ProductsAbaqus/StandardAbaqus/CAE Establishing geostatic equilibriumThe geostatic procedure is normally used as the first step of a geotechnical analysis; in such cases gravity loads are applied during this step. Ideally, the loads and initial stresses should exactly equilibrate and produce zero deformations. However, in complex problems it may be difficult to specify initial stresses and loads that equilibrate exactly. Abaqus/Standard provides two procedures for establishing the initial equilibrium. The first procedure is applicable to problems for which the initial stress state is known at least approximately. The second, enhanced, procedure is also applicable for cases in which the initial stresses are not known; it is supported for only a limited number of elements and materials. Establishing equilibrium when the initial stress state is approximately knownThe geostatic procedure requires that the initial stresses are close to the equilibrium state; otherwise, the displacements corresponding to the equilibrium state might be large. Abaqus/Standard checks for equilibrium during the geostatic procedure and iterates, if needed, to obtain a stress state that equilibrates the prescribed boundary conditions and loads. This stress state, which is a modification of the stress field defined by the initial conditions (Initial conditions in Abaqus/Standard and Abaqus/Explicit), is then used as the initial stress field in a subsequent static or coupled pore fluid diffusion/stress (with or without heat transfer) analysis. If the stresses given as initial conditions are far from equilibrium under the geostatic loading and there is some nonlinearity in the problem definition, this iteration process may fail. Therefore, you should ensure that the initial stresses are reasonably close to equilibrium. If the deformations produced during the geostatic step are significant compared to the deformations caused by subsequent loading, the definition of the initial state should be reexamined. If heat transfer is modeled during the geostatic step through the use of coupled temperature–pore pressure elements, the initial temperature field and thermal loads, if specified, must be such that the system is relatively close to a state of thermal equilibrium. Steady-state heat transfer is assumed during a geostatic step. Input File Usage GEOSTATIC Abaqus/CAE Usage Step module: Create Step: General: Geostatic Establishing equilibrium when the initial stress state is unknownTo obtain equilibrium in cases when the initial stress state is unknown or is known only approximately, you can invoke an enhanced procedure. Abaqus automatically computes the equilibrium corresponding to the initial loads and the initial configuration, allowing only small displacements within user-specified tolerances. (The default tolerance is .) The procedure is available with a limited number of elements and materials and is intended to be used in analyses in which the material response is primarily elastic; that is, inelastic deformations are small. The procedure is supported for both geometrically linear and geometrically nonlinear analyses. However, in general, the performance in the geometrically linear case will be better. Therefore, it might be advantageous to obtain the initial equilibrium in a geometrically linear step, even though a geometrically nonlinear analysis is performed in subsequent steps. Input File Usage Use the following option to invoke the enhanced procedure: GEOSTATIC, UTOL=displacement tolerance Abaqus/CAE Usage Step module: Create Step: General: Geostatic: Incrementation tabbed page: Automatic: Max. displacement change LimitationsThe following limitations apply to the enhanced procedure:
Optional modeling of coupled heat transferWhen coupled temperature–pore pressure elements are used, heat transfer is modeled in these elements by default. However, you may optionally choose to switch off heat transfer within these elements during a geostatic step. This feature may be helpful in reducing computation time if temperature and associated heat flow effects are not important. Abaqus/CAE Usage Switching off the heat transfer part of the physics is not supported in Abaqus/CAE. Vertical equilibrium in a porous mediumMost geotechnical problems begin from a geostatic state, which is a steady-state equilibrium configuration of the undisturbed soil or rock body under geostatic loading. The equilibrium state usually includes both horizontal and vertical stress components. It is important to establish these initial conditions correctly so that the problem begins from an equilibrium state. Since such problems often involve fully or partially saturated flow, the initial void ratio of the porous medium, , the initial pore pressure, , and the initial effective stress must all be defined. If the magnitude and direction of the gravitational loading are defined by using the gravity distributed load type, a total, rather than excess, pore pressure solution is used (see Coupled pore fluid diffusion and stress analysis). This discussion is based on the total pore pressure formulation. The z-axis points vertically in this discussion, and atmospheric pressure is neglected. We assume that the pore fluid is in hydrostatic equilibrium during the geostatic procedure so that where is the user-defined specific weight