Appendix I: SP3D example ...................................................................................... 15
Appendix II: Tips for embankment dam studies........................................................ 20
This manual is produced as part of the CEATI Dam Safety Interest Group Project “Investigation of Geophysical Methods for Assessing Seepage and Internal Erosion in
Embankment Dams”, Project number T992700-0205, Initiative “Development of Self-Potential and Electrical Resistivity Methods for Investigation of Embankment Dam Conditions”
Sub-task “SP Modelling and Interpretation”, Sub-task #SP3.
~ UBC-Geophysical Inversion Facility,
Department of Earth and Ocean Sciences, University of British Columbia,
6339 Stores Road, Vancouver, BC, V6T 1Z4.
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SP3D MANUAL July 5, 2005
Introduction SP3D is a flexible forward modelling program for calculating the self-potential distribution resulting from seepage flow through a 3D volume of earth (such as an earthfill dam) that is discretized using a mesh of rectangular cells. It is run in the MS Windows environment, using a graphical user interface (GUI) or alternately from the command line. The UBC-GIF utility MeshTools3D is used to examine resulting scalar or vector quantities throughout the model volume. A second UBC-GIF utility, SP-data-viewer, enables the comparison of contour maps and line plots of data calculated by SP3D (predicted data) and field measurements (observed data). This document provides details regarding the use of SP3D. A brief outline of background theory is presented, followed by an outline showing the essential procedure involved in using this program. Finally, a short section outlines some suggestions for viewing calculated results, and a case example is included as an appendix. The bulk of this manual provides details on file structures and parameters for controlling the calculations. Other related documentation includes: • Theoretical papers published in the scientific literature (see “References” at the end of the document); • A manual in HTML format for the UBC-GIF 3D viewer and model builder called MeshTools3D (see
the UBC-GIF website at http://www.eos.ubc.ca/research/ubcgif/software/documentation.htm for the latest version of this utility and it’s documentation);
• A short instructions sheet for the UBC-GIF data viewer called SP-data-viewer. SP3D requires several input files that describe mesh discretization and hydraulic conditions within the 3D volume. The required format of these files matches that of output files generated from the software Visual MODFLOW™. General notes on the use of Visual MODFLOW™ for seepage analyses are outlined in this document, with a focus on how to generate the files required for use with SP3D. However, the user is directed to the documentation provided with Visual MODFLOW™ for a more thorough treatment of its application to seepage or groundwater flow studies. Background Coupled Flow Theory The self-potential response to seepage flow is governed by the electrokinetic phenomenon called streaming potential. The streaming potential phenomenon may be described using linear flow laws through the theory of coupled flow. Electrical current flow may arise from secondary gradients within a system in much the same way that Ohm’s law describes the flow of current in a conductive medium resulting from an applied voltage difference. Temperature, chemical or hydraulic gradients can induce current flow, and an electrical potential gradient may in turn induce the flow of heat, chemical compounds or fluid. Consequently, a generalized macroscopic flow law may be defined to describe flow in terms of both primary and secondary gradients jΦ∇ , where the cross-coupling coefficients, Lij, link these
secondary gradients to the primary flux term, iΓ , as shown in Equation 1 (De Groot,1951). ∑ Φ∇⋅−=Γ
jjiji L (1)
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Where thermal and chemical concentration gradients are considered negligible, two coupled flow equations emerge in application to the study of streaming potential: φ∇−∇−= ekhKq (2) φσ ∇−∇−=+= hLJJJ condconv (3) Equation 2 describes volumetric fluid flux, q [m/s] using Darcy’s law and an electro-osmotic fluid flow term, where K [m/s] is hydraulic conductivity, h [m] is hydraulic head, ke [m/s per V/m] is the coefficient of electro-osmotic permeability, and φ [V] is electrical potential. In the absence of external current sources, the hydraulic flow equation may be decoupled and seepage analysed directly using Darcy’s law in materials where K > 10-9 m/s (Mitchell, 1991), and particularly in application to embankment dams where large hydraulic gradients exist. The current density J [A/m2] described in Equation 3 consists of Jconv, which represents the convection or streaming current, and Jcond, which describes the flow of conduction current. Based on the convection current approach developed by Sill (1983), the streaming current, Jconv is described using L [A/m2], the streaming current cross-coupling conductivity. This cross-coupling term is a function of both a streaming potential coupling coefficient C, which is defined through laboratory-based permeameter measurements, and the bulk electrical conductivity of the medium, by the relation L = Cσ . The term Jcond is described using Ohm’s law where σ is electrical conductivity [S/m]. Because electrical charge is conserved, the divergence of total current density J in the domain must equal
the time rate of change of volumetric charge, ρe. That is 0=∂∂
+⋅∇t
J eρ . The total current density is
equal to the sum of the convection and conduction current densities. Therefore, an equation used to solve for electrical potentials can be written by taking the divergence of Equation 3, where ρe is the volumetric charge density [C/m3] and I is the current flow per unit volume [A/m3].
