Effects of the slope toe evolution on the behaviour of a slow-moving large landslide

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Corominas MOUNTAIN RISKS - Topic Meeting WB1 Dynamic

1 Effects of the slope toe evolution on the behaviour of a slow-moving large landslide A. Ferrari, A. Ledesma, J. Corominas MOUNTAIN RISKS - Topic Meeting WB1 Dynamic spatial modelling of landslide hazards 11-1/11 9, CNR Padova, Padova, Italy

2 Introduction Ability to predict evolution over time for slow-moving landslides is a crucial requirement in the hazard management process Variation of pore water pressure within the slope is frequently recognized as the main cause for accelerations to occur and quantitative relationships among groundwater level and landslide velocity are pursued Several problems arise in predicting the mobility of slow-moving landslides, when viscous models are used (Van Asch et al. 7): o hysteresis in the relationship between movements and groundwater fluctuations o the validity of laboratory tests on soil viscosity for the prediction of landslide velocities in the field These issues are here discussed for the analysis of the movements of the Vallcebre landslide

3 Landslide velocity vs GWL fluctuations Displacement rate versus piezometric level for Fosso San Martino landslide (Bertini et al. 1986). The relation between velocity and groundwater height in the La Valette landslide, for respectively two periods of rising and falling limbs of the groundwater level (Van Asch et al. 7).

4 Analytical solution for 1 Block (infinite slope) sliding on a plane with Newtonian viscosity When one block is considered, the motion equation reads: W sin( ) ( N U ) tan( ') c ' A A ds z dt W d s g dt W where W is the block weight, is the plane inclination, N is the plane reaction component perpendicular to the plane, U is the resultant force of pore water distribution on the block base, and c are the shearing resistance parameters, A is the block base area, is the Newtonian viscosity, z is the slip zone thickness, s is the displacement, t is the time and g the gravity acceleration. N T f U When the ground water level is assumed to be linearly variable in time, the equation can be conveniently written in a dimensionless form: s t hs T d S dt ds a e ft dt in which coefficients a, e and f are functions of the problem parameter values and of the initial and final ground water level position.

5 Displacement (mm) Velocity (mm/day) Velocity (mm/day) GWL depth (m) 1 Analytical solution for 1 Block sliding on a plane with Newtonian viscosity 3 d S dt ds a e ft dt E-6 E-6 3E-6 E-6 seconds h (m) 15.5 (º) 5 (º) 7.7 c (kpa) (kn.m-3) (kpa.s) 1.51E+7 z (m).31 w (kn.m-3) Time (day) GWL depth (m)

6 The Vallcebre landslide

7 95 m The Vallcebre landslide LLarg torrent Upper unit A' Intermediate unit 1 3m Lower unit A S scarp cracked house main direction of movements borehole tension crack pond Vallcebre torrent upslope dipping surface Corominas et al. 5

8 The Vallcebre landslide Vallcebre torrent Corominas et al. 5 The toe of the slope extends to the Vallcebre torrent. The landslide has been pushing the torrent toward the opposite bank, shifting its bed to the west for several meters. This caused the landslide toe to override the opposite slope and to assume a back tilted shape. As a consequence of the reached configuration landslide movements result in mass accumulation at the slope toe.

9 Slope toe evolution local slope failures toe erosion transport of blocks June 7 The toe of the landslide is being continuously eroded by the Vallcebre torrent. Local slope failures are observable in the front

10 Slope toe evolution October 8 3 December 8 The toe of the landslide is being continuously eroded by the Vallcebre torrent. Local slope failures are observable in the front

11 Velocity (mm/day) Displacement (mm) GWL depth (m) Analysis of displacement trends 6 8 Displacement at borehole S Nov-96 1-Jan-97 1-Mar-97 1-May-97 1-Jul-97 1-Sep-97 1-Nov-97 1-Jan-98 1-Mar-98 Time Continuous movements with acceleration phases mainly associated to pore water pressure increase

The sliding mass is assumed as composed of two rigid blocks sliding on two different planes: the toe mass (indicated as Block 1)

12 The Vallcebre landslide lower unit as a Blocks system In the proposed formulation only the lower unit of the landslide is considered. The sliding mass is assumed as composed of two rigid blocks sliding on two different planes: the toe mass (indicated as Block 1) on the back titled slope, and the landslide body (Block ) on the plane. The blocks are in contact through a separation boundary which is inclined of with respect to the horizontal plane. Different shearing resistance angles can be set for the three surfaces.

