Groundwater flow and Coupled analysis

Duc Bui

Groundwater flow and Coupled analysis

Duc Bui

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Abstract
AI

The research focuses on enhancing the PLAXIS software for effective simulation of groundwater flow and coupled flow-deformation analysis in both saturated and partially saturated soils. It presents a comprehensive approach by modifying the existing undrained analysis and incorporates the Barcelona Basic Model to address the mechanical behavior of unsaturated soils. The study includes detailed formulations of governing equations, verification of numerical methods, and emphasizes the need for a simultaneous solution of displacement and pore pressure in practical applications.

Figures (410)

Fig. 1.1: A visualisation of soil mechanics showing the role of the surface flux boundary conditions (Fredlund, 1996) (groundwater flow boundary conditions). In the areas where the upward flux (i.e. evaporation and evapotranspiration) exists, suction above phreatic level increases (and degree of saturation decreases) and the water level is lowered with time while in the case of downward flux (i.e. precipitation) suction decreases (and degree of saturation increases) and the water level rises with time. In the case of zero net surface flux, the pore water pressure profile become in equilibrium at a hydrostatic condition (Figure 1.1).

Fig. 5.1: Effect of the parameter g, on the retention curve, (g, = 2.0 and g, =-1.0)

Fig. 5.3: Effect of the parameter g, on the retention curve, (g, = 1.0 and g, = 2.0) The effective saturation is defined as:

Fig. 5.4: Mualem - Van Genuchten: head - degree of saturation

Fig. 5.7: Linearized V an Genuchten: head - relative permeability

Fig. A 1.4: Active pore pressure in time vs height in PLAXIS 3D

Fig. A1.3: Degree of saturation in time vs height in PLAXIS 2D

Fig. A1.7: Degree of saturation in time vs height (existing PlaxFlow)

Fig. A3.2: Active pore pressure in time vs height in PLAXIS 2D

Fig. A3.4: Active pore pressure in time vs height in PLAXIS 3D

Fig. A3.3: Degree of saturation in time vs height in PLAXIS 2D

Fig. A3.5: Degree of saturation in time vs height in PLAXIS 3L

Fig. A3.6: Active pore pressure in time vs height (existing PlaxFlow) Fig. A3.7: Degree of saturation in time vs height (existing PlaxFlow)

Fig. B1.4: Active pore pressure in time vs height in PLAXIS 3D

Fig. B1.2: Active pore pressure in time vs height in PLAXIS 2D

Fig. 1.7: Degree ot saturation in time vs height (existing Plaxrlow)

Fig. B3.2: Active pore pressure in time vs height in PLAXIS 2D

Fig. B3.5: Degree of saturation in time vs height in PLAXIS 3D

Fig. B3.4: Active pore pressure in time vs height in PLAXIS 3D

Fig. B3.5: Degree of saturation in time vs height (existing PlaxFlow)

Fig. B4.3: Active pore pressure in time vs height in PLAXIS 3D

Fig. B4.4: Active pore pressure in time vs height (existing PlaxFlow)

Fig. C 1.3: Degree of saturation in time vs height in PLAXIS 2D

Fig. C 1.4: Relative permeability in time vs height in PLAXIS 21

Fig. C 1.6: Degree of saturation in time vs height in PLAXIS 3D

Fig. C 1.7: Relative permeability in time vs height in PLAXIS 3D

Fig. C 1.8: Active pore pressure in time vs height (existing PlaxFlow)

Fig. C 1.9: Degree of saturation in time vs height (existing PlaxFlow)

Fig. C 2.3: Degree of saturation in time vs height in PLAXIS 2D

Fig. C 2.4: Relative permeability in time vs height in PLAXIS 2D

Fig. C 2.5: Active pore pressure in time vs height in PLAXIS 3D Fig. C 2.6: Degree of saturation in time vs height in PLAXIS 3D

Fig. C 2.7: Relative permeability in time vs height in PLAXIS 3D

Fig. U 2.y: Degree of saturation in ume vs height (exisung Plaxtlow)

Fig. C 3.3: Degree of saturation in time vs height in PLAXIS 2D Fig. C 3.4: Relative permeability in time vs height in PLAXIS 2D

Fig. C 3.6: Degree of saturation in time vs height in PLAXIS 3D

Fig. C 3.7: Relative permeability in time vs height in PLAXIS 3D

Fig. U 3.9: Degree ot saturation in time vs height (existing Plaxtlow)

Fig. C 4.3: Degree of saturation in time vs height in PLAXIS 2D

Fig. C 4.2: Active pore pressure in time vs height in PLAXIS 2D

Fig. C 4.6: Degree of saturation in time vs height in PLAXIS 3D

Fig. C 4.4: Relative permeability in time vs height in PLAX 1S 2D

Fig. C 4.7: Relative permeability in time vs height in PLAXIS 3D

Fig. C 4.9: Degree of saturation in time vs height (existing PlaxFlow)

