Slope Stability and Ultimate Limit State

Introduction The aim is to discuss the application of finite element method to slope stability analysis. The topics to be covered include: • Options for generation of pore pressures in PLAXIS, with special consideration of slope stability • Options for generation of in situ stresses in PLAXIS • Analysis of stability of slopes with numerical modellingPLAXIS

Slope Stability and Ultimate Limit State Applied Theory Prof Minna Karstunen Introduction The aim is to discuss the application of finite element method to slope stability analysis The topics to be covered include: • Options for generation of pore pressures in PLAXIS, with special consideration of slope stability • Options for generation of in situ stresses in PLAXIS • Analysis of stability of slopes with numerical modelling/PLAXIS Water Pressures Water Pressures (general) • Water pressures – External water pressures (loads on boundaries) – Internal water pressures (pore pressures) • Effective stress analysis – Total stress: From weight and external load – Pore pressure: p active = p steady + pexcess Water Pressures (general) • pexcess are only generated in clusters for which the type of material behaviour is specified as Undrained • Plastic calculation or consolidation • Time-dependent dissipation or generation in consolidation analysis (controlled by permeability parameters) • Input of unit weight of fluid is required (can model other fluids than water) Water Pressures (general) • ‘Steady-state’ pore pressures psteady – Represent stable hydraulic condition – Generated in the Water condition mode • ‘Steady-state’ pore pressures psteady A Generation from phreatic levels • Simple cases, not good for natural slopes B Generation by groundwater flow calculation • Steady state or transient (PlaxFlow) Water Pressure generation • General phreatic level – A series of points where the water pressure is zero can be specified – Pressures increase linearly with depth depending on γw – PLAXIS does not allow negative pore pressures above the phreatic level (all assumed zero) – this is conservative! Water Pressure Generation • General phreatic level – Crossings of phreatic level and existing geometry lines not introduce additional geometry points, so there is a danger that the external water pressures are not calculated accurately Water Pressure Generation • General phreatic level – Allows to define pressures throughout the model • To allow for discontinuous pore pressures can use Cluster phreatic levels – Pressure head – Interpolate from adjacent clusters or lines (good for modelling artesian conditions) – To generate boundary conditions for groundwater flow calculation Water Pressure Generation • Clusters that should have zero pore pressure can be defined as dry (Cluster dry option) • Better way to set pore pressures zero in structural materials, is to specify the material as Non-porous • Also possible to use user-defined pore pressures Plane strain model L Should generally be > 2L Use 15-noded elements Material Properties Parameter Name Material model Model Type of behaviour Type Soil unit weight above γunsat phreatic level Soil unit weight below γsat phreatic level Horizontal permeability kx Vertical permeability ky Young's modulus Eref Poisson's ratio ν Cohesion cref Friction angle ϕ Dilatancy angle ψ Clay MC Undrained 15 Peat MC Undrained Sand MC Drained 16 18 11 20 kN/m3 1⋅10-4 1⋅10-4 1000 0.33 2.0 24 0.0 2⋅10-3 1⋅10-3 350 0.35 5.0 20 0.0 1.0 1.0 3000 0.3 1.0 30 0.0 m/day m/day kN/m2 kN/m2 ° ° • Create three material sets • Assign data to appropriate clusters • Create mesh: medium coarseness Unit kN/m3 Initial conditions • Unit weight of water 10 kN/m3 • Water pressures hydrostatic: phreatic level through points (0.0;6.0) and 40.0;6.0) • Boundary conditions during consolidation (see instructions): – Left boundary closed due to symmetry – Right boundary also closed – Bottom boundary open (sand underneath) • Generate water pressures Initial conditions (continues) • Generate water pressures • Switch & deactivate the embankment • Generate initial stress: K0-procedure – Default values of K0=1-sinφ’ (Jaky’s formula) adopted • Input is now complete! Calculations Phases: – – – – 1st construction phase, days Consolidation 200 days 2nd construction phase, days Consolidation until excess pore pressures have dissipated (minimum pore pressure) Need calculation phases in total (see instructions) Select points for curves: A toe of embankment, B at centre of clay layer (to plot excess pore pressures) Output Displacement increments after undrained construction of embankment Output Excess pore pressures after undrained construction of embankment Output Excess pore pressure contours after consolidation to Pexcess < 1.0 kN/m2 Output: Curves Program Excess PP [kN/m2] -10 -20 Point B -30 -40 200 400 600 Time [day] Development of excess pore pressure in point B 800 Safety Analysis • Important to consider not just the final stability, but also the stability during construction • Global factor of safety immediately after 1st and 2nd stages of construction and long term using Phi-c –reduction calculations (see instructions) Safety Analysis: Output Shadings of the total displacement increments indicating the likely long-term failure mechanism Magnitude of strains not important! Safety Analysis: Output Sum-Msf Sum-Msf 1.4 long term safety factor 1.38 1.3 1.2 safety factor (1st construction stage) 1.13 1.1 safety factor (2nd construction stage) 1.06 1e3 2e3 |U| [m] IUI [m] 3e3 4e3 Updated Mesh Analysis (optional) • The embankment settles over 0.5m within years • Part of the fill will settle to be below the phreatic level and is therefore subject to buoyancy forces • This effect can be taken into account by using Updated mesh and Updated water pressure options (see instructions) Updated Mesh Analysis: Output |U| [m] 0.5 0.4 0.3 0.2 0.1 0 200 400 600 Time [day] Settlements of the embankment at centreline, updated mesh calculation compared with regular calculation 800 Updated Mesh Analysis: Output Displacement [m] 0.5 0.4 0.3 0.2 0.1 0 200 600 400 800 1000 Time [day] Settlements of the toe of the embankment, updated mesh calculation compared with regular calculation