13 The Blocks model: safety factor The wedge method is applied to compute the safety factor. For the interaction force R, the mobilized shearing resistance angle is fixed using F (Seed and Sultan, 1967). U1 W1 W tan ' tan ' m F U e1 Rpar, U d1 R e d3 Rpar,1 Rper, a1 c R c1 T N1 T1 Rper,1 d U N Block 1 Block q U3 Q Block 1, Translation perpendicular to the (1) N R per,1 W cos U U cos( ) Block 1, Translation parallel to the plane () R par,1 T1 W1sin U sin( ) Block 1, Rotation (3) N1a1 R per c1 Ue1 W1b 1 U1d 1 Block 1, Failure criteria N tan ' FT () plane Block, Translation perpendicular to the plane N R W cos U U cos( ) (5) per, Block, Translation parallel to the plane R T Q W sin U U sin( ) (6) par, 3 Block, Rotation (7) Na R per c Ue Wb Ud U3d3 Qq Block, Failure criteria N tan ' FT (8)

14 Horizontal component of the interaction force (kn) Safety factor, F The Blocks model: safety factor Block ' Block F The safety factor is computed by the wedge method Inclination of the boundary ( ) Influence of the assumptions on the boundary

W1 The b1 Blocks model: motion b W T1 During motion, Rdisplacement compatibility is considered E R c1 e N1 W1 c a1 Block 1 T N a e1 U d1 Rpar,1 a1 U1 R Rper, c1 N1 T1 Rper,1 During movement all

15 W1 The b1 Blocks model: motion b W T1 During motion, Rdisplacement compatibility is considered E R c1 e N1 W1 c a1 Block 1 T N a e1 U d1 Rpar,1 a1 U1 R Rper, c1 N1 T1 Rper,1 During movement all available shearing resistance is mobilized Rpar, R c d s s1 U e U W N d3 T Block q U3 Q T1 N 1 tan ' 1, tan ' T N, R R tan( ' ) par per Block 1, Translation perpendicular to the plane (1) N R per,1 W cos U U cos( ) Block 1, Translation parallel to the plane ds d s () R par,1 T1 W1 sin U sin( ) l1 m1 z dt dt Block 1, Rotation (3) N1a1 R per c1 Ue1 W1b 1 U1d 1 Block 1, Failure criteria N tan ' T () 1 1 1

16 Numerical solution for Blocks motion START The differential equation for the Blocks case is in the form: ( a bs) d S e ds f lt dt dt TRUE t = t = t + t t > tfin? FALSE Update boundary conditions which does not have an analytical solution. Mass conservation An Eulerian integration scheme is adopted, in which the masses of the blocks are considered constant within each time step. W W ( s), W W ( s ) Must consider mass loose from the toe At the 1 end 1of the time step, mass values are updated according to the computed displacement increment. FALSE i = 1 i = i + 1 i nsteps? Solve for F TRUE W W s h W t 1 t t t 1 1 d e W W s h t 1 t t d TRUE velocity =? TRUE FALSE F 1? FALSE t Solve for motion W e is the eroded weight at the toe and h is the block height (normal to the plane Compute acceleration Update velocity Compute displacement Update block masses STOP

17 Displacement, s (mm) Velocity, v (mm/day) Safety factor, F The Blocks model Synthetic cases Evolution of the safety factor, velocity and displacement as a function of the viscosity of the material at the slip surface /z (kpa.s.m -1 ) 1.e6.5e6 5.e6 7.5e6 1.e e6 /z = 1.e6 kpa.s.m e e6 1.e /z (kpa.s.m -1 ) 1.e6.5e6 5.e6 7.5e6 1.e Time (day)