‘ig. C4.8: Active pore pressure in time vs height (existing PlaxFlow)

Fig. D1.5: Active pore pressure in time vs height in PLAXIS 3D

Fig. D1.3: Degree of saturation in time vs height in PLAXIS 2D

Fig. D1.4: Pore pressure at the Gauss point at the top of the column in time in PLAXIS 2D

Fig. D1.6: Degree of saturation in time vs height in PLAXIS 3D

Fig. D1.7: Pore pressure at the Gauss point at the top of the column in time in PLAXIS 3D

Fig. D1.8: Active pore pressure in time vs height (existing PlaxFlow)

.D1.9: Degree of saturation in time vs height (existing PlaxFlow)

Fig. D1.10: Pore pressure at the Gauss point at the top of the column in time (existing PlaxFlow)

Fig. D2.4: Pore pressure the top of the column in time in PLAXIS 2D

Fig. D2.5: Active pore pressure in time vs height in PLAXIS 31

Fig. D2.7: Pore pressure the top of the column in time in PLAXIS 3D

Fig. D3.4: Degree of saturation in time vs height in PLAXIS 2D

Fig. D3.7: Degree ot saturation in time vs height in PLAX 1S 3D

Fig. D3.5: Pore pressure at node and Gauss point at the top of the column in time in PLAXIS 2D

Fig. D3.8: Pore pressure at node and Gauss point at the top of the column in time in PLAXIS 3D

‘ig. D3.9: Active pore pressure in time vs height (existing PlaxFlow)

Fig. D3.10: Degree of saturation in time vs height (existing PlaxFlow)

Fig. D3.11: Pore pressure at the Gauss point at the top of the column in time (existing PlaxFlow)

Fig. D4.5: Pore pressure at node and Gauss point at the top of the column in time in PLAXIS 2D

Fig. D4.3: Active pore pressure in time vs height in PLAXIS 2D Fig. D4.4: Degree of saturation in time vs height in PLAXIS 2D

Fig. D4.8: Pore pressure at node and Gauss point at the top ot the column in time in PLAXIS 3D

Fig. D4.9: ig. D4.9: Active pore pressure in time vs height (existing PlaxFlow)

Fig. D4.10: Degree of saturation in time vs height (existing PlaxFlow)

Fig. D4.8: Pore pressure at the Gauss point at the top of the column in time (existing PlaxFlow)

Tab. G1.1: Input data for loam layer (B9)

This lesson demonstrates the applicability of PLAXIS to agricultural problems. The potato field lesson involves a loam layer on top of a sandy base. Regional conditions prescribe a water level at the position of the material interface. The water level in the ditches remains unchanged. The precipitation may vary on a daily basis due to weather conditions. The calculation aims to predict the variation of the water content in the loam layer in time as a result of time- dependent boundary conditions. Fig. G 1.1: Potato field geometry

Tab. G1.3: Prescribed flux (Qpin =0 and @nax= 1m The precipitation fluxes are given in Table G1.3. The threshold values for ponding and precipitation (evapotranspiration) are chosen as 1 m and 0 at the top of the boundary, respectively.

Fig. G1.4.2D: Active pore pressure after steady state calculation (PLAXIS 2D)

Fig. G1.5.2D: Degree of saturation after steady state calculation (PLAXIS 2D)

Fig. G1.7.2D: Degree of saturation after 4.5 days (PLAXIS 2D)

Fig. G1.9.2D: Degree of saturation after 9 days (PLAXIS 2D)

Fig. G 1.5.3D: Degree of saturation after steady state calculation (PLAXIS 3D) Fig. G1.4.3D: Active pore pressure after steady state calculation (PLAXIS 3D)

Fig. G 2.1: Triangular earth dam with a constant head on the left side and seepage on the right side

Fig. G2.3.2D: Groundwater head (PLAXIS 2D)

Fig. G2.6.3D: Total discharge at cross section B-B: Q=0.4982 m3/day/m (PLAXIS 3D)

Fig. G3.2.2D: Finite element mesh (PLA XIS 2D) Fig. G3.1: Geometry of the problem

Figure G3.1 shows the geometry and boundary conditions of the problem. As indicated in the figure there is a 10 m wide impermeable dam founded on a soil layer of 10m thick. The bottom of the soil layer is considered to be impermeable. A 5.0 m wall is placed under the dam. At the left side of the dam (as shown in figure) the water level is 15.0 m while at the right side the water level is 13.0 m. The wall is simulated by means of an impermeable interface. The element mesh is locally refined around the wall particularly at the tip of the wall. 6 noded and 15 noded elements are alternately used. The problem is also simulated with PlaxFlow to compare outputs. Permeability of soil is 1.0 m/day.

