Flac Finite Element Method Software#q=flac3d 7.0 Free Download Updated FREE

Flac Finite Element Method Software#q=flac3d 7.0 Free Download

FLAC

TOUGH-FLAC was originally adult and applied for modeling coupled THM processes in unsaturated fractured tuff (Rutqvist et al., 2002).

From: Developments in Dirt Science , 2015

Numerical Geomechanics Studies of Geological Carbon Storage (GCS)

Jonny Rutqvist , ... Frederic Cappa , in Scientific discipline of Carbon Storage in Deep Saline Formations, 2019

Numerical Models for GCS Geomechanics

The numerical simulator TOUGH-FLAC was developed in the late 1990s as a pragmatic approach for modeling geomechanical processes coupled with multiphase flow and rut send, including those occurring during deep clandestine CO ₂ injection (Rutqvist et al., 2002). TOUGH-FLAC is based on linking the multiphase flow and heat transport simulator TOUGH2 (Pruess et al., 2012) with the geomechanical simulator FLAC^3D (Itasca Consulting Group, 2011). At the fourth dimension, TOUGH2 was already established and widely used for modeling multiphase flow aspects of GCS, using the equation of state module ECO2N for CO₂–brine mixtures, whereas the link to FLAC^3D provided the capability of modeling geomechanical aspects of GCS (Rutqvist et al., 2002; Rutqvist and Tsang, 2002).

Since the initial development of TOUGH-FLAC, an increasing number of numerical simulators have been developed or adapted to written report geomechanics and coupled THM processes associated with GCS. These include FEMH (Deng et al., 2012), OpenGeoSys (Goerke et al., 2011), CODE_BRIGHT (Vilarrasa et al., 2010), ECLIPSE-VISAGE (Ouellet et al., 2011; Olden et al., 2012), STARS (Bissell et al., 2011), NUFT-SYNEF (Morris et al., 2011), COMSOL Myltiphysics (Alonso et al., 2012), DYNAFLOW (Preisig and Prévost, 2011), CMG-Gem (Siriwardane et al., 2013), Sierra (Martinez et al., 2013), DuMu^x (Beck et al., 2016), Lagamine (Li and Laloui, 2016), also as other simulators in which multiphase flow codes such every bit TOUGH2, ECLIPSE, GEM, and STOMP have been linked with geomechanical codes (eastward.g., Rohmer and Seyedi, 2010; Ferronato et al., 2010; Tran et al., 2010; Jha and Juanes, 2014; Lei et al., 2015; Orlic, 2016).

Most of the aforementioned simulators are based on continuum numerical modeling approaches to coupled THM in deformable porous media, including continuum elastic and elasto-plastic constitutive mechanical behavior. Other codes take been developed and adapted for modeling of detached fractures or fracturing associated with CO₂ injection and caprock integrity. For example, Castelletto et al. (2013), linked the IFPEN flow dynamic simulator to a finite chemical element structural code that tin can represent error geometry accurately using interface elements in 3-D. Pan et al. (2014) linked TOUGH2 to RDCA (rock discontinuous cellular automaton) for modeling caprock fracturing and detached fracture shear activation, and Bao et al. (2015) linked a finite element method (FEM) lawmaking to a bounded distinct chemical element method (DEM) code for modeling of fracturing or fault activation in a caprock. Fault activation and induced seismicity is currently a hot topic related to any underground injection activities and the same continuum or discontinuum codes could be adjusted to model such processes. For example, Rutqvist et al. (2007) demonstrated modeling of fault activation using TOUGH-FLAC in which the fault architecture was explicitly discretized and special algorithms were used to calculate earthquake magnitudes every bit well as potential error permeability changes and leakage (Rutqvist et al., 2016).

Some coupled fluid catamenia and geomechanical simulators tin also include geochemistry of various levels of sophistication, from nonreactive to fully reactive solute transport, due east.g., past linking TOUGHREACT to FLAC^3D (Rutqvist et al., 2002), Retraso to CODE_BRIGHT (Kvamme and Liu, 2009), or STOMP-CO2-R to ABAQUS (Nguyen et al., 2016a), or past fully coupled THMC models (Yin et al., 2012; Zhang et al., 2016). Such capabilities tin be used to assess long-term geochemical and geomechanical changes in reservoir and caprock when exposed to CO_two.

