for two dimensional analysis of Santa Cruz case study , Failure planes, (Collins, Znidarcic, 2004)

Dynamic Programming+ FEM Pham & Fredlund, 2003 Critical Slip : Minimum value of an Optimal Function f

Stage i

Stage i+1 Stage i

Stage i+1 Stage i

j Si i

ij

j

(ij)

l ij

R i

Rij

k

l ij

f

(ij) Rij

i

j

Sij Sij

ij

ij

f

i

k

(ij)

ij i

ij

Dynamic Programming Advantages: zShape zThe zNo

of Slip is not defined, more efficient

stress strain behavior , more flexible

need to limit equilibrium

zLess

Safety Factor

zHomogeneous,

and submerged

and nonhomogeneous , wet

Dynamic Programming (DP) z Combining

Partial general differential equation and DP technique z FEM stresses within the slope z DP Technique to find the Optimal path or slip surface z FS in Slip surface FS

fi

Li

fi

i

Li

i

Li Li

Dynamic Programming FEM Soil Behavior Model =>σx , σy , τxy , θ (Mohr) => σn , τn Strength

c'

fi

n

u a tan '

u a u w tan

b

Partial Differential Equations (stress balance) x

x

xy

y

Fx 0,

xy

x

y

y

Fy 0

Dynamic Programming Min of Auxiliary function G min

Ri F S S i

Si actuating forces acting in ith segment Ri resisting forces acting in ith segment

Si

S ij

ij ij

l

Ri

Rij

f ij ij

l

Softwares z Slices:

SLOPE/W, CHASM, GALENA , GSLOPE z FEM SVSolid , ROCSCIENCE , 3DFEMFAT, Slide 5.0 z DP DYNPROG, SVDynamic

Conclusion z In

situ properties are essential. z The analysis is directly related to the spatial variations of the soil. z The methods of slices, infinite and dynamic programming are applicable for unsaturated soil. z The strength characteristics as well as hydraulic characters are necessary for analysis

References z

z

L.W. Abramson et al (1996), Slope Stability and Stabilization Methods, John Wiley and Sons, 629 p. H.T.V Pham and D.G. Fredlund, (2004), Dynamic Programming method in slope stability computation, http://www.soilvision.com/subdomains/unsaturate dsoil.com/Docs/Papers/2004/01DynamicProgram mingMethod.pdf