Fig. G3.4.2D: Groundwater head (PLAXIS 2D)

Fig. G3.4.3D: Groundwater head (PLAXIS 3D)

Fig. G4.3.2D: Groundwater head (PLAXIS 2D)

Fig. G4.5.3D: Total discharge Q=0.1531 m°’/day/m (PLAXIS 3D - 10 noded tetrahedral elements)

Fig. G4.4.3D: Flow field (PLAXIS 3D - 10 noded tetrahedral elements) Fig. G4.3.3D: Groundwater head (PLAXIS 3D)

Fig. G5.3.2D: Active pore pressure (PLAX IS 2D)

Fig. G5.4.3D: Flow field (PLAXIS 3D) Fig. G5.3.3D: Active pore pressure (PLAXIS 3D)

Fig. G6.3.2D: Finite element mesh (PLAXIS 2D - 15 noded elements Fig. G6.2: Monograph for Muskat problem (Kang- Kun Lee and Darrell I. Leap, 1997)

Fig. G6.4.3D: Flow field and phreatic surface (PLAXIS 3D)

Fig. G7.1.2D: Geometry and FE mesh (PLAXIS 2D)

In this example a column of soil with a well inside is simulated. Geometry of the problem and the finite element mesh is shown in Figure G7.1. Phreatic line is at the top boundary to generate fully saturated soil. The side and the bottom boundaries are closed for flow, therefore inflow or outflow can only occur through the top boundary. The total discharge of well is consider 1 m°/day. This example is calculated in PLAXIS 2D (plane strain and axi-symmetric) and in PLAXIS 3D.

Fig. G7.2.2D.2: Flow field (PLAXIS 2D - axi-symmetric)

Fig. G7.3.2D.1: Total discharge leaving the domain; Q=1.0 m°/day/m (PLAX! 2D - plane strain)

Fig. G7.3.2D.2: Total discharge leaving the domain; Q=1.0 m°/day/rad (PLAXIS 2D - axi-symmetric)

Fig. G7.3.3D: Total discharge leaving the domain; Q=1.0 m°/day (PLAXIS 3D) Qummary:

In this example a block of soil with a drain inside is simulated with PLAXIS 2D and PLAXIS 3D. Geometry of the problem and the finite element mesh is shown in Figure G8.1. The block is 50 m long, 20 m high (and 10 m wide in case of 3D) and the drain is exactly in the middle. The initial water level is at 18 m. Permeability of soil is 1 m/day and coarse material (from standard data set) is used for retention curve. Steady state type of calculation is used. The minimum head of drain is 10 m.

Fig. G8.3.2D: Degree of saturation (PLA XIS 2D)

Fig. G8.5.2D: Total discharge in soil; Q=4.473 m°/day/m (PLAXIS 2D) Fig. G8.4.2D: Flow field (PLAXIS 2D)

Fig. G8.5.3D: Total discharge in soil; Q=4.476 m°/day/m (PLAXIS 3D)

Fig. G9.2.3D: Geometry and FE mesh (PLAXIS 3D)

Fig. G9.3.2D6: Active pore pressures (6-noded elements)

Fig. G9.3.2D15: Active pore pressures (15-noded elements)

Fig. G10.1.3D: FE mesh (PLAXIS 3D 10 noded elements) Tab. G10.1: Van Genuchten parameters

Fig. G10.2: Comparison of phreatic level for non- homogeneous rectangular dam made by Bardet & Tobita (2002)

Fig. CA1.3.2D: Horizontal effective stresses (PLAXIS 2D)

Fig. CA1.2.3D: V ertical effective stresses (PLAXIS 3D)

Fig. CA1.4.2D: Vertical total stresses (PLAX IS 2D)

Fig. CA1.3.3D: Horizontal effective stresses (PLA XIS 3D)

Fig. CA1.4.2D: Horizontal total stresses (PLA XIS 2D)

Fig. CA1.4.3D: Horizontal total stresses (PLA XIS 3D)

The consolidation phenomenon will be practically finished when the argument of the exponential function is about 4 or 5 (Verruijt, 1993). This will be the case when T =2. Verification: The problem of one dimensional consolidation can be formulated by a differential equation (Terzaghi, 1923):

Fig. CA3.2: Active pore pressure for case 1a (PLAXIS 2D)

Fig. CA3.3: Vertical displacement for case 1a (PLAXIS 2D

Fig. CA3.5: Vertical displacement for case 1a (PLAXIS 3D Foundation)

Fig. CA3.9: Vertical displacement for case 1b (PLAXIS 2D)

Fig. CA3.8: Active pore pressure for case 1b (PLAXIS 2D)

Fig. CA4.1: Geometry boundary conditions for problem CA4

Fig. CA4.F: Increase of water head as a function of time in problem CA4

Fig. CA4.4; Active pore pressure for case 2a (PLAXIS 3D Foundation)