It
hL e −∂∂
=∇⋅∇−∇⋅∇−ρ
φσ )()( (4)
Under steady-state flow conditions and in the absence of external current sources within the domain, the right hand side of Equation 4 becomes zero. Regardless of the nature of the hydraulic flow regime, steady-state behaviour may be assumed in the analysis of electrical flow, based on the magnitude of hydraulic and electrical relaxation times (Wurmstich, 1995). The relations governing any analysis of the self-potential response to seepage are given in Equations 5 and 6. Both transient and steady-state forms of the hydraulic flow equation are given in Equation 5, where Q [m3/s.m3] is volumetric flow, and SS [m-1] is specific storage.
QhKQthShK s =∇⋅∇−+∂∂
=∇⋅∇− )(;)( (5)
)()( hL∇⋅∇=∇⋅∇− φσ (6)
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Numerical Modelling Procedure For the quantitative study of the SP response to seepage in embankment dams, numerical methods must be applied to determine both the hydraulic and electrical flow regimes. The three-dimensional forward modelling procedure described here includes the application of Visual MODFLOW™ for a rigorous seepage analysis (Equation 5), followed by the application of SP3D using a cell-centred finite volume approach to find a solution to the electrical flow problem defined by Equation 6. The hydraulic head values in each grid cell resulting from the seepage analysis are converted to sources of streaming current, based on the cross-coupling conductivity structure of the subsurface. The calculated distribution of streaming current sources is subsequently used, along with a specified electrical resistivity structure and boundary conditions, to iteratively solve for the electrical potential distribution throughout the 3D domain. The solver is based upon a code developed for calculating electromagnetic fields in three dimensions. Details about the problem and its numerical solution are provided in Haber et al (2000). The resulting facility is a three-dimensional numerical tool that generates the SP response to seepage, requiring the user to specify grid geometry and a mesh spacing that define the hydraulic flow domain under study, hydraulic boundary conditions, and the distribution of the hydraulic and electrical properties K, L and σ , within the domain. General Procedure for Forward Modelling Self-Potential Fields using SP3D The following flow chart encapsulates SP3D processing flow from a user’s point of view.
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The remainder of this section outlines a 6-step procedure for modelling the self-potential response to seepage flow using the program SP3D. In the appendix this procedure is illustrated by working through each step for one example. {Note: in the following text and in the GUI programs, we interchangeably describe the electrical properties of the earth using electrical conductivity σ (S/m) and electrical resistivity ρ (Ohm-m)} 1. Define the problem. Delineate the area under study. The user must decide the physical extents of the model and what level of analysis to perform, i.e. whether to perform a localized study of hydraulic flow or to include the influence of regional flow in the analysis. The suitability of a steady-state versus transient seepage analysis, and a saturated versus variably flow approach must also be assessed on a case-by-case basis. For the electrical flow analysis in SP3D, a steady-state approach is always assumed, as discussed in the previous section detailing coupled flow theory. SP3D is capable of analysing output resulting from both saturated and unsaturated flow analyses. 2. Discretize the earth. Discretization of the model domain is performed entirely in the Visual MODFLOW™ environment.
a. Define the dimensions of the model domain. i. The user is prompted for domain dimensions and cell size upon creating a new project in Visual
MODFLOWTM, and a rectilinear grid is generated. b. Design the mesh.
All functions pertaining to grid design are located within the Input → Grid menu in Visual MODFLOWTM. i. Inactive cells within the rectilinear mesh may be used to delineate irregular topography, such as
the sloped surface of an embankment. Cells may be defined as inactive using the menu function Inactive Cells, which restricts them from any calculations performed within Visual MODFLOWTM. The discrete approximation of a stepped surface should not affect the final solution given an appropriate choice of cell size.
ii. Mesh discretization is controlled through the Edit menu function. The level of discretization is a
compromise between calculation speed, memory capacity and accuracy. Calculations are faster when fewer cells are used, yet higher accuracy requires a greater number of cells. For a given problem, the cell size should be large enough to represent the average physical properties used to characterize the material under study, but small enough to allow variations within a single soil or geologic unit to be represented effectively. Consequently, the use of non-uniform mesh spacing is preferred where large gradients are anticipated. A comparison of solutions resulting from a series of coarser grids will help to determine the maximum cell size appropriate for a given zone.
3. Construct the hydraulic model. The hydraulic model is defined within Visual MODFLOW™. The model property zones defined within MODFLOWTM are subsequently used in SP3D to delineate the distribution of electrical properties.
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a. Define model property zones.
All functions pertaining to the assignment of hydraulic properties in the model are located within the Input → Properties menu in Visual MODFLOWTM. i. Each soil/geologic unit or material to be represented in the model should be defined as a unique
conductivity zone. The user delineates zones manually using the Assign menu function within the Input → Properties → Conductivity menu in Visual MODFLOWTM. Cells within each zone are assigned a number, and each zone is characterized by a given hydraulic conductivity value, which may be defined as isotropic or anisotropic. The hydraulic conductivity of each zone may be subsequently displayed and edited using the Database menu function. The use of hydraulic conductivity zones to define specific units within the model is critical, as this zone information is used by SP3D to assign electrical properties to each soil/geologic unit.
ii. For transient hydraulic analyses only: Storage properties (specific storage, specific yield,
effective and total porosity) must be defined for all cells in the model using the Assign menu function in the Input → Properties → Storage menu. The user may delineate separate zones that define these parameters. This zonal information is not used by SP3D. N.B. Upon creating a new project, the user is prompted for default property values, which include hydraulic conductivity, specific storage, specific yield, effective and total porosity. These values characterize zone #1 and are initially assigned to every grid cell. Although hydraulic conductivity is the only property of interest in steady-state seepage analyses, Visual MODFLOWTM may require the user to enter default values for all parameters before proceeding.
b. Define hydraulic boundary conditions.
