Seepage Modeling with SEEP/W - GeoStudio 2007 version 7.22

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Table of Contents SEEP/W 11.4 Drain flux values 161 11.5 Unit flux versus total flux? 162 11.6 Flow above phreatic line 163 11.7 Pressure boundary with depth 164 11.8 Summing graphed data 165 12 Illustrative Examples ....................................................................... 169 13 Theory ............................................................................................. 171 13.1 Darcy’s law 171 13.2 Partial differential water flow equations 171 13.3 Finite element water flow equations 173 13.4 Temporal integration 174 13.5 Numerical integration 175 13.6 Hydraulic conductivity matrix 177 13.7 Mass matrix 178 13.8 Flux boundary vector 179 13.9 Density-dependent flow 182 14 Appendix A: Interpolating Functions ............................................... 185 14.1 Coordinate systems 185 14.2 Interpolating functions 187 Field variable model ................................................................................................. 187 Interpolation function derivatives .............................................................................. 188 References ............................................................................................... 191 Index 196 Page vi
SEEP/W Chapter 1: Introduction 1 Introduction The flow of water through soil is one of the fundamental processes in geotechnical and geoenvironmental engineering. In fact, there would little need for geotechnical engineering if water were not present in the soil. This is a nonsensical statement: if there were no water in the soil, there would be no way to sustain an ecosystem, no humans on earth and no need for geotechnical and geo-environmental engineering. However, the statement does highlight the importance of water in working with soil and rock. Flow quantity is a key parameter in quantifying seepage losses from a reservoir or indentifying a potential water supply for domestic or industrial use. Pore-pressures associated with groundwater flow are of particular concern in geotechnical engineering. The pore-water pressure, whether positive or negative, is an integral component of the stress state within the soil and consequently has a direct bearing on the shear strength and volume change behavior of soil. Research in the last few decades has highlighted the importance of moisture flow dynamics in unsaturated surficial soils as it relates to the design of soil covers. Historically, analyses of groundwater flow have focused on flow in saturated soils and flow problems were typically categorized as being confined or unconfined situations. Flow beneath a structure would be a confined flow problem, while flow through a homogeneous embankment would be an unconfined flow problem. Unconfined flow problems were often considered more difficult to analyze because the determination of the location of the phreatic surface (i.e., the transition from positive to negative pore water pressures) was integral to the analyses. The phreatic surface was considered an upper boundary and any flow that may have existed in the capillary zone above the phreatic line was ignored. It is no longer acceptable to simply ignore the movement of water in unsaturated soils above the phreatic surface. Not only does it ignore an important component of moisture flow in soils, but it greatly limits the types of problems that can be analyzed. It is central to the analysis of problems involving infiltration and moisture redistribution in the vadose zone. Transient flow problems such as the advance of a wetting front within an earth structure after rapid filling are typical examples of situations in which it is impossible to simulate field behavior without correctly considering the physics of flow through unsaturated soils. Fortunately, it is no longer necessary to ignore the unsaturated zone. With the help of this document and the associated software, flow through unsaturated soils can be incorporated into numerical models so that almost any kind of seepage problem can be analyzed. In general, all water flow is driven by energy gradients associated with the total head of water as represented by the components of pressure head (or pore water pressure) and elevation. The term seepage often is used to describe flow problems in which the dominant driving energy is gravity, such as a case in which seepage losses occur from a reservoir to a downstream exit point. In other situations such as consolidation, the primary driving energy may be associated with the creation of excess pore-water pressures as a result of external loading. However, both of these situations can all be described by a common set of mathematical equations describing the water movement. As a result, the formulation used to analyze seepage problems can also be used to analyze the dissipation of excess pore-water pressures resulting from changes in stress conditions. In the context of the discussions and examples in this document and in using the SEEP/W software, the term seepage is used to describe all movement of water through soil regardless of the creation or source of the driving energy or whether the flow is through saturated or unsaturated soils. Simulating the flow of water through soil with a numerical model can be very complex. Natural soil deposits are generally highly heterogeneous and non-isotropic. In addition, boundary conditions often change with time and cannot always be defined with certainty at the beginning of an analysis. In some Page 1
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Chapter 6: Analysis Types SEEP/W ON
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Chapter 6: Analysis Types SEEP/W Fi
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Chapter 7: Functions in GeoStudio S
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Chapter 8: Numerical Issues SEEP/W
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15 Chapter 9: Flow nets, seepage fo
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Chapter 9: Flow nets, seepage force
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Chapter 11: Modeling Tips and Trick
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Chapter 12: Illustrative Examples S
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Chapter 13: Theory SEEP/W k x k y Q
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Chapter 13: Theory SEEP/W L = a des
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Chapter 13: Theory SEEP/W Table 13-
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Chapter 13: Theory SEEP/W [ C] = wh
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Chapter 13: Theory SEEP/W { Q} = q
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Chapter 13: Theory SEEP/W Figure 13
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Chapter 13: Theory SEEP/W Page 184
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References SEEP/W Figure 14-1 Globa
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References SEEP/W In equation form,
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References SEEP/W Table 14-4 Interp
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References SEEP/W Burland J.B. 1996
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References SEEP/W Swanson, D. 1991.
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SEEP/W Index Adaptive time stepping
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SEEP/W Seepage faces ..............
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Seepage Modeling with SEEP/W - GeoStudio 2007 version 7.22

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