Fig. CA4.7: Vertical displacement for case 2a (PLAXIS 3D Foundation)

Fig. CA4.10: Active pore pressure for case 2b (PLAXIS 3D Foundation)

Tab. CA5.1: Input data for loam layer (B9)

The example of Potato filed which is calculated by transient calculation, is chosen for fully coupled flow-deformation analysis (example G1). This lesson demonstrates the applicability of PLAXIS to agricultural problems. The potato field lesson involves a loam layer on top of a sandy base. Regional conditions prescribe a water level at the position of the material interface. The water level in the ditches remains unchanged. The precipitation may vary on a daily basis due to weather conditions. The calculation aims to predict the variation of the water content in the loam layer in time as a result of time-dependent boundary conditions. Fig. CA5.1: Potato field geometry

Fig. CA5.3.2D: Finite element mesh (15 noded elements)

Fig. CA5.5.2D: Degree of saturation after steady state phase (imposing head)

Fig. CA5.7.2D: Active pore pressure and external water load after 5 days

Fig. CA5.8.2D: Degree of saturation after 5 days

Fig. CA5.9.2D: Deformed mesh after 5 days

Fig. CA5.11.2D: Active pore pressure after 9 days

Fig. CA5.3.3D: Finite element mesh (10 noded elements)

Fig. CA5.9.3D: Deformed mesh after 5 days Fig. CA5.10.3D: Flow field after 5 days

Fig. CA6.2.3D: Geometry and finite element mesh of the dam and sub-soil (PLAXIS 3D)

Fig. CA6.4.2D: Degree of saturation for high reservoir level (PLAXIS 2D)

Fig. CA6.3.3D: Steady-state pore pressure for high reservoir level (PLAXIS 3D)

Fig. CA6.4.3D: Degree of saturation for high reservoir level (PLAXIS 3D.

Fig. CA6.7.2D: Degree of saturation after rapid drawdown (PLAXIS 2D)

Fig. CA6.6.2D: Active pore pressure after rapid drawdown (PLAXIS 2D)

Fig. CA6.6.3D: Active pore pressure after rapid drawdown (PLAXIS 3D)

Fig. CA6.8.2D: Flow field after rapid drawdown (PLAXIS 2D)

Fig. CA6.9.2D: Active pore pressure after slow drawdown (PLAX IS 2D)

Fig. CA6.10.2D: Degree of saturation after slow drawdown (PLAXIS 2D)

Fig. CA6.13.2D: Degree of saturation for low reservoir level (PLAX IS 2D) Fig. CA6.12.2D: Steady-state pore pressure for low reservoir level (PLAXIS 2D)

Fig. CA6.13.3D: Degree of saturation for low reservoir level (PLAX IS 3D)

Fig. CA6.14.3D: Flow field for low reservoir level (PLAXIS 3D)

Fig. CA6.15.2D: Safety factors for different situations (PLAXIS 2D)

Fig. CA6.15.3D: Safety factors for different situations (PLAXIS 3D)

Fig. CA6.16.PF: Steady-state pore pressure distribution for high reservoir level (PlaxFlow)

Fig. CA6.19.PF: Steady-state pore pressure distribution for low reservoir level (PlaxFlow)

Fig. CA6.17.PF: Pore pressure distribution after rapid draw down (PlaxFlow)

Fig. USM 1.2: Shear stress versus axial strain for different suction (Plaxis)

Fig. USM1.5: Specific volume versus mean effective stress p‘ (Plaxis)

Fig. USM 1.4: Stress path in p’-q space (Plaxis)

Fig. USM 1.8: Stress path in p’-q space (Gonzalez & Gens, 2008)

Fig. USM1.9: Specific volume versus mean effective stress p’ (Gonzalez & Gens, 2008)

‘ig. USM1.11: a) Suction versus mean effective stress p’; b) suction versus deviatoric stress q; c) stress path in p’-q space; d) specific volume versus mean effective stress p’ (Sheng et al., 2003)

The material data of the soil is given in Table 2. For initialisation 100 kPa is assumed for preoverburden pressure (POP). Fig. USM2.1:; Geometry and FE mesh used for footing problem

Fig. 1: Skempton’s B-parameter versus degree of saturation

Tab. 1: Bulk modulus of water in the classical mode

Fig. 2: Geometry and finite element model of the problem

Excess pore pressures P., 94, (Pressure = negative) Maximum Value = -9.802 kN/m2 (Element 352 at Node 966) Minimum Value = -9.802 kN/m? (Element 267 at Node 903)

First of all, results of each case are provided and then the results are compared with each other. Figure 6 shows the stresses and active water pore pressures al the end of the initial phase (gravity loading). As Bishop stress is used, to explain how the effective stresses are calculated, degree of saturation is needed (Eq. 2) which is plotted in Figure 7.

