Contents Introduction Soil permeability 1D theory of Terzaghi FE implementation of consolidation Influence of constitutive model and parameters • Influence of compressibility of water • Influence of void ratio dependent permeability • Influence of constitutive model Example Embankment construction
Consolidation Dr Minna Karstunen U i University i off S Strathclyde h l d With help from Dennis Waterman, Marcelo Sanchez, Antonio Gens & Helmut Schweiger Contents Introduction Soil permeability 1D theory of Terzaghi FE implementation of consolidation Influence of constitutive model and parameters • Influence of compressibility p y of water • Influence of void ratio dependent permeability • Influence of constitutive model Example - Embankment construction Types of Analyses for Geotechnical Problems D i d Drained Undrained Loading/Construction/Excavation: very slow (in relation to the soil permeability) Loading/Construction/Excavation: very fast (in relation to the soil permeability) Intermediate cases: consolidation analysis Both mechanical and hydraulic (flow) problems interact More o e co complex p e co computations: putat o s coup coupled ed a analysis a ys s Example Excess pore water pressure Consolidation Initial state Undrained loading Consolidation Example 1973 1984 Ekofisk tank Other Examples Construction at intermediate rates Change of hydraulic conditions Consolidation v Changes in total Changes in pore water + Changes in effective = pressure u stress ’v stress v u ’v v time v ’v v u time time time settlement Transient flow occurs in all saturated soils subjected to a change in external load or a change in boundary pore water pressures, but it is important to distinguish to main groups of soils: • Sands and gravels (with k > 10-4 m/s): the process is usually very rapid Consolidation is not relevant in these soils (generally) • Clays (and possibility silts and peats): due to its low permeability and high compressibility, consolidation is very relevant Basic theory of groundwater flow Darcy´s law h q k k i L h q k k dy dy p h y w q : flow h : total head y: vertical coordinate p : water pressure Permeability of Soils Dependence on grain (pore) size Soil k (cm/s) Clean gravel >1 Clean sand (coarse) - 10-2 Sand mixture 10-2 - 5x10-3 Fi sand Fine d 5x10 10-22 -10 10-33 Silty sand 2x10-3 -10-4 Silt 5x10-33 -10 10-55 10-6 and less Clay Harr (1962) Permeability often anisotropic q x k x x q y k y y Permeability of Soils Dependence on void ratio FE formulation of consolidation (3) Hydraulic (flow) problem: continuity equation Flow matrix Coupling matrix Water compressibility matrix FE formulation of consolidation (4) Global system of equations Step-by-step integration procedure < < ; Generally, fully implicit) FE formulation of consolidation (5) Time step Automatic time stepping is required C iti l ti Critical time step t C Consolidation lid ti analysis l i Prescribed time Maximum excess pore pressure Boundary Conditions Flow boundary conditions Prescribed groundwater head Cl Closed d fl flow b boundary d Closed consolidation boundaries Boundary Conditions Seepage surfaces Seepage surface Groundwater head = y Boundary Conditions Sources and sinks Infiltration Prescribed flow Prescribed head Drain line element Potts & Zdravkovic (1999) 1D Consolidation – Numerical Simulation applied load = 100 kPa soil layer 2D = 10 m drainage at top and bottom Investigate influence of: compressibility of pore water (by means of B-value) permeability depending on void ratio elastic-plastic soil behaviour (by means of changing constitutive model) 1D Consolidation – Numerical Simulation reference elastic pore w ater com pressible (B=0.85) perm eability e-dependent H ardening Soil m odel settle ement [mm] 20 40 60 80 100 0.01 0.1 10 tim e [days] 100 1000 1D Consolidation – Numerical Simulation ex xcess po ore press sure [kPa a] -100 -80 -60 -40 reference elastic pore w ater com pressible (B=0.85) perm eability e-dependent e dependent Hardening Soil m odel -20 0.01 0.1 10 tim e [days] 100 1000 1D Consolidation – Numerical Simulation Elastic Hardening Soil model distribution of excess pore pressures at 50% consolidation along centre line Example l – Embankment b k Construction C i influence of consolidation on stability influence fl off construction speed d is investigated d •"fast" construction: days of consolidation per placement of m embankment •"slow" construction: days of consolidation per placement of m layer embankment b k t Example – Embankment Construction influence of consolidation on stability "slow": max excess pore pressure: 86 kPa "fast": fast : max max excess pore pressure: 100 kPa Example – Embankment Construction influence of consolidation on stability "slow": stable "fast": fast : failure Example – Embankment Construction influence of consolidation on stability excess e cess po pore ep pressure essu e [ [kPa] a] excess pore pressure [kN/m2] -50 fast -40 -30 slow -20 -10 0 time [days] Time [day] 12 16 Example p – Embankment Construction influence of consolidation on stability Chart vertical displacements [m] Displacement [m] 0.06 Point C Point C fast 0.05 0.04 slow 0.03 0.02 0.01 0 30 60 Time [day] time [days] 90 120 ... Intermediate cases: consolidation analysis Both mechanical and hydraulic (flow) problems interact More o e co complex p e co computations: putat o s coup coupled ed a analysis a ys s Example... pressure Consolidation Initial state Undrained loading Consolidation Example 1973 1984 Ekofisk tank Other Examples Construction at intermediate rates Change of hydraulic conditions Consolidation. .. fully implicit) FE formulation of consolidation (5) Time step Automatic time stepping is required C iti l ti Critical time step t C Consolidation lid ti analysis l i Prescribed time