C. Lanni(1), E. Cordano(1), R. Rigon(1), A. Tarantino(2)

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Maurice Barker
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Landslide Processes: from geomorphologic mapping to

Tarantino(2) (1) Dipartimento di Ingegneria Civile ed

1 Landslide Processes: from geomorphologic mapping to dynamic modelling (6-7 February, Strasbourg, France) A tribute to Prof. Dr. Theo van Asch C. Lanni(1), E. Cordano(1), R. Rigon(1), A. Tarantino(2) (1) Dipartimento di Ingegneria Civile ed Ambientale (2) Dipartimento di Ingegneria Meccanica e Strutturale University of Trento (Italy)

y GEOtop model (Rigon et al., 2006) - www.geotop.org - To assess the water-pressure field within soil thickness Ψ(x,t) y GEOtop solves both Energy and Water Balance.

2 y GEOtop model (Rigon et al., 2006) To assess the water-pressure field within soil thickness Ψ(x,t) y GEOtop solves both Energy and Water Balance. - 1D solution for the Energy Balance equation - 3D solution for the Mass Balance equation Every soil pixel is composed of a number of layer chosen by the user and the field equations are solved using the Finite Difference Method (FDM)

3 Two plane slopes converging to a central channel y Boundary Conditions On the sides AB, BC, CD, DE No flux through soil-bedrock interface q=0 y On the sides AF and EF q = Irain cosα or ψ = ψ top ψ top = surface water head

How Does GEOtop solve Richards Equation?

Equation is written in 1D form : C(ψ) θ t = z K ψ z (ψ) z cosα + S with z = normal

mass balance Lateral Flows are computed in explicit manner, using Darcy law: K( ψ 1 )

4 How Does GEOtop solve Richards Equation? In GEOtop vertical and lateral subsurface water flow are decoupling So, Richards Equation is written in 1D form : C(ψ) θ t = z K ψ z (ψ) z cosα + S with z = normal slope direction Sink Term It contains the effect of lateral flow and energy flux on mass balance Lateral Flows are computed in explicit manner, using Darcy law: K( ψ 1 ) ψ ψ i+1, j i, j Δx S = K( ψ 3 ) ψ i, j +1 ψ i, j Δy ( Δy Δz)+ + K( ψ 4 ) ψ i, j ψ i, j 1 ( Δx Δz) Δy + K( ψ 2 ) ψ i, j ψ i 1, j Δx /( Δx Δy Δz)

5 How Do we define the C(ψ) and K(ψ) functions? Using van Genuchten-Mualem Model VAN GENUCHTEN (1980) for the Hydraulic Capacity function ψ = 1 θ θ r β θ sat θ r 1 m 1 1 n θ θ sat θ r [ ] [ ] [ ] Actual volumetric water content Saturates volumetric water content Residual volumetric water content β[ L 1 ],m,n Shape parameters of the model, with m=1-1\n MUALEM (1976) for the Hydraulic Conductivity function θ θ K(ψ) = K r sat θ sat θ r θ θ r θ sat θ r 1 m m 2 K sat [ LT 1 Saturated Hydraulic ] conductivity

6 Mohr-Coulomb failure criterion extended to unsaturated conditions τ = c'+ [( σ u a )+ χ( ψ) ( u a u w )] tanφ' σ ( σ u a ) ( ) u a u w τ c' φ' FL 2 [ FL 2 ] total stress net stress matrix suction χ Parameter ranging between 0 and 1, depending on the degree of saturation [ FL 2 ] [ FL 2 ] [ FL 2 ] [ ] shear strengh effective cohesion effective angle of shear strengh χ valued according to Khalili & Kabbaz empirical relation (1998) u χ = a u w ( u a u w ) b 0.55 if ( u a u w ) b < ( u a u w ) b χ =1 if ( u a u w ) b ( u a u w ) b where: ( ) b FL 2 u a u w [ ] is the air-entry value matrix suction