To consider the complete set of THMC couplings in 1 simulation requires a large number of input parameters that might non be readily available, such as parameters for geomechanical–geochemical interactions. In fact, simplified models might be sufficient for studying subsets of coupled processes. For example, when studying large-scale geomechanical changes and the potential for error reactivation driven by large-scale reservoir pressure changes, a single-phase fluid period model coupled with geomechanics might be sufficient (e.g., Chiaramonte et al., 2011). Moreover, analytical and semianalytical models (e.g., Streit and Hillis, 2004; Soltanzadeh and Hawkes, 2009; Selvadurai, 2009; Mathias et al., 2010; Rohmer and Olivier, 2010; Yang et al., 2015), models with a reduced dimensionality, i.e. vertically integrated models, (Bjørnarå et al., 2016), or numerical multiphase flow models linked with analytical geomechanical models (eastward.g., Lucier et al., 2006; Chiaramonte et al., 2008; Vidal-Gilbert et al., 2010) can also be useful for first-social club analysis and quick assessment of suitability of a CO₂ injection-site.

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Coupled Thermo-Hydro-Mechanical-Chemic Processes in Geo-Systems

J. Rutqvist , ... Y. Tsang , in Elsevier Geo-Engineering Book Serial, 2004

iii. Model Conceptualization of the DST

The DST is false with TOUGH-FLAC in a 2 dimensional cross department oriented normal to the drift centrality ( Figure 2a). The highly fractured stone mass at the exam site is modeled as a dual-permeability medium, which consists of interacting matrix and fracture continua (Birkholzer and Tsang, 2000). Fracture mapping at the site shows 3 dominating fracture sets (Nieder-Westermann, 1998, Section 7.4.v):

Effigy 2. TOUGH-FLAC simulation of the DST: (a) schematics of two-dimensional model geometry; (b) conceptual model for stress-permeability coupling; (c) normal stress versus aperture human relationship for fractures

1)

Ane prominent vertical, southeast trending

ii)

One less prominent vertical, southwest trending

three)

One less prominent subhorizontal

The higher up-mentioned fracture sets take been derived through line mapping along sections of the ESF at Yucca Mount. The average spacing for mapped fractures of length larger than ane one thousand is nigh 0.three to 0.iv m. However, detailed cell mapping has shown that well-nigh 80% of the fractures at the site are less than one meter, and therefore the fracture spacing counting all fractures would be less than 0.three m. Moreover, air-permeability tests conducted in short-interval (0.iii thou) packed-off boreholes sections show that hydraulic conducting fractures exist at least every 0.3 m (Wang et al., 2001, Section 6.1). This evidence of a highly fractured rock justifies the using a continuum modeling approach.

For the Yucca Mountain site, incorporation of stress effects into hydraulic properties is based on a conceptual model of a highly fractured rock mass that contains three orthogonal fracture sets, as shown in Figure 2b. Porosity correction factor (F _ϕ) and permeability correction factors (F _kx , F _kx , F _kx ) calculated from the initial and electric current apertures (b _1i , b _2i , b _3i and b _ane , b ₂ , b ₃ , respectively) in fracture sets 1, 2, and 3, according to:

(1) $F_{\phi }=\frac{b_1+b_2+b_3}{b_{\mathrm{one}i}+b_{2i}+b_{3i}}$

(2) $F_{kx}=\frac{b_2^3+b_3^3}{b_{2i}^3+b_{\mathrm{three}i}^3},F_{\mathrm{thousand}y}=\frac{b_{\mathrm{i}}^3+b_3^3}{b_{1i}^{\mathrm{iii}}+b_{3i}^3},F_{kz}=\frac{b_1^3+b_2^{\mathrm{three}}}{b_{1i}^{\mathrm{iii}}+b_{\mathrm{two}i}^3}$

where fractures in sets 1, two, and 3 are assumed to be equally spaced and oriented normal to x, y, and z directions, respectively, and a parallel-plate fracture catamenia model is adopted. The capillary pressure is corrected for porosity and permeability changes according to a Leverett (1941) type of human relationship:

(3) $F_{\text{p}c}=\sqrt{\frac{F_g}{F_{\phi }}}$

where

(iv) $F_k=\sqrt[3]{F_{kx}\times F_{ky}\times F_{\mathrm{thou}z}}$

In this study, the current fracture aperture b depends on the current effective normal stress σ' _north , according an exponential function:

(5) $b=b_r+b_m=b_r+b_{\max }[\text{e}\text{x}\text{p}(d{{\sigma }^{\prime }}_n)]$

where b _r is a remainder aperture, b _{one thousand} is mechanical aperture, b _max is the maximum mechanical aperture, and d is a parameter related to the curvature of the role (Effigy 2c). Equation (v) can be inserted into Equation (2) to derive expressions for rock-mass permeability correction factors in x, y, and z directions.

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Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-Systems

M. Chijimatsu , ... Y. Sugita , in Elsevier Geo-Engineering Book Series, 2004

iv.5 The INERIS/ANDRA model

The two-stage menses option in FLAC allows numerical modelling of the flow of two immiscible fluids through porous media. A clarification of the concepts involved in the mathematical description of multi-phase catamenia may exist found in reference books such as "Fundamentals of Numerical Reservoir Simulation" ( Peaceman, D. W., 1977). Some of these concepts are addressed below.

In a two-stage menstruation trouble, the void space is completely filled past 2 fluids. One of the fluids (the liquid fluid, identified past the subscript lq) wets the porous medium more than the other (the gas fluid, identified by subscript gz). Equally a issue, the pressure in the non-wetting fluid will be college than the pressure in the wetting fluid. The pressure difference P _gz -P _lq is the capillary pressure P _c , which is a part of saturation Due south _lq . Darcy's law is used to depict the flow of each fluid. The effective intrinsic permeability is given as a fraction of the unmarried-fluid intrinsic permeability. The fractions (or relative permeability) are functions of saturation, S _lq .

In add-on to the mechanical balance of momentum, the mechanical constitutive equations and compatibility equation, some boosted equations are used for coupled calculations, equally follows.

The transport equations of liquid and gas components are described past the Darcy's law:

(xiii) $\{\begin{array}{c}{q}_r{}^{lq}=-k_{ij}{}^{\mathrm{fifty}q}{\kappa }_r{}^{lq}\frac{\partial }{\partial xj}(p_{lq}-{\rho }_{\mathrm{fifty}q}{m}_k{x}_k)\\ q_{\mathrm{fifty}}{}^{\mathrm{thousand}\mathrm{50}}=-{\mathrm{one\; thousand}}_{ij}{}^{\mathrm{fifty}q}{\kappa }_r{}^{\mathrm{1000}z}\frac{\partial }{\partial xj}(p_{gz}-{\rho }_{gz}{g}_k{x}_k)\end{array}$

where thousand _ij is saturated mobility tensor, κ _r the relative permeability for the fluid, and μ the dynamic viscosity.

The constitutive equations are

(14) $\{\begin{array}{c}{S}_{lq}\frac{\partial P_{lq}}{\partial t}=-\frac{M_{lq}}{\varphi }\left[\frac{\partial {\zeta }_{lq}}{\partial t}-\varphi \frac{\partial {\mathrm{Due\; south}}_{lq}}{\partial t}-{\mathrm{South}}_{lq}\frac{\partial \epsilon }{\partial t}\right]\\ {\mathrm{South}}_{gz}\frac{\partial P_{\mathrm{thousand}z}}{\partial t}=-\frac{{\mathrm{One\; thousand}}_{gz}}{\varphi }\left[\frac{\partial {\zeta }_{gz}}{\partial t}-\varphi \frac{\partial {\mathrm{Southward}}_{\mathrm{yard}z}}{\partial t}-S_{\mathrm{50}q}\frac{\partial \epsilon }{\partial t}\right]\end{array}$

where K _lq , K _gz are liquid and gas bulk modules.