Fig. 7: Results after the initial phase for coarse material: Degree of saturation

Fig. 9: Results after the initial phase for fine material: Degree of saturation

Fig. 10: Results after the phase 1 for coarse material: left) vertical total stress; middle) vertical effective stress; right) active pore pressure

Fig. 12: Results after phase 1 for coarse material: Degree of saturation

Fig. 14: Excess water pore pressure in fine material at the end of phase 1.

Fig. 15: Results after phase 1 for fine material: Degree of saturation

Here it is shown how to convert old PlaxFlow material data set to the new one. In the new material data set, Ca, is removed because it can simply be derived from the equivalent bulk modulus of water K,,/n and water weight \;:

Domenico Gallipoli

PhD Thesis of Domenico Gallipoli, 2000

The thesis focuses on three different areas: development of constitutive models for unsaturated soils, improvement of the finite element code “Compass” for coupled flow-deformation analysis involving unsaturated soils and application of the improved code to the simulation of pressuremeter tests in unsaturated soils. On the constitutive side, a unique relationship is proposed between degree of saturation, suction and specific volume by introducing dependency on specific volume in the simplified van Genuchten equation. This is a significant improvement over the common assumption of a state surface expression for degree of saturation. If combined with an elasto-plastic stress-strain model predicting the variation of specific volume, the proposed relationship is capable of reproducing irreversible changes of degree of saturation and changes of degree of saturation experimentally observed during shearing. Predictions show very good agreement with experimental results from tests on compacted Speswhite Kaolin published in the literature. On the numerical side, a number of changes to the code “Compass” have been performed. The new relationship for degree of saturation is implemented in the code and the implementation is validated against three benchmark problems. Use of the new relationship for degree of saturation results in significantly different predictions to those obtained if a conventional state surface expression for degree of saturation is used (as present in the original code). Implementation of the water and air continuity equations in “Compass” has been corrected by expressing these equations in terms of flux velocities relative to the soil skeleton. This is the form in which the equations should be expressed if they are to be combined with Darcy’s law for liquid and gas flows. The simulation of a notional laboratory test shows that the incorrect combination of Darcy’s law with absolute flux velocities, as present in the original code, causes significant errors. The convergency algorithm at constitutive level employed in the code has been corrected by introducing residual flux terms in the two flow equations, analogous to residual forces in the equilibrium equation. These terms must be taken into account if a convergency algorithm for an elasto-plastic stress-strain model is used and the relationship assumed for variation of degree of saturation involves any dependency on net stresses. A numerical study of a notional laboratory test shows that omission of residual flux terms results in substantial errors and may cause failure to converge. The plane_strain formulation of code “Compass” has been corrected by imposing the condition of nullity only on the out-of-plane component of the total strain rate vector instead of the out-of-plane component of each single contribution to the total strain rate, as was done in the original code. Such inconsistency, due to the history of development of finite element programs, also appears in other examples published in the literature. Numerical simulations of two types of bi-axial tests show that significantly different results are generally predicted by the correct and incorrect formulations, and also provide an explanation why this type of error was difficult to detect in codes implementing traditional models for saturated soils. The potential of the enhanced version of code “Compass” for analysing boundary value problems is demonstrated by simulations of pressuremeter tests in unsaturated soil. This study also provides some initial insight into the interpretation of pressuremeter tests in unsaturated soil by simulating tests at different loading rates in a normally consolidated soil. The mechanical behaviour of the soil is represented by the elasto-plastic Barcelona Basic Model of Alonso, Gens and Josa (1990) while the variation of degree of saturation is modelled by the new relationship proposed in the thesis. The entire range of loading rates, from undrained to fully drained (with respect to liquid), is simulated. Relatively small changes of suction are predicted even in the fastest test and the computed cavity pressure-cavity strain relationships are all very similar regardless of loading rate. It may therefore be possible to model even rapid pressuremeter tests in unsaturated soils as a drained (constant suction) process. Further work is required to investigate the generality of this conclusion.

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Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

Antonio Gens

International Journal for Numerical and Analytical Methods in Geomechanics, 2003

This paper presents a complete finite-element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress-strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time-stepping scheme which automatically adjusts the time-step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non-linearity caused by suction-dependent plastic yielding, suction-dependent degree of saturation , and saturation-dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress-strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction.