7 y the Indefinite Slope Stability Model H << L tan φ ' (γ wψ ) (γ wψ b ) FS = + tan φ ' tan α γ h sin α cos α if ψ < ψ b γ wψ ) tan φ ' ( FS = + tan φ ' tan α γ h sinα cosα if ψ ψ b 0.45 assuming cohesionless soil (c =0) and ua=uatm ψ b [L] = 0.55 (ua uw )b γw Air-entry value suction head

8 The goal of the study is to investigate the role of some factors on the processes of pore-water pressure redistribution and, hence, on safety factor of the slope. Angle of the slope Soil Type Antecedent Soil Moisture Conditions Rainfall Intensity and Duration Different Values of these features are chosen as described below

9 y Angle of the slope STEEP SLOPE GENTLE SLOPE 9 Two cases analyzed: steep and gentle slope i. ii. STEEP SLOPE, when the angle of the slope is tan φ ' = 0.7 tan α1 GENTLE SLOPE, when the angle of the slope is smaller (or tan φ ' = 1.0 tan α 2 bigger than the frictional angle of the soil is the same) than the frictional angle of the soil

10 Physical, Mechanical and Hydraulic features Two cases analyzed: SANDY SOIL and SANDY-SILT SOIL SANDY SOIL S1 % sand = 80 % silt = 20 φ'= 35 o K sat =10 4 m /s COARSE-GRAINED SOIL SANDY-SILT SOIL S2 % sand = 40 % silt = 60 φ'= 30 o K sat =10 6 m /s FINE-GRAINED SOIL Through physical properties and soil texture it is possible to get the shape parameters of the van Genuchten model using Vereecken PTF (1989)

11 Tree different initial condition considered in the analysis: CI1 Wet Antecedent Condition CI2 Moderately Wet Antecedent Condition CI3 Dry Antecedent Condition Water Content Profile

(z) = ψ bottom + γ w (H z) Initial Water-pore

following values of initial safety factor of

20 for CI3 initial condition tan φ ' (γ wψ )

12 y Initial Soil Moisture Conditions are implemented by linear pore pressure profile ψ (z) = ψ bottom + γ w (H z) Initial Water-pore pressure profile Chosen so as to obtain the following values of initial safety factor of the slope: FS=1.05 for CI1 initial condition FS=1.10 for CI2 initial condition FS=1.20 for CI3 initial condition tan φ ' (γ wψ ) (γ wψ b ) + tan φ ' tan α γ h sinα cosα 0.45 FS = 0.7 if steep slope case 1.0 if gentle slope case (steep) 0.05 (gentle) for CI (steep) 0.10 (gentle) for CI (steep) 0.20 (gentle) for CI3

y Rainfall DATA by Paneveggio Station (in Alpine region)

l coordinate (Gauss-Boaga): Est 1711557 North 5132115

Rainfall Intensity (mm/h) Duration (h) tp1 24 2 tp2 10 6

13 y Rainfall DATA by Paneveggio Station (in Alpine region) elevation: 1760 m a.s.l coordinate (Gauss-Boaga): Est North Province of Trento (Italy) Return Time = 100 years Rainfall Intensity (mm/h) Duration (h) tp tp tp tp1 tp2 tp3 High Intensity Short Duration Medium Intensity Medium Duration Low Intensity Long Duration

14 CI1 WET ANTECEDENT CONDITION and tp1 SHORT RAINFALL DURATION 1. NEGLIGIBLE EFFECTS OF LATERAL-FLOW ON THE TRIGGERING CONDITIONS 2. HIGH INCREASE OF THE PRESSURE HEAD ON THE FIRST LAYER θ C(ψ ) = K z (ψ ) (ψ cosα ) + S z t z negligible effects of the lateral water flow on the reaching of the failure conditions Until failure time Ψfailure ψ (z,t) ψ (x,z,t) Amount of water needed to reach the failure tp1 VCI1 = I tp1 t tp1 failure = 24 *1.7 = 41 mm