All functions pertaining to the assignment of boundary conditions are located within the Input → Boundaries menu in Visual MODFLOWTM. i. Boundary conditions are assigned by the user on a cell-by-cell basis in the Visual MODFLOWTM
environment. ii. The choice of hydraulic boundary conditions is problem-specific, and may consist of specified
flux, specified head, or mixed boundary types. In unconfined flow problems, such as the study of embankment dams, useful boundary types include:
• No-flow boundary: default condition at limits of MODFLOW mesh. • Constant head: used to define head imposed by upstream reservoir and/or tailwater • Specified head and flux (“Drain” boundary in MODFLOWTM): used to simulate a
seepage face 4. Run Visual MODFLOWTM. The selection of the numeric engine used in the hydraulic flow analysis is performed through the Setup menu in Visual MODFLOWTM. All other functions pertaining to the forward modelling solution are located within the Run menu.
i. The user must select the numeric engine used to run the seepage analysis from within the Setup → Numeric Engines menu. The USGS MODFLOW numeric engine permits saturated flow analyses only, and is the primary option in stand-alone versions of Visual MODFLOWTM.
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Solutions generated using this approach give predicted hydraulic head values in cells at or below the phreatic surface. MODFLOW-SURFACT is an advanced module that may be used to perform variably saturated flow analyses from the Visual MODFLOWTM platform, and is a useful tool in solving difficult unconfined flow problems. Users of the MODFLOW-SURFACT numeric engine must specify additional parameters that define properties of the unsaturated zone above the phreatic surface, which are not discussed here. Solutions generated using MODFLOW-SURFACT give the predicted hydraulic head distribution throughout the domain. When running SP3D using the output from a MODFLOW-SURFACT analysis, the user may choose whether or not to include the head distribution above the phreatic surface in the calculation of streaming current sources.
ii. Parameters influencing the forward modelling solution, including analysis type, solver
parameters, initial head values, and recharge options, are controlled within the Run menu. The hydraulic flow analysis is initiated by selecting Run → Translate/Run.
iii. Visual MODFLOWTM files required by SP3D include *.vmg (grid) and *.vmp (parameter) files,
which are automatically output when running Visual MODFLOWTM. An output *.asc file that defines the hydraulic head in each grid cell must be created by the user. This file should be generated from the Output menu in Visual MODFLOWTM, when hydraulic head contours are displayed in the Output window. The user must select File → Export → “XYZ ASCII” using the preferred coordinate system, and must specify the *.asc file extension. {Note: the model may have to be viewed in layer mode in order to export valid head data.}
5. Construct and verify the electrical model. The electrical model is defined within SP3D, and six input files are required. Three files are generated from the Visual MODFLOWTM analysis (*.vmg, *.vmp, *.asc), and three files are specific to SP3D (sp3d.inp, zone file, receiver locations file). Complete descriptions of these files are included in the SP3D Input File Format section. SP3D may be run as a Windows-based program (SP3Dgui.exe) or directly from the command line (sp3d.exe). Usage of the Windows-hosted program SP3Dgui is outlined here. Instructions on running sp3d.exe are included in the section entitled Running SP3D from the Command Line.
a. Specify input files.
i. Note that file names and paths should not contain spaces. ii. Each input filename can be specified with a path that is absolute or relative to the working
directory so it does not matter where they reside on your computer. MODFLOW file names: Specify MODFLOW file names (*.vmg, *.vmp, *.asc) and the numeric engine used in the seepage analysis. If MODFLOW was used to perform the hydraulic analysis, hydraulic head values are only calculated below the phreatic surface, and SP3D considers all hydraulic head values above the phreatic surface to be zero. If MODFLOW-SURFACT was used to perform the hydraulic analysis, hydraulic head values are calculated for the unsaturated zone above the phreatic surface. The user may choose to include or discard these head values for the purposes of the electrical flow analysis in SP3D. If “SURFACT (sat)” is selected, a saturated-flow approach is used to calculate the streaming current source distribution in the model. If “SURFACT (unsat)” is
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chosen, all predicted head values are accepted and included in the SP3D forward model.
Zone file: The user may create a new file by selecting Edit. The electrical properties for each model zone defined in Visual MODFLOWTM must be entered. These include saturated and unsaturated resistivity, and streaming current cross-coupling coefficient. {Note: the streaming current cross-coupling conductivity (L) should be entered as a positive quantity.} In embankment dam studies, the resistivity of the reservoir water and the elevation of upstream and downstream water levels must be specified. The water levels should coincide with Constant head boundaries specified in Visual MODFLOWTM and should be consistent with the height/elevation system used to define the z-axis, as defined in the *.asc file. Hydraulic conductivity is read in from the .vmp file and displayed for reference. The user can add an optional comment to help identify the zone. The padding resistivity must be specified by the user. This value is used to help define the electrical properties of the padded grid (see item b below). In embankment dam studies, the padding resistivity is often used to represent foundation material/bedrock. The position of the phreatic surface is used to assign saturated and unsaturated resistivity values within a given zone. When “SURFACT (sat)” or “SURFACT (unsat)” is selected as the numeric engine, the phreatic surface is defined using the condition: head = elevation (z). If a distinct zone is used to delineate surface water, the user should identify this zone number as it is also used to help identify unsaturated cells in the model. When all parameters are entered, use the “Save” button to create the zone file. Receiver locations file: The user must specify a 3 column file containing the reference electrode position (to which all electrical potential data predicted by the forward model are referenced) that also includes at least one coordinate defining an actual or simulated measurement electrode position. These data points are used to create the data_phi.txt output file; see input line E below.
b. Specify padding conditions.