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Coupled hydro-mechanical analysis of expansive soils: Parametric identification and calibration

Abhishek Rawat

Journal of Rock Mechanics and Geotechnical Engineering, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Experimental and numerical approaches of the hydro-mechanical behaviour of a quasi-saturated compacted clayey soil

Jacques Monnet

E3S Web of Conferences, 2016

The present research is funded by the French National Project « TerreDurable », which is dedicated to the study of soils in quasi-saturated conditions (close to saturation) for the analysis of stability and settlement of earth structures such as embankment, dams. A global presentation of the drying-wetting test shows the volume change, air entry and soil-water characteristics of the soil at slurry and oven-dried conditions. Unsaturated undrained triaxial test was carried out in order to investigate the variation of pore-water pressure from quasi-saturated domain to saturation. The experimental results of the triaxial test are then modeled using a two-dimensional explicit finite difference program (Flac 2D). A constitutive law developed in the TerreDurable project allows better understanding the behaviour of quasi-saturated soils using the water retention curve of quasi-saturated domain proposed by Boutonnier (2007, 2010). A simple effective stress model is used (Cam Clay) by taking into account both the suction and the compressibility of equivalent fluid (water + air). The results from numerical calculation and experimental measurements are compared.

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Modelling Volume Change and Mechanical Properties With Hydraulic Models

Thomas Baumgartl

Soil Science Society of America Journal, 2004

Volume Change by Internal and External Stresses Volume change of soils may be caused either by external (mechanical) or internal (hydraulic) stresses or a combination of both. A com-Processes of volume change in a porous system like plete description of volume change must therefore include both mesoil can either occur in a two-phase system (solid-water chanical and hydraulic stresses. By combining theories of mechanical or solid-air) or a three-phase system (solid-water-air). and hydraulic stress states, a hydraulic function, which predicts the For reasons of simplification, it is generally assumed change of water volume as a function of the stress state parameter that air-filled pores are interconnected to the atmosphere soil water suction (water retention curve), is adopted to model volume and that the influence of pore air pressure buildup during change. The utilization of such a continuous function also enables the derivation of soil mechanical parameters (e.g., preconsolidation stress, volume changes can therefore be neglected. The stress Youngs modulus) by determining mathematically the point of maxi-state can be defined by two kinds of stresses within the mum curvature and inflection point. This information can then be soil. It is a result of external (mechanical) stresses and used to calculate the preconsolidation stress according to the method internal (hydraulic) stresses. Mechanical stresses are of Casagrande. The presented calculation has considerable advantages transmitted via the solid phase. Volume change occurs compared with the graphic method of Casagrande or other methods. when maximum shear resistances between particles are On the basis of stress-strain relationships of various textured and exceeded. Hydraulic stresses or internal stresses are structured soils and soil substrates and various test procedures (oedocaused by the water phase in the pore system and influmeter test, triaxial test, shrinkage test), volume change is modeled using ence the shearing resistances. When stresses are applied, the described method. It is shown that modeling volume change by they will be positive in a two-phase system (water-satuthe van Genuchten equation using the software RETC is possible with high accuracy. Soil mechanical parameters are derived using the pa-rated soil), but may also be positive in the short term rameters of the van Genuchten equation. The comparison of results in a three-phase system (water-unsaturated soil), while of this method with the Casagrande and a statistical method shows that compaction caused by external stresses will redistribute these methods have deficiencies when the data sets have a high variwater into a pore system with a modified pore-size distriability, the samples are not homogeneous, and when the stress-strain bution. At the state of equilibrium of the water phase curve is flat. The accuracy of the mathematical method in contrast is within the pore system (equivalent with the pore size very high and the calculated preconsolidation stress very reliable. distribution), hydraulic stresses will be generally negative and can be characterized by tensile stresses. Under

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An effective stress approach for hydro-mechanical coupling of unsaturated soils

Hiram Arroyo

E3S Web of Conferences, 2016

The simulation of the mechanical and hydraulic behaviour of soils is one of the most important tasks in soil mechanics. It is inaccurate to consider that the behaviour of saturated and unsaturated soils as if their governing laws were utterly different, this last condition is not sufficient to do so. However, unlike the laws governing the behaviour of saturated soils, those used to describe the behaviour of unsaturated soils lack the simplicity and predictability associated to the complexity of the phenomena that occur within these porous media. This is why it is important to establish a unified soil mechanics theory to reconcile saturated and unsaturated soil mechanics. In the present work, we describe a simple analytical equation to obtain effective stresses for any type of soil. The equation is coupled to an elastoplastic constitutive model which is capable to reproduce the stress-strain relationship of soil taking into account the hydro-dynamic coupling.

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complex problems, digital datasets to accompany worked examples and problems, solutions to end-of-chapter problems, weblinks, extended case studies, and more. Craig's Soil Mechanics is the definitive text for civil engineering students worldwide

Gloria DM

Now in its eighth edition, this bestselling text continues to blend clarity of explanation with depth of coverage to present students with the fundamental principles of soil mechanics. From the foundations of the subject through to its application in practice, Craig's Soil Mechanics provides an indispensable companion to undergraduate courses and beyond. Revised and fully reworked throughout, several chapters have been significantly extended or had fresh topics added to ensure this new edition reflects more than ever the demands of civil engineering today. New to this edition: Rewritten throughout in line with • •