of the pore fluid (see Permeability). (The pore fluid is not in hydrostatic equilibrium if there is significant steady-state flow of pore fluid through the porous medium: in that case a steady-state coupled pore fluid diffusion/stress analysis must be performed to establish the initial conditions for any subsequent transient calculations—see Coupled pore fluid diffusion and stress analysis.) If we also take to be independent of z (which is usually the case, since the fluid is almost incompressible), this equation can be integrated to define where is the height of the phreatic surface, at which and above which and the pore fluid is only partially saturated. We usually assume that there are no significant shear stresses , . Then, equilibrium in the vertical direction is where is the dry density of the porous solid material (the dry mass per unit volume), g is the gravitational acceleration, is the initial porosity of the material, and s is the saturation, (see Permeability). Since porosity is the ratio of pore volume to total volume and the void ratio is the ratio of pore volume to solids volume, is defined from the initial void ratio by Abaqus/Standard requires that the initial value of the effective stress, , be given as an initial condition (Initial conditions in Abaqus/Standard and Abaqus/Explicit). Effective stress is defined from the total stress, , by where is a unit matrix. Combining this definition with the equilibrium statement in the z-direction and hydrostatic equilibrium in the pore fluid gives again using the assumption that is independent of z. is the position of the surface that separates the dry soil from the partially saturated soil. The soil is assumed to be dry () for , and it is assumed to be partially saturated for and fully saturated for . In many cases s is constant. For example, in fully saturated flow everywhere below the phreatic surface. If we further assume that the initial porosity, , and the dry density of the porous medium, , are also constant, the above equation is readily integrated to give where is the position of the surface of the porous medium, . In more complicated cases where s, , and/or vary with height, the equation must be integrated in the vertical direction to define the initial values of . Horizontal equilibrium in a porous mediumIn many geotechnical applications there is also horizontal stress, typically caused by tectonic action. If the pore fluid is under hydrostatic equilibrium and , equilibrium in the horizontal directions requires that the horizontal components of effective stress do not vary with horizontal position: only, where is any horizontal component of effective stress. Initial conditionsThe initial effective geostatic stress field, , is given by defining initial stress conditions. Unless the enhanced procedure is used, the initial state of stress must be close to being in equilibrium with the applied loads and boundary conditions. See Initial conditions in Abaqus/Standard and Abaqus/Explicit. You can specify that the initial stresses vary only with elevation, as described in Initial conditions in Abaqus/Standard and Abaqus/Explicit. In this case the horizontal stress is typically assumed to be a fraction of the vertical stress: those fractions are defined in the x- and y-directions. In problems involving partially or fully saturated porous media, initial pore fluid pressures, , void ratios, , and saturation values, s, must be given (see Coupled pore fluid diffusion and stress analysis). In partially saturated cases the initial pore pressure and saturation values must lie on or between the absorption and exsorption curves (see Sorption). A partially saturated problem is illustrated in Wicking in a partially saturated porous medium. You may also specify initial temperatures in the model if heat transfer is modeled during the geostatic procedure. Boundary conditionsBoundary conditions can be applied to displacement degrees of freedom 1–6 and to pore pressure degree of freedom 8 (Boundary conditions in Abaqus/Standard and Abaqus/Explicit). If coupled temperature–pore pressure elements are used, boundary conditions on temperature degree of freedom 11 can also be applied to nodes belonging to these elements. If the enhanced procedure is used and nonzero boundary conditions are applied, it is the user's responsibility to ensure that the displacements corresponding to the tolerances specified are larger than the displacements in the analysis; otherwise, the displacements at the nonzero boundary nodes will be reset to zero with the tolerances specified. The boundary conditions should be in equilibrium with the initial stresses and applied loads. If the horizontal stress is nonzero, horizontal equilibrium must be maintained by fixing the boundary conditions on any nonhorizontal edges of the finite element model in the horizontal direction or by using infinite elements (Infinite elements). If heat transfer is modeled, the temperature boundary conditions should be in equilibrium with the initial temperature field and applied thermal loads. LoadsThe following loading types can be prescribed in a geostatic stress field procedure:
If heat transfer is modeled, the following types of thermal loading can also be prescribed (Thermal loads). These loads are not supported in Abaqus/CAE during a geostatic analysis.