In order to solve for the distribution of streaming potentials throughout the model, SP3D imposes an electrical no-flow boundary at the edges of the mesh. In order to prevent boundary effects from influencing the solution within the limits of the model, the extents of this original mesh must be expanded with the use of padding cells.
i. The user must specify the electrical resistivity structure of the padding cells, using one of four
options. The dimensions of the padded grid must also be specified (see descriptions for sp3d.inp Lines G and H in the SP3D Input File Format section).
c. Specify the solver parameters.
Solver parameters determine how the large system of equations is solved. They include preconditioner type and convergence criteria (see descriptions for sp3d.inp lines K and L in the SP3D Input File Format section). The default solver parameters should be sufficient for most applications. See Haber et al (2000).
d. Save input parameters.
Once the user has entered parameters for the required forward calculations, this run-specification must be saved by selecting File → Save. The details of this set of SP3D calculations will be saved in a file called sp3d.inp in the working directory. All output files created by SP3D will be stored
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in the same directory as sp3d.inp . e. Verify model.
Once the sp3d.inp file is created, the “verify” button in the GUI should become active. This feature may also be selected using Forward model → Verify. The user should verify each component of the model using MeshTools3D to ensure that the model parameters are correct before proceeding. This would include items such as the delineation of the upstream reservoir in embankment studies, and the distribution of physical properties. The following output files are generated using the Verify function: mesh.txt, mesh_padd.txt, sigma.txt, sigma_padd.txt, Kx.txt, head.txt, L.txt, I_src.txt, Jconv.fld, q.fld Verification is done by clicking the “model” button and looking at the above files using Meshtools3D.
6. Run SP3D.
i. Output files have well defined file names that you cannot adjust. See the section on SP3D Output Files below.
ii. Note that you can return to this set of calculations and investigate results or re-run individual runs
by opening SP3D’s GUI and selecting File → Open to open the sp3d.inp file that was created when the specification set was saved.
iii. When calculations are complete click the “log” button to see the log file for each run. This log
file should be checked to ensure that the specified tolerance was attained within a reasonable number of iterations. The majority of the log file contains a listing of parameters used for this calculation, and it is useful for reminding one of just how that outcome was obtained when results are examined at a later date.
7. View results. View SP forward calculation results using MeshTools3D by selecting View → model. View a 2-D contour plot of the predicted data set (data_phi.txt) by selecting View → data. The section entitled Viewing SP3D Results provides further details on viewing output files, and comparing predicted and observed data. Running SP3D from the Command Line The following instructions outline the use of SP3D as a command line program. The three input files (sp3d.inp, zone file, receiver locations file) must be created according to the formats specified in the SP3D Input File Format section below. SP3D may be run from a command prompt in the working directory by typing SP3D VERIFY to generate model files that allow the user to verify the input parameters using MeshTools 3D before solving the system. Once the user is satisfied with the model parameters, the command SP3D runs the forward model.
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SP3D Input File Format The operation of SP3D is controlled by a series of parameters that are provided to the program via an input file that must be called sp3d.inp. In order to understand what SP3D is doing and how results are generated it is necessary to understand the meaning of each parameter. When running SP3D using the Windows-hosted GUI, this input file is generated automatically for each run. When running SP3D from the command line, the input file must be created according to the format specified below. Note that file names and paths should not contain spaces. Also note that TABS should not be used in any UBC-GIF input or output files, so you must replace TAB characters with SPACES if files are made or modified in a spreadsheet. The input file is a text file with 13 lines containing parameters as follows (the “|” symbol means “or”). Each line is described in detail below. A) grid .vmg file B) property .vmp file C) hydraulic head .asc file D) zone file E) receiver locations file F) NONE G) padding type (1 - 4) H) pad_length_x pad_length_y pad_length_z I) expansion rate J) SURFACT_SAT | SURFACT_UNSAT | MODFLOW K) droptol tol iter L) preconditioner: 0= SSOR, 1= ILU M) ADV_OUTPUT Input File Line A: grid: *.vmg file Automatic output file from Modflow containing the dimensions of each cell in the grid (mesh), and which cells are active and inactive. Input File Line B: properties: *.vmp file Automatic output file from Modflow containing the number of user-defined soil/geologic zones and which cell corresponds to which zone. The assigned hydraulic conductivity for each zone is also defined in this file. Input File Line C: hydraulic head: *.asc file User-generated output file from Visual MODFLOWTM containing calculated hydraulic head values for each cell. Note that MODFLOW assigns inactive cells a dummy head value of 1.0e+30, and unsaturated cells (if a saturated flow approach is used) head values of -1.e+30 or 888.88. Input File Line D: zone file: (e.g. zonepar.txt) A file that specifies the electrical properties of each model zone, and lists parameters that define upstream/downstream water levels, water properties, and the electrical resistivity of padding cells.
