HM_002 Uniaxial Sedimentation using Pre-Existing Sediment
Contents
This example extends the uniaxial consolidation example HM_001 by considering overpressure build up and dissipation during the sedimentation of a 1000m column. The 1000m column is represented as pre-existing material and gravity is ramped up slowly over the equivalent deposition time. This is used to provide a base case solution and to introduce the modelling issues. The pre-existing sediment assumptions is not valid, however, as in reality the drainage path from the base of the model to the free surface gradually increases from zero to 1000m over the deposition time. In contrast, with the pre-existing sediment the drainage path is always ca. 1000m.
This example focuses on model set up and simulation of large-scale coupled problems.
The example documentation assumes that the user is familiar with mesh generation and single field geomechanical modelling functionality and the following examples should undertaken beforehand:
1Mech_001 Mechanical Analysis Introduction
2HM_001 Introduction to Hydro-Mechanical Analysis - Uniaxial Consolidation
Analytical equations for the development of overpressure in in a basin at constant sedimentation rate were developed by Gibson (1958) and further discussed in Gibson (1967) and Wangen (2010) amongst others. The solution assumes a shallow basin where the porosity reduction is negligible; i.e. the geometrical impact of compaction may be neglected. The key assumption of the model is that Porosity (φ) is a linear function of the vertical effective stress (σ'v); i.e.
Substitution in the mass conservation equation and solution for the special case of constant sedimentation rate and zero surface pore pressure then gives
Note that rearrangement of the expression for porosity gives
Wangen (2010, p.403) provides overpressure predictions for a particular set of material parameters comprising;
A solution, obtained by very approximate integration using a multi-point trapezoidal rule, is provided in Excel worksheet hm_002\Results\hm_002.xlsm\Analytical.
Overpressure at 1 Ma for three Different Permeability Values
Overpressure at the Base of the Column vs. Time for three Different Permeability Values References Gibson, R. E. 1958. The progress of consolidation in a clay layer increasing in thickness with time. Géotechnique, 8, 171–182. Gibson, R. E., England, G. L. & Hussey, M. J. L. 1967. The theory of one-dimensional consolidation of saturated clays. Géotechnique, 17, 261-273. Wangen, M. 2010. Physical Principles of Sedimentary Basin Analysis, Cambridge University Press.
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The objective is to simulate the sedimentation and consolidation of1000m of sediment over a period of 1.0 Ma. The complete sediment column exists in the initial configuration and gravity is ramped up over 1.0 Ma. The model is analysed in uniaxial strain conditions; i.e. the vertical sides of the model are constrained in the horizontal direction, and the base of the model is constrained in the vertical direction. Gravity is the only load type and the top surface of the model is prescribed zero pore pressure (pf); i.e. free drainage, resulting in a gradual dissipation of pore pressure in the model. A structured mesh of 40 linear quadrilateral (QPM4) elements is used.
Material Properties The material corresponds to "HM_002_elastic" in the "training.mdb" material database, The material parameters is chosen to match the parameters assumed the simulations presented by Wangen (2010, p.403). The primary mechanical properties for this material are:
The additional material parameters related to the porous flow field are:
Notes 1The simulation uses isotropic permeability. In general, however, soils exhibit transverse isotropic flow with the horizontal permeability often between 5 to 100 times larger than the vertical permeability. In this case orthotropic permeability may be defined via Permeability_x, Permeability_y and Permeability_z. Furthermore, permeability is dependent on the current porosity, so that in applications where significant compaction is used permeability is defined as a function of porosity. This may be either isotropic via Permeability_vs_porosity or orthotropic via Permeability_x_vs_porosity, Permeability_y_vs_porosity and Permeability_z_vs_porosity. 2The Biot constant (Biot_constant) defines the contribution of the pore pressure to the total stress via the effective stress relationship
The Biot constant may either be user defined (as in this case) or may be computed automatically via the relationship
3The material is specified as fully saturated ( Fluid_saturation = 1.0). 4The material is saturated with fluid number 1.
Fluid Properties The properties of the pore fluid must be specified. The principal parameters are:
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The initial data file for the project is: HM_002\Data\hm_002_Case1.dat. The basic data includes: 1A single group which is assigned the "hm_002_elastic" properties defined using Group_control_data and Group_data data structures. The Porous_flow_type = 4 i.e. a coupled geomechanical/porous flow. A structured mesh of 4-noded elements is used. 2Material properties (Material_data) for "hm_002_elastic" exported from material database training.mdb using the "Set data for geomechanical only" option. The material data is stored in hm_002_elastic.mat in the HM_002\Data directory. 3Fluid properties (Fluid_data) for water. 4Time scaling data (Time_scaling_data) with target time step 1E-5 Ma; i.e. ca. 100,000 steps for the sedimentation time (see Mech_002). 5Global damping (Damping_global_data) for the geomechanical field with 2% percentage damping (see Mech_002). 6One global load case corresponding to zero pore pressure on the surface of the model (line 3). 7Support data (Support_data) defining: (a) Geomechanical field: line 1 fixed vertically and lines 2 and 4 fixed horizontally. (b) Porous flow field: Line 3 is defined as prescribed. 8Point history (History_point) data: (a) Set 1: Output of stress and pore pressure at the base of the column (b) Set 2: Output of pore pressure at 21 points evenly distributed throughout the depth of the column. 9Mesh control (Mesh_control) and Structured mesh generation data (Unstructured_mesh_data) defining a uniform mesh with 40 elements. 10 Couple control (Couple_control_data) and control data (Control_data) (see later).
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The Group_control_data structure defines the active groups in each field. Generally all groups are active in all fields.
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The Couple_control_data data structure defines the active fields for the analysis and additional data to control the coupling process. The data structure is only required if more than one field is active. The majority of the data may be assigned default values. For coupled hydro-mechanical simulations the default coupling scheme is: 1Fixed Stress algorithm 2Incremental staggered solution strategy 3Data exported from porous flow field: pore pressure and saturation 4Data exported from geomechanical field: Coordinates, porosity
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Coupling of the geomechanical and porous flow fields is achieved by treating the geomechanical field as an incremental analysis with the time step length corresponding to the time step of the porous flow field; i.e. 1A single porous flow step is performed in each time step for the coupled problem. 2The geomechanical field is solved using an "Incremental" control option where multiple time steps (iterations) are performed in each increment to achieve the explicit solution (dynamic relaxation) of the geomechanical field. This is necessary as the geomechanical and porous flow fields are "strongly coupled" due to the dependence of pore pressure on the volumetric strain rate.
The data controlling the solution strategy is specified via the Control_data (Geomechanical field) and Porous_flow_control_data (porous flow field) data structures. Often the data for the porous flow field can be set using the default values so that only the Control_data data structures is specified.
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The result files for the project are in directory: HM_002\results and the high definition history files can be displayed in excel file hm_002.xlsx. The evolution of pore pressure and effective stress are shown below. The predicted maximum overpressure at the base of the column is ca. 1.35 MPa which is close to the analytical prediction.
Pore Pressure Evolution at the Base of the Column as a Function of Time
Effective Vertical Stress and Pore Pressure as a Function of Time Depth and Time
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