Predefined fieldsThe following predefined fields can be specified in a geostatic stress field procedure, as described in Predefined Fields:
Material optionsAny of the mechanical constitutive models available in Abaqus/Standard can be used to model the porous solid material. However, the enhanced procedure can be used only with the elastic, porous elastic, extended Cam-clay plasticity, and Mohr-Coulomb plasticity models. Use of a nonsupported material model with this procedure may lead to poor convergence or no convergence if displacements are larger than the displacements corresponding to the tolerances specified. Abaqus will issue a warning message if the procedure is used with a nonsupported material model. If a porous medium will be analyzed subsequent to the geostatic procedure, pore fluid flow quantities such as permeability and sorption should be defined (see About pore fluid flow properties). If heat transfer is modeled, thermal properties such as conductivity, specific heat, and density should be defined for both the solid and the pore fluid phases (see Thermal properties if heat transfer is modeled for details on how to specify separate thermal properties for the two phases). ElementsAny of the stress/displacement elements in Abaqus/Standard can be used in a geostatic procedure. Continuum pore pressure elements can also be used for modeling fluid in a deforming porous medium. These elements have pore pressure degree of freedom 8 in addition to displacement degrees of freedom 1–3. However, the enhanced procedure can be used only with continuum and cohesive elements with pore pressure degrees of freedom and the corresponding stress/displacements elements. Use of nonsupported elements with this procedure may lead to poor convergence or no convergence if displacements are larger than the displacements corresponding to the tolerances specified. Abaqus will issue a warning message if the procedure is used with a nonsupported element. Continuum elements that couple temperature, pore pressure, and displacement can be used if heat transfer needs to be modeled. These elements have temperature degree of freedom 11 in addition to pore pressure degree of freedom 8 and displacement degrees of freedom 1–3. See Choosing the appropriate element for an analysis type for more information. OutputThe element output available for a coupled pore fluid diffusion/stress analysis includes the usual mechanical quantities such as (effective) stress; strain; energies; and the values of state, field, and user-defined variables. In addition, the following quantities associated with pore fluid flow are available:
If heat transfer is modeled, the following element output variables associated with heat transfer are also available:
The nodal output available includes the usual mechanical quantities such as displacements, reaction forces, and coordinates. In addition, the following quantities associated with pore fluid flow are available:
If heat transfer is modeled, the following nodal output variables associated with heat transfer are also available:
All of the output variable identifiers are outlined in Abaqus/Standard output variable identifiers. Input file templateHEADING … MATERIAL, NAME=mat1 Data lines to define mechanical properties of the solid material … DENSITY Data lines to define the density of the dry material PERMEABILITY, SPECIFIC= Data lines to define permeability, , as a function of the void ratio, e CONDUCTIVITY Data lines to define thermal conductivity of the solid grains if heat transfer is modeled CONDUCTIVITY,TYPE=ISO, PORE FLUID Data lines to define thermal conductivity of the permeating fluid if heat transfer is modeled SPECIFIC HEAT Data lines to define specific heat of the solid grains if transient heat transfer is modeled in a subsequent step SPECIFIC HEAT,PORE FLUID Data lines to define specific heat of the permeating fluid if transient heat transfer is modeled in a subsequent step DENSITY Data lines to define density of the solid grains if transient heat transfer is modeled in a subsequent step DENSITY,PORE FLUID Data lines to define density of the permeating fluid if transient heat transfer is modeled in a subsequent step LATENT HEAT Data lines to define latent heat of the solid grains if phase change due to temperature change is modeled LATENT HEAT,PORE FLUID Data lines to define latent heat of the permeating fluid if phase change due to temperature change is modeled … INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC Data lines to define the initial stress state INITIAL CONDITIONS, TYPE=PORE PRESSURE Data lines to define initial values of pore fluid pressures INITIAL CONDITIONS, TYPE=RATIO Data lines to define initial values of the void ratio INITIAL CONDITIONS, TYPE=SATURATION Data lines to define initial saturation INITIAL CONDITIONS, TYPE=TEMPERATURE Data lines to define initial temperature BOUNDARY Data lines to define zero-valued boundary conditions ** STEP GEOSTATIC CLOAD and/or DLOAD and/or DSLOAD Data lines to specify mechanical loading FLOW and/or SFLOW and/or DFLOW and/or DSFLOW Data lines to specify pore fluid flow CFLUX and/or DFLUX Data lines to define concentrated and/or distributed heat fluxes if heat transfer is modeled BOUNDARY Data lines to specify displacements or pore pressures END STEP |