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Chapter 1 -Soil Mechanics Review Part A

abrham sol

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The prediction of one-, two-, and three-dimensional heave in expansive soils

hung vu

Canadian Geotechnical Journal, 2004

The prediction of heave in unsaturated, expansive soils has historically been studied primarily as a onedimensional type analysis. This paper proposes a methodology that can be used for the prediction of one-, two-, or three-dimensional heave. It is suggested that negative pore-water pressures (i.e., soil suctions) can be estimated through a saturated-unsaturated seepage analysis. The results of the seepage analysis are then used as input for the prediction of displacements in a stress-deformation analysis. The formulation of the governing partial differential equations for both seepage and stress-deformation is based on the general theory of unsaturated soils using two independent stress state variables. The elasticity parameter functions required for a stress-deformation analysis can be calculated from various tests, including conventional one-dimensional oedometer tests. The proposed method is studied and tested against data collected on a case history involving a slab-on-ground floor on Regina clay. The predicted results from the twodimensional analysis agree well with the measured data in terms of both total vertical displacements and final water contents in the soil. The results of a parametric study are also presented to show the effect of measured soil parameters (i.e., swelling index and initial void ratio) and assumed parameters (i.e., Poisson's ratio and coefficient of earth pressure at rest) on the predicted displacements.

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Hydrodynamic derivation of the work input to fully and partially saturated soils

Mario Liu

Journal of the Mechanics and Physics of Solids, 2018

In 'Rational Mechanics' the work input per unit element volume can be identified from the local energy balance, itself being derived through localization from the global energy balance of an arbitrary volume. On the other hand, in the search of meaning for an effective stress of partially and fully saturated soil media, in 'Soil Mechanics' some define the work input by adopting material assumptions and simplified homogenization. The final result depends on effective stress and various pressures that are not seen in the rational mechanics work input expression. To resolve the discrepancy in the structure of the work input, this paper establishes a third approach based on the 'Hydrodynamic procedure', which operates solely at the level of unit volumes and thus does not require localization. The derived equations fully agree with Rational Mechanics, and yield the same work input expressions. The bonus for employing the more comprehensive Hydrodynamic procedure is that it also reveals the meaning of the effective stress in relation to the various pressures.

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Antonio Gens

2003

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Numerical Simulation of Water Level Effects on Soil Behavior under Cyclic Loading

Syks Ever

The alarming evidence of rising shallow ground water level and the widespread structural problem have mitigated the extra demand to develop special geotechnical awareness, standard testing and designing procedures to minimize the impact of wetting on soil behavior in the semi-arid region. Terzaghi (1943) suggested that the submergence of soil mass reduces the soil stiffness to half, which in turn doubles the settlement. Geotechnical procedures to estimate collapse potential with means to control and limit the rising ground water level have been addressed. This paper was to evaluate the effect of water table rise on settlement of footing. Two-dimensional model of soil and shallow foundation in PLAXIS software was created. The analysis has been done using Mohr-Coulomb constitutive model. Also, the effect of foundation size settlement efficiency was calculated. The results obtained will be valuable in verifying Terzaghi's intuitive reasoning and explaining the observed additional s...

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Alternative Method for Analysing Hydromechanical Behaviour of Unsaturated Soils

Márcia Mascarenha

Soils and Rocks, 2016

The suction-control techniques commonly used for laboratory studies of mechanical behaviour of unsaturated soils are much more time consuming than standard soil mechanics tests. In addition, few laboratories have the required apparatus for testing unsaturated soils. This paper proposes an alternative method of analysing hydromechanical behaviour of unsaturated soils with high-porosity. The method is divided in three tasks: 1) verification of the effect of void ratio changes on the water retention curve using filter paper; 2) determining water content changes by evaporation under the same test conditions; and 3) performing saturated and unsaturated consolidation tests. Unsaturated tests make use of samples that are less than 100% saturated and there is no suction control during the test. Therefore, only initial water content is known. Significant suction changes take place due to void closure and evaporation while testing. The results obtained using the proposed methodology showed the stress and suction path and enhance the understanding of the hydromechanical behaviour of unsaturated soils. The results also showed that analyses of water content alone cannot explain some unexpected results, such as: 20% initial water content samples present less deformation than 16% samples.

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Numerical Simulation of the Mechanical Response of the Tunnels in the Saturated Soils by Plaxis

Mohamed Allal

The forecast of settlement and movements caused by tunneling represents a significant challenge of technology. The evaluation of these movements is indeed of primary importance in order to prevent them.