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For each zone as defined in Visual MODFLOWTM, the following 3 values are entered per line (separated by spaces):
Saturated electrical resistivity [Ohm.m] Unsaturated electrical resistivity [Ohm.m] Streaming current coupling coefficient [A/m2] (Note: positive value must be entered)
After the zone information, the following values are included on separate lines:
Resistivity of water [Ohm.m] Padding resistivity [Ohm.m] (used to simulate foundation or host material) Upstream reservoir level [metres] Downstream surface water level [metres] Upstream base level [metres] (default = 0) Downstream base level [metres] (default = 0) Zone value that corresponds to water (OPTIONAL – if no individual zone is defined in Visual
MODFLOWTM to delineate surface water, the user may leave the line blank or enter zero). N.B.: The water levels should be consistent with the height/elevation coordinate system used to
define the z-axis, as defined in the SP3D input *.asc file. Input File Line E: receiver locations file: (e.g. recv.txt) A three column file listing the coordinates of all measurement points (actual or simulated) for which electrical potential (SP) data is required. The first line in the file specifies the coordinates of the reference electrode. All subsequent lines should contain measurement electrode coordinates according to the format shown below. Note that SP3D calculates potentials (phi) at the centers of all active cells in the 3D model. However, measurement points in the recv.txt file can be anywhere in the model. Measurements at specified points will be interpolated from potentials in the nearest cells. Xbase Ybase Zbase X1 Y1 Z1 : Xn Yn Zn If the Z value is less than -9999, the electrode is placed on the ground surface (uppermost active cell). All coordinates should follow the convention given by the *.asc file. Input File Line F: NONE Reserved for future use. Input File Line G: padding type (1 - 4) Used to specify the electrical resistivity values of the padding cells. Type 1 - Extend all model boundary properties to edges of padded grid. Type 2 - Assign padding resistivity (used to simulate foundation or host material) to all padding cells
below the model, and air to all padding cells above. Existing X and Y boundaries are extended
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to the edges of the padded grid. Type 3 - Assign padding resistivity to the bottom and air to the top padding cells. Padding cells along Y-
axis are set to padding resistivity (used to simulate canyon walls). Existing X boundaries are extended.
Type 4 - Air is assigned to the top padding cells. All other model boundaries are extended to the limits of
the padded grid. Input File Line H: pad_length_x pad_length_y pad_length_z Padding cells are added to all sides of the model. Each value is a multiple of the given model dimension. An x-value of n results in padding each side of the model in the x-dimension out to a distance equal to n times the model's original length. Input File Line I: expansion rate The size of each padding cell is the expansion rate times the size of the adjacent cell closest to the model. Input File Line J: SURFACT_SAT | SURFACT_UNSAT | MODFLOW The numeric engine used to perform the hydraulic flow analysis. The selection of MODFLOW indicates that a saturated flow approach was used in the hydraulic analysis, such that dummy hydraulic head values are assigned to cells above the phreatic surface. SP3D sets these head values to zero. When SURFACT_SAT is entered, the predicted hydraulic head values in the unsaturated zone are not used in the calculation of streaming current source terms. When SURFACT_UNSAT is entered, all head values resulting from the hydraulic flow analysis are used. Input File Line K: Parameters specifying convergence criteria: droptol - only used if ILU preconditioner is chosen. Sets the threshold for dropping small terms in
the factorization. tol - tolerance for convergence. iter - maximum number of iterations to perform. Input File Line L: A parameter specifying which preconditioner is to be used in the calculations. Enter 0 or 1 to specify which preconditioner to use as follows. The preconditioner is a component of the solver which converts the very large system of equations into a more efficient form. Details can be found in texts on linear algebra, and the solver used in SP3D is described in Haber et al (2000). 0 - SSOR 1 - ILU Input File Line M (optional - command line only): ADV_OUTPUT If ADV_OUTPUT is specified, the following additional output files are generated, each one based upon
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the mesh defined in the file mesh.txt. zone.txt : zone model div_Jcond.txt : Div * -sigma*Grad*phi model div_Jconv.txt : Div * -L*Grad*h model div_Jtotal.txt : Div*J = Div*(-sigma*G*phi - L*G*h) Jtotal.fld : -sigma*G*phi - L*G*h field SP3D Output Files Mesh model and vector field files are in a format that can be loaded into MeshTools3D. Models based on the padded mesh may be viewed in terms of the model mesh by removing the padded cells within MeshTools3D (refer to MeshTools3D manual). The output file data_phi.txt may be viewed in MeshTools3D as a draped contour plot, or in SP-data-viewer as a 2-D contour plot. Single column output files with extension *.txt store one number corresponding to each cell in the grid. These files list values starting from the top southwest corner of the grid in the order of Z (elevation) decreasing, X (easting) increasing, Y (northing) increasing. The following output files are produced from SP3D: mesh.txt : Mesh before padding. mesh_padd.txt : Mesh after padding.