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Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-Systems

S.M. Hsiung , ... One thousand.S. Nataraja , in Elsevier Geo-Technology Book Series, 2004

two.2 Numerical model

The analyses were conducted using a continuum approach using the FLAC computer code ( Itasca Consulting Grouping, Inc., 2000). A two-dimensional vertical cantankerous section was configured for numerical assay. This cross section intersected the axis of the heated drift at middistance betwixt the thermal bulkhead and its terminus. The FLAC models had a dimension of 1,000 m in width and 740 thou in height, with the origin of the coordinates located at the eye of the heated drift. A five-grand bore circular drift was located with its center 500 m from the left boundary and 500 g from the bottom of the model domain.

Fixed horizontal displacement boundaries were applied to the sides and a fixed vertical displacement boundary to the bottom of the model. The tiptop of the model coincided with the ground surface. Initial stresses consistent with overburden depth were applied as initial in-situ conditions.

The FLAC models included 3 thermal-mechanical lithologic units: Tptpul unit on the height, Tptpmn unit in the centre, and Tptpll unit on the bottom. The Tptpmn unit was 36 m thick, and its bottom was at 482 m from the lesser of the model domain. Note that the heater drift was located in the midheight of the Tptpmn unit.

The stone-mass mechanical and force properties used for the 3 units were obtained from a CRWMS M&O,report (CRWMS M&O, 1999) provided past the technical monitoring squad and are listed in Tables 1 and 2. The acronym RMQ in Tables i and 2 means Rock-Mass Quality. The dilation bending for each unit was taken every bit half the respective friction bending. The rock-mass friction angle for the Tptpmn unit of measurement provided in CRWMS Grand&O, (1999) was greater than the intact rock friction angle. The intact-rock friction angle was used in the assay instead of the rock-mass value for the Tptpmn unit. To report the sensitivity of rock-mass properties on the thermal-mechanical furnishings, two variations of rock-mass properties also were modeled for each rock unit (Tables three and 4).

Table 1. Rock-mass mechanical properties.

Unit	RMQ *	Young's modulus, GPa	Poisson'southward Ratio	Bulk Density, kg/giii
Tptpul	2	14.28	0.23	ii,160
Tptpmn	2	12.02	0.21	two,250
Tptpll	ii	12.02	0.21	2,250

*

Rock-Mass Quality

Table 2. Stone-mass strength backdrop.

Unit of measurement	RMQ	Cohesion, MPaT	ensile Force, MPa	Friction Angle, Degree
Tptpul	2	1.4	i.xiii	46.00
Tptpmn	2	two.3	1.36	48.xv
Tptpll	2	1.4	1.thirteen	46.00

Tabular array 3. Rock-mass mechanical properties for sensitivity analyses.

Unit	RMQ	Young's modulus, GPa	Poisson's Ratio	Bulk Density, kg/yardthree
Tptpul	1	ix.03	0.23	2,160
	5	20.36	0.23	2,160
Tptpmn	1	viii.98	0.21	two,250
	v	24.71	0.21	ii,250
Tptpll	1	8.98	0.21	two,250
	5	24.71	0.21	2,250

Table 4. Stone-mass force properties for sensitivity analyses.

Unit	RMQ	Cohesion, MPa	Tensile Strength, MPa	Friction Bending, Degree
Tptpul	ane	1.1	0.90	44.00
	5	ii.9	2.26	47.00
Tptpmn	one	1.9	i.16	48.xv
	five	3.9	ii.22	48.15
Tptpll	1	1.one	0.90	44.00
	5	ii.9	2.26	47.00

The measured temperature data were obtained from the technical monitoring team. These data were presented in 3-dimensional grids in a 2-twenty-four hours interval. Data selected as input for analyses were at three, 6, and 9 months and one, ii, 3, and four years of heating, and at the cross section 23 1000 from the thermal bulkhead. A temperature distribution in the rock mass after 4 years of heating is shown in Figure 1. When conducting the analyses, temperature changes between heating times were applied to simulate the heating procedure as a function of time. The thermal expansion coefficients, based on laboratory measurements (CRWMS G&O, 1999), for three rock units modeled are shown in Effigy 2. Information technology can be observed that the thermal expansion coefficients vary more than a gene of v–7 from 25 to 300 EC. Ii rock-mass failure criteria were used in the analyses to examine their effect on the stone-mass responses to the heating process: Mohr-Coulomb and ubiquitous failure criteria. When the ubiquitous failure benchmark was used, fracture sets with dip angles (counterclockwise from the positive horizontal centrality) of 82, 83.five, and 80.5 degrees were assumed for the Tptpul, Tptpmn, and Tptpll units, respectively (CRWMS M&O, 2000). The fracture cohesion, tensile strength, friction angle, and dilation bending were assumed to be 0.1 MPa, 0.0 MPa, 41 degrees, and 20.5 degrees for all three units (CRWMS M&O, 2000).