Increase of pressure head at the first layer lower than the tp1 case Amount

15 CI1 WET ANTECEDENT CONDITION and tp3 LONG RAINFALL DURATION 1. Negligible effect of LATERAL-FLOW on the triggering conditions 2. Increase of pressure head at the first layer lower than the tp1 case Amount of water needed to reach the failure tp 3 CI1 V =I tp 3 t tp 3 failure = 7 * 2.9 = 20 mm <V tp1 CI1

16 Why these differences? Itp1>Itp3 qinf = I tp i ψ = K z (ψ ) cosα z Same initial value of k(ψ), but Itp1>Itp3. So: ψ tp1 ψ tp 3 > z z VCI1tp3<VCI1tp1 Ψ(z) at the failure time ΔΨÎΔV ΔV tp1 tp3 Ψfailure

17 CI3 DRY ANTECEDENT CONDITION and tp3 LONG RAINFALL DURATION 1. NOT NEGLIGIBLE effect of LATERAL-FLOW on the triggering conditions PIEZOMETRIC LINE ψ ψ 0 ; 0 x z at the failure time ψ center ψ toe θ C(ψ ) = K z (ψ ) (ψ cosα ) + S z t z It needs to solve 3D Richards Equation ψ (z,t) ψ (x,z,t)

18 CI1(wet) vs CI3(dry) Suction profile Ψ(z) at the failure time tp1 short rainfall duration Center Ψ=855 mm Center Ψ=875 mm Ψcenter Ψbottom = 11 mm Ψcenter Ψbottom = 31 mm Toe Ψ=844 mm Toe Ψ=844 mm Dry Antecedent Soil Moisture Conditions amplify the role of lateral flow on instability conditions

19 CI1(wet) vs CI3(dry) Suction profile Ψ(z) at the failure time tp3 long rainfall duration Center Ψ=870 mm Center Ψ=930 mm Ψcenter Ψbottom = 26 mm Ψcenter Ψbottom = 86 mm Toe Ψ=844 mm Toe Ψ=844 mm Long Rainfall duration amplify the role of lateral flow on the instability conditions

20 1. Negligible effects of LATERAL-FLOW 2. Very High Increase of pressure head at the first layer ψ ψ =0 ; 0 x z Ψfailure At any time during the simulation ψ center ψ toe θ C(ψ ) = K z (ψ ) (ψ cosα ) + S z t z negligible effects of lateral water flow ψ (z,t) ψ (x,z,t)

21 IN CASE OF: 1. WET ANTECEDENT SOIL MOISTURE CONDITION (CI3) 2. SHORT RAINFALL DURATION (AND HIGH INTENSITY) (tp1) 3. FINE-GRAINED SOIL TYPE (S2) A. GENERALLY THE COLLAPSE DEPENDS ON VERTICAL PORE- WATER PRESSURE REDISTRIBUTION B. THESE FEATURES INCREASE THE POSSIBILITY OF SLOPE FAILURE IN THE UPPER LAYERS OF THE SOIL TICKNESS OTHERWISE: 1. DRY ANTECEDENT SOIL MOISTURE CONDITION (CI1) 2. LONG RAINFALL DURATION (AND HIGH INTENSITY) (tp1) 3. COARSE-GRAINED SOIL TYPE (S1) A. LATERAL FLOW PLAYS AN IMPORTANT ROLE ON THE SLOPE STABILITY CONDITIONS B. GENERALLY SLOPE FAILURE OCCOURS NEAR THE SOIL BEDROCK INTERFACE

22 Look at this slides at or

16 Rainfall on a Slope

Rainfall on a Slope 16-1 16 Rainfall on a Slope 16.1 Problem Statement In this example, the stability of a generic slope is analyzed for two successive rainfall events of increasing intensity and decreasing