These files define the 3D mesh used by SP3D. They have the following format: nx ny nz x0 y0 z0 dx_1 dx_2 ... dx_nx dy_1 dy_2 ... dy_ny dz_1 dz_2 ... dz_nz Parameters are defined as follows: nx, ny, nz - number of cells in the X, Y, and Z directions. x0, y0, z0 - coordinates of the top south west corner of the mesh: dx, dy, dz - cell widths. An example of mesh files is given in the Appendix I showing the embankment example.
sigma.txt : Conductivity model {based on mesh.txt}. sigma_padd.txt : Padded conductivity model {based on mesh_padd.txt}.
These files contain the electrical conductivity for all cells in the model. The first number is the value of the top south-western cell. The values are ordered such that Z (depth) changes the fastest, followed by X (easting), followed by Y (northing). Although electrical resistivity values are input to define each zone of the model, the electrical conductivity structure of the model is listed in the output file. These values may be toggled to be displayed as resistivity within MeshTools3D. Air cells are assigned an electrical conductivity value
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of 1e-8 S/m. For improved visual representation of topography in MeshTools3D, these cells may be ignored.
head.txt : Hydraulic head model {based on mesh.txt}. Kx.txt : Hydraulic conductivity (Kx) model {based on mesh.txt}.
Inactive cells are assigned hydraulic conductivity values in Visual MODFLOW, even though they are not included in the calculation of hydraulic flow. Consequently, SP3D assigns a dummy hydraulic conductivity of 1e-30 m/s to all inactive cells to improve the visual representation of this parameter in MeshTools3D.
L.txt : Streaming current cross-coupling coefficient {based on mesh.txt}.
Air cells are assigned a null cross-coupling coefficient value of 1e-12 A/m2. When MODFLOW or SURFACT (sat) are selected for numeric engine, all cells above the phreatic surface are assigned a cross-coupling coefficient value of 1e-12 A/m2. For improved visual representation of surface topography and/or topography of the phreatic surface in MeshTools3D, these cells may be ignored.
I_src.txt : Streaming current source model Div*-L*Grad*h {based on mesh_padd.txt}.
In a steady-state electrical flow analysis, the streaming current source terms are equal in magnitude and opposite in sign to the conduction current source terms.
phi.txt : Electrical potential model (in Volts) {based on mesh_padd.txt}. q.fld : Fluid flux vector field (in m/s) -k*Grad*h {based on mesh.txt} Jconv.fld : Streaming current vector field (in A/m2) -L*Grad*h {based on mesh.txt} Jcond.fld : Conduction current vector field (in A/m2) -sigma*Grad*phi {based on mesh.txt}
When vector fields are displayed in MeshTools3D, the colour bar displays the log10 (amplitude). The three columns of the *.fld files list the x, y and z components of the vector field.
data_phi.txt : Four column file: [x y z phi (in mV)] of SP corresponding to coordinates
specified in receiver locations file. sp3d.log : Log file (always generated). Viewing SP3D Results When SP3D finishes its forward modelling calculations, 14 output files are created. When the ADV_OUTPUT option is selected via the command line, an additional 5 files are generated. All 3D models used for the calculations, and 3D results of the calculations, can be viewed from the graphical user interface by clicking the “model” button on the tool bar (or using the View menu). A selection of the available models will be presented, and the user can select one or two models to view. Upon selection, these models will be displayed in the UBC-GIF utility, MeshTools3D, which can display one or two models of scalar or vector parameters. Also a corresponding data set can be draped over the model if one is available. There is a separate manual for this utility.
UBC-GIF, Earth and Ocean Sciences, SP3D manual, July, 2005.
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Alternatively, the forward modelled measurements (predicted data) can be viewed by clicking the data button on the tool bar (or using the View menu). This will pop up the UBC-GIF utility called “sp-data-viewer” with a contour map of the predicted measurements that were specified by the receiver locations file (see Input File Line E). This viewer can also display a second data set, for example one that contains measurements from a field survey. Line profiles can be selected on either of these contour maps by clicking with the mouse, and line graphs of the selected profile from both contour maps will be displayed together for comparison. The UBC-GIF utility also has a short instruction page with details about using this tool. References De Groot, S.R. (1951), “Thermodynamics of Irreversible Processes ”, in Selected Topics in Modern Physics, Vol.3, J.de Boer, H.Brinkman and H.B.G.Casimir, ed. North Holland Publishing Company, Amsterdam. Haber, E., Ascher, U., Aruliah, D., and D.W. Oldenburg (2000), “Fast Simulation of 3D Electromagnetic Problems using Potentials”, J. Comput.Phys., 163, p.p.150–171. Mitchell, J. K. (1991), “Conduction Phenomena: From Theory to Geotechnical Practice, Geotechnique, 43(3), p.p. 299-340. Sheffer, M.R. (2002), “Response of the Self-Potential Method to Changing Seepage Conditions in Embankment Dams”. M.A.Sc. thesis, University of British Columbia. Sill, W.R. and T.J. Killpack (1982), “SPXCPL: Two-Dimensional Modeling Program of Self-Potential Effects from Cross-Coupled Fluid and Heat Flow -User’s Guide and Documentation for Version 1.0”, Earth Sciences Laboratory, University of Utah Research Institute, Salt Lake City. Report for U.S. Department of Energy, Division of Geothermal Energy. Sill, W.R. (1983), “Self-Potential Modeling from Primary Flows”, Geophysics, 48(1), p.p.76-86. Wilt, M.J. and D.K. Butler (1990), “Numerical Modeling of SP Anomalies: Documentation of Program SPPC and Applications ”, in Geotechnical Applications of the Self Potential (SP) Method , Report 4, Department of the Army, US Army Corps of Engineers, Technical Report REMR-GT-6. Wurmstich, B. (1995), “3-D Self-Consistent Modeling of Streaming Potential Responses: Theory and Feasibility of Applications in Earth Sciences”. Ph.D. thesis, Texas A&M University.