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Modeling Volume Change and Mechanical Properties with Hydraulic Models

Thomas Baumgartl

Soil Science Society of America Journal, 2004

Volume change of soils may be caused either by external (mechanical) or internal (hydraulic) stresses or a combination of both. A com-Processes of volume change in a porous system like plete description of volume change must therefore include both mesoil can either occur in a two-phase system (solid-water chanical and hydraulic stresses. By combining theories of mechanical or solid-air) or a three-phase system (solid-water-air). and hydraulic stress states, a hydraulic function, which predicts the For reasons of simplification, it is generally assumed change of water volume as a function of the stress state parameter that air-filled pores are interconnected to the atmosphere soil water suction (water retention curve), is adopted to model volume and that the influence of pore air pressure buildup during change. The utilization of such a continuous function also enables the derivation of soil mechanical parameters (e.g., preconsolidation stress, volume changes can therefore be neglected. The stress Youngs modulus) by determining mathematically the point of maxi-state can be defined by two kinds of stresses within the mum curvature and inflection point. This information can then be soil. It is a result of external (mechanical) stresses and used to calculate the preconsolidation stress according to the method internal (hydraulic) stresses. Mechanical stresses are of Casagrande. The presented calculation has considerable advantages transmitted via the solid phase. Volume change occurs compared with the graphic method of Casagrande or other methods. when maximum shear resistances between particles are On the basis of stress-strain relationships of various textured and exceeded. Hydraulic stresses or internal stresses are structured soils and soil substrates and various test procedures (oedo-

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Numerical and experimental modeling of geomechanical behavior of partially saturated soils

Prof. Ali Noorzad

International Journal of Geo-Engineering

The Barcelona Basic Model (BBM) has been implemented in a finite difference-based computer program to simulate the behavior of unsaturated soils subjected to wetting. The BBM implementation was verified using analytical solutions, and the proposed model has been used to simulate the response of a compacted embankment under complete saturation and suction induced conditions. Numerical analyses indicate that considerable amount of total and differential settlements could develop at the top surface of the embankment. BBM is executed into FLAC2D extending a defined module for modified Cam Clay (MCC) and has been set up an analytical solution for suction-dependent stress and strain. Evaluating the effect of anisotropy and nonlinear apparent tensile strength in unsaturated soils, a modification to BBM formulation has been proposed and optimized by developing numerical analyses to reduce the size of elastic region of loading collapse (LC) curve. Then, an experimental study in the literatur...

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Advanced Unsaturated Soil Mechanics and Engineering Charles & Bruce

Mohammad Asif

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A fully coupled flow deformation model for cyclic analysis of unsaturated soils including hydraulic and mechanical hystereses

Nasser Khalili

Computers and Geotechnics, 2008

A fully coupled flow-deformation model for describing time-dependent behaviour of unsaturated soil is presented. The proposed hydro-mechanical model is formulated based on the theory of multiphase mixtures using the effective stress approach and the bounding surface viscoplastic constitutive model. The governing equations for the flow model are derived using the conservation equations of mass and momentum. The deformation of the solid skeleton is described using the bounding surface viscoplasticity framework to capture the time-dependent stress-strain behaviour of geomaterials. The constitutive model is based on the viscoplastic consistency theory and the bounding surface plasticity model. The proposed viscoplasticity model allows a smooth transition from rate-independent plasticity to rate-dependent viscoplasticity. The hardening parameter representing the size of the bounding surface is defined as a function of viscoplastic strain, viscoplastic strain rate, and suction. For unsaturated soils, the suction hardening effect is described using the coupled influence approach where suction has a multiplicative effect to the viscoplastic volumetric hardening. The numerical results are then presented demonstrating the capability of the proposed model in describing time-dependent behaviour of unsaturated soils.

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Coupled solid-fluid FE-analysis of geotechnical problems involving partially saturated soils

Michael Pertl

GAMM-Mitteilungen, 2010

A numerical model for coupled solid-fluid FE-analyses of geotechnical problems involving partially saturated soils is described. As constitutive model for partially saturated soil serves the Barcelona Basic Model, which is formulated in terms of net stress and capillary pressure. Different stress update algorithms are compared for this model regarding the accuracy and efficiency. The application of the numerical model is demonstrated by numerical simulations of the impoundment of an earth dam and of the injection of compressed air into water saturated soil.

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A new insight into modelling the behaviour of unsaturated soils

Felix Darve

International Journal for Numerical and Analytical Methods in Geomechanics, 2012

Understanding the response of partially saturated soils under different loads is important for the design and construction of economical and safe geotechnical engineering structures. This paper presents a coupled elastoplastic constitutive model for predicting the hydraulic and stress-strain-strength behaviour of unsaturated soils. The model proposed is built according to the following principle. A constitutive relation is given for each phase (solid, liquid and gas) and coupling relations between each phases are also derived. In the present case, we assume that each phase is not miscible and that pressure in voids not filled by water remains more or less constant, which is reasonable for most geotechnical problems. Therefore, the model is written in a classical manner with a non associated elastoplastic model for the granular skeleton behaviour; an incompressible liquid phase; a water retention description; and an assumption of the existence of an effective stress concept defined by Bishop.

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