Figure one. Temperature distribution in the rock mass after four years of heating.

Figure ii. Thermal expansion coefficients of the three stone units.

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Anchor Plates in Multilayer Soil

Hamed Niroumand , Khairul Anuar Kassim , in Blueprint and Construction of Soil Anchor Plates, 2016

nine.2.4 Krishna'south Method

Krishna (2000) investigated the behavior of large size anchor plates in two-layered sand using an explicit two-dimensional finite difference program (FLAC 2D). Soil is assumed to be a Mohr–Coulomb strain softening/hardening material. The geotechnical backdrop of backfill of anchor foundations are very sensitive to construction and compaction methods. There is no satisfactory method to analyze the beliefs of ballast plates in such nonhomogeneous cohesionless soil conditions. The ii-layered soil for this analysis consisted of two cases: (1) a layer of loose sand overlaid by a dumbo sand layer and (two) a layer of dense sand overlaid by a loose sand layer, as shown in Fig. 9.vii. For the analysis he chose sections of Chattahoochee River sand both in dumbo and loose conditions (Vesic and Clough, 1968). In the analyses, the width of the anchor plate (B) was 1   yard and the embedment ratio was varied from 2 to 8. The upper layer thickness (D) is varied from minimum of B to maximum of (D+twoB). The material properties of the anchor plate were kept abiding. It was causeless that the plate was sufficiently stiff as non to bear on the pullout response. Fig. 9.eight shows the variation of width for different D/B ratios. The ultimate pullout capacity changes, with an increment where the bottom layer is dense sand and pinnacle layer is loose sand. Fig. 9.9 shows displacement vectors and plastic regions at failure in layered cohesionless soils.

Figure nine.7. Anchor plate analyzed by Krishna (2000).

Figure 9.8. Ultimate uplift capacity against ratio by Krishna (2000).

Effigy 9.9. Displacement vectors and plastic regions at failure for B=1   m and embedment ratio, D/B = 4 in layered soils in FLAC 2D by Krishna (2000).

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Chaff and Lithosphere Dynamics

E.B. Burov , in Treatise on Geophysics, 2007

half dozen.03.vi.6 Dynamic Stability Analysis Using Straight Numerical Thermomechanical Models

In order to substantiate the growth times of convective instabilities derived from simple glutinous models, and response of the lithosphere to horizontal shortening, Burov and Watts (2006) carried out sensitivity tests using a big-strain thermomechanical numerical model (FLAC-Para(o)voz v9) that allows the equations of mechanical equilibrium for a visco-elasto-plastic plate to be solved for whatsoever prescribed rheological force contour (e.yard., Cundall, 1989; Poliakov et al., 1993). Like models have been used past Toussaint et al. (2004), for example, to determine the office that the geotherm, lower crustal composition, and metamorphic changes in the subducting chaff may play on the evolution of continental standoff zones. Burov and Watts (2006) ran 2 separate serial of tests ( Figures 12 and 13 ) using rheological properties that matched cases with weak pall rheology (crème-brû50ée, Figure iv , left) and potent mantle rheology (jelly-sandwich, Figure 4 , correct), as well equally some intermediate rheology profiles with weak or stiff mantle. The goal of these experiments is to exam what these and intermediate rheology models imply almost the stability of mountain ranges and the structural styles that develop. The following sections bear witness the results of stability tests and continental collision tests.

Effigy 12. Setup of the numerical thermomechanical model aimed to study gravitational mechanical stability of the lithosphere (top) and evolution of continental collision (bottom). The numerical model is based on fully coupled thermomechanical large strain viscoelastoplastic numerical code Paro(a)