UBC-GIF, Earth and Ocean Sciences, SP3D manual, July, 2005.
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Appendix I: SP3D example Introduction
This example involves a field-scale zoned embankment situated in a bedrock valley. The image to the right shows how this embankment is modelled with a rectangular-celled mesh. The image shows the model of electrical conductivity (units of S/m) sliced through at 30m North. Move your mouse over to see the solid version.
In order to calcuate the self-potential anywhere within this 3D model, a detailed seven-step procedure is outlined in the SP3D manual. The steps are:
1. Define the problem 2. Discretize the earth 3. Construct the hydraulic model 4. Run Visual MODFLOWTM 5. Construct and verify the electrical model 6. Run SP3D 7. View Results
Steps 1 through 4 are carried out within the Visual MODFLOWTM environment. For this example, the zones employed for this model are shown in the image below, taken from the Visual MODFLOWTM program.
Input files for this scenario
Once the hydraulic parameters and behaviour have been determined, SP3D can be run. The following input files are required, and are specified in the SP3D Graphical User Interface (GUI). See the SP3D manual (SP3D Input File Format) for details about each file, and the parameters and formats of these files.
Input parameters file: sp3d.inp D:\gif\SP\case_example\emb.vmg ! grid .vmg file D:\gif\SP\case_example\emb.vmp ! property .vmp file D:\gif\SP\case_example\emb.asc ! hydraulic head .asc file D:\gif\SP\case_example\zonepar.txt ! zone file D:\gif\SP\case_example\recv.txt ! receiver locations file NONE ! 3 ! padding type 1 1 1 ! padding length factor (x,y,z) 1.3 ! padding expansion rate MODFLOW ! type of modflow input 0.01 1e-008 500 ! droptol tol iter 1 ! preconditioner: 0=SSOR, 1=ILU
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Zone parameters file: zonepar.txt 350 800 5e-005 ! zone 1 - shell: rho_sat (Ohm.m), rho_unsat (Ohm.m), L_sat (A/m^2) 125 300 1e-005 ! zone 2 - core: rho_sat (Ohm.m), rho_unsat (Ohm.m), L_sat (A/m^2) 300 700 2e-005 ! zone 3 - transition: rho_sat (Ohm.m), rho_unsat (Ohm.m), L_sat (A/m^2) 1000 1000 1e-005 ! zone 4 - bedrock: rho_sat (Ohm.m), rho_unsat (Ohm.m), L_sat (A/m^2) 100 ! resistivity of water 1000 ! impervious resistivity 85 ! upstream reservoir level 0 ! downstream surface water level 0 ! upstream base level 0 ! upstream base level
Receiver locations: recv.txt
This is a three-column file containing specific locations where SP is to be calculated. The first line in the file specifies the coordinates of the reference electrode. All subsequent lines contain measurement electrode coordinates. Note that SP3D calculates potentials (phi) at the centers of all active cells in the 3D model. However, measurement points in the recv.txt file can be anywhere in the model. Measurements at specified points will be interpolated from potentials in the nearest cells. See SP3D manual "Input File Formats", Line E, for details.
MODFLOW output files
These three files contain the grid, soil/geologic zones, and calculated hydraulic head values respectively: emb.vmp emb.vmg emb.asc
SP3D output files are:
mesh.txt, and mesh_padd.txt
These files define the 3D mesh used by SP3D. Their format is not self-explanatory, so refer to the SP3D manual (Output Files) for details. They are small text files so to view them, you may open them in a simple text editor such as the Windows NotePad.
The mesh.txt file describes the mesh used to define the model, and the mesh_padd.txt file defines the model after augmenting with padding zones necessary for maintain suitable boundary conditions for the calculations. See the SP3D manual, "General Procedure" section, part 5.b. "Specifying padding conditions", and Input File Format Lines G and H.
The following files are available for viewing in MeshTools3D as soon as the "Verify" action has been performed in SP3D (see SP3D manual, "General Procedure" section, part 5.b).
File name associated mesh file description units Kx.txt mesh.txt X-component of Hydraulic conductivity m/s L.txt mesh.txt cross coupling coefficient A/m^2 head.txt mesh.txt hydraulic head m I_src.txt mesh_padd.txt Streaming current source A/m^3 sigma.txt mesh.txt Electrical conductivity S/m sigma_pad.txt mesh_padd.txt Electrical conductivity, including padding zone. S/m Jconv.fld mesh.txt Convection portion of current density (vectors) A/m^2 q.fld mesh.txt Fluid flux m/s
UBC-GIF, Earth and Ocean Sciences, SP3D manual, July, 2005.