18 Displacement, Velocity, v (mm/day) s (mm) Velocity, v (mm/day) Velocity, Safety v factor, (mm/day) F Groundwater Safety depth, factor, d (m) F The Blocks model Synthetic cases Evolution of the safety factor, velocity and displacement as a consequence of the groundwater level fluctuation for two different values of viscosity /z (kpa.s.m -1 ).e6.e /z (kpa.s.m -1 ) /z (kpa.s.m -1 ).e6.e6.e7.e /z =.e6 kpa.s.m -1 /z =.e7 kpa.s.m Grounwater depth, d (m) Relationship between velocity and groundwater level depth for two different values of viscosity /z (kpa.s.m 35 /z (kpa.s.m -1 ) ) 3.e6.e6 3 5.e7.e Time (day) )/z 35 (kpa.s.m-1)

19 Displacement, s (mm) Velocity, v (mm/day) The Blocks model Synthetic cases Velocity and displacement evolution induced by a toe weight reduction of %. 8 6 % toe weight reduction in 1 day in 3 days in 6 days % toe weight reduction in 1 day in 3 days in 6 days Time (day)

20 Safety factor, F The Blocks model: application to the Vallcebre landslide l 1 (m) l (m) 5 h (m) 15.5 ( ) 13 ( ) 6.1 ( ) 8 sat,1 (kn.m -3 ) sat, (kn.m -3 ) (kn.m -3 ) 18 1 ( ) 7.8 ( ) 7.8 ( ) 3. z 1 (kpa.s.m -1 ) 7.9e7 z (kpa.s.m -1 ) 7.9e7 Geometry Laboratory testing Back analysis reference condition W 1 /W (%) GWL depth 6.6 m -8-8 W 1 /W 1 (%) 6. m 5.8 m 5. m 5. m.6 m Influence of the toe weight variations on the stability of the system

21 1-Nov-96 1-Dec-96 1-Jan-97 1-Feb-97 1-Mar-97 1-Apr-97 1-May-97 1-Jun-97 1-Jul-97 1-Aug-97 1-Sep-97 1-Oct-97 1-Nov-97 1-Dec-97 1-Jan-98 1-Feb-98 1-Mar-98 1-Apr-98 1-May-98 1-Jun-98 1-Jul-98 1-Aug-98 1-Sep-98 1-Oct-98 Displacement (mm) Velocity (mm/day) Safety factor, F The Blocks model: application to the Vallcebre landslide model model measured measured model Model response for the period January 1997 March 1998

22 z (kpa.s.m -1 ) RMSE (mm) The Blocks model: application to the Vallcebre landslide block blocks Values of / z and corresponding root mean squared error (RMSE) obtained from the best fitting of the measured displacements for several values of the block inclination ( )

23 Velocity (mm/day) The Blocks model: application to the Vallcebre landslide 1 1 model points linear fit Grounwater depth, d (m) Relationship between groundwater level depth and computed instantaneous velocity for the period 1/11/1996 9/1/1998.

24 GWL depth (m) Velocity (mm/day) Velocity (mm/day) Displacement (mm) GWL Simulations with the Blocks model no toe erosion toe erosion: 5%/year 6 1 Displacement at borehole toe erosion: S %/year initial relationship 6 initial relationship 6 initial relationship Grounwater depth, d (m) Grounwater depth, 1 d (m) Grounwater depth, d (m) 8 Simulation of the evolution of the relationship among the groundwater level depth and the instantaneous velocity caused by a synthetic groundwater level fluctuation repeated for years. Different erosion scenarios are considered Nov-96 1-Jan-97 1-Mar-97 1-May-97 1-Jul-97 1-Sep-97 1-N Displacement at borehole S Time

25 Conclusions A simplified mechanical model has been developed to analyse the effects of the slope toe evolution on the activity of slow moving landslides To take into account the toe wedge allows obtaining a satisfactory back analysis of acceleration phases with parameter values close to the ones obtained in laboratory testing (lower viscosity) The analysis of the Vallcebre landslide pointed out that to consider the toe wedge does not introduce hysteresis in the relationship between the GWL depth and the instantaneous velocity From the first simulations, it seems that the long term behaviour of the landslide would be affected by the mass accumulation at the toe

26 Thanks for your attention

29 v (mm/day) Simulations with the Blocks model Velocidad instantanea Promedio movil h promedio 1h GWL d (m)

4. Stability analyses

4. Stability analyses 4. CHAPTER 4 A slope is understood to be a portion of a natural hillside the original profile of which has been modified in a manner of relevance for its stability. A slide is considered to be a state