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Four of these models are shown in the following figures.
Kx.txt L.txt
head.txt sigma.txt
For comparison the padded version of the conductivity model (sigma_padd.txt) is shown below (as a mesh rather than with solid blocks):
The following files are available for viewing in MeshTools3D after SP3D has calculated all potentials.
File name associated mesh file description units phi.txt mesh_padd.txt Potentials in all model cells Volts Jcond.fld mesh.txt Conduction portion of current density (vectors) A/m^2
Several images of models and combinations of models are shown below.
UBC-GIF, Earth and Ocean Sciences, SP3D manual, July, 2005.
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sigma.txt (colour scale is different from sigma image above)
phi.txt ovelayed on top of sigma.txt
Jcond overlayed on top of hydraulic head
phi.txt
Jcond.fld
q.fld
Two other text files are produced when SP3D performs calculations, data_phi.txt and sp3d.log. Details follow:
data_phi.txt: contains measured potentials according to locations specified in the recv.txt file - see SP3D manual, Input Files line E. It is a four column file with locations (X, Y, Z) and potential referenced to the location in the first line of recv.txt. The image to the right shows the data plotted using the UBC-GIF SP-data-viewer, with one curving profile plotted as a line graph.
The next image shows this viewer comparing calculated data to field measurements (simulated, and based on data_phi.txt) in the left-hand contour plot. In this mode both profiles are plotted on the graph.
UBC-GIF, Earth and Ocean Sciences, SP3D manual, July, 2005.
pg. 19
sp3d.log: The log file containing details of this SP3Drun. For this example, the log file is as follows:
SP3D - Version 20030925 Developed by UBC-Geophysical Inversion Facility (C) Copyright 2003, The University of British Columbia All Rights Reserved SP3D started on: 9/25/2003 14:31:33 grid file: D:\gif\SP\case_example\emb.vmg property file: D:\gif\SP\case_example\emb.vmp hydraulic head file: D:\gif\SP\case_example\emb.asc zone file: D:\gif\SP\case_example\zonepar.txt receiver locations file: D:\gif\SP\case_example\recv.txt padding type: 3 padding length factor: 1.0 1.0 1.0 padding expansion rate: 1.30 numeric engine used in seepage analysis: MODFLOW parameters (droptol, tol, maxiter): 1.00E-02 1.00E-08 500 preconditioner: ilu reading zone file: D:\gif\SP\case_example\zonepar.txt zone number: 1 saturated resistivity: 3.500000E+02 unsaturated resistivity: 8.000000E+02 cross-coupling coefficient: 5.000000E-05 zone number: 2 saturated resistivity: 1.250000E+02 unsaturated resistivity: 3.000000E+02 cross-coupling coefficient: 1.000000E-05 zone number: 3 saturated resistivity: 3.000000E+02 unsaturated resistivity: 7.000000E+02 cross-coupling coefficient: 2.000000E-05 zone number: 4 saturated resistivity: 1.000000E+03 unsaturated resistivity: 1.000000E+03 cross-coupling coefficient: 1.000000E-05 resistivity of water: 1.000000E+02 padding resistivity: 1.000000E+03 upstream water level: 8.500000E+01 downstream water level: 0.000000E+00 size of original mesh: 70 x 10 x 20 = 14000 size of expanded mesh: 92 x 20 x 34 = 62560 setup cpu time: 0:00:02.89 Solving system ..... norm: 2.9645E-09 number of iterations: 66 TOTAL cpu time: 0:00:16.43 SP3D ended on: 9/25/2003 14:31:51
Finally, there is a file called data_phi2.txt provided with the example. This was created to simulate a field data set. It was not produced by SP3D. You can change this file with a text editor or spreadsheet to more closely resemble a likely field survey data set. Don’t forget to replace TAB characters with spaces if you make files for UBC-GIF codes using a spreadsheet.
UBC-GIF, Earth and Ocean Sciences, SP3D manual, July, 2005.
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Appendix II: Tips for embankment dam studies Visual MODFLOWTM environment
• The convention is that the upstream-downstream direction lies along the x-dimension of the model. The upstream end should be closest to the origin. If possible, the x-dimension should be collinear with the predominant upstream-downstream direction of flow through the embankment. An existing grid delineating X and Y coordinates for the site may be used as long as the predominant flow direction is east-west. Otherwise, the model should be designed such that the x-dimension is roughly coincident with the upstream-downstream direction.
• Drain cells are the most effective way to model a seepage face using MODFLOW. • In cases of complicated geometry where steep gradients exist, delineation of the reservoir as an
independent zone exhibiting a high hydraulic conductivity value may help to ensure convergence of the model.
• MODFLOW-SURFACT is used to solve difficult flow problems, or when a variably saturated
flow approach is desired. If the purpose for using SURFACT is solely to get model convergence, and a saturated flow approach is desired (or the user does not wish to include the unsaturated head values), the “SURFACT_SAT” option should be chosen to discard all head values above the phreatic surface for the purposes of the SP3D analysis.
• the user should be careful with the selection of Model coordinates versus World coordinates in
Visual MODFLOWTM when creating the *.asc file. The user should always output the coordinate system they wish to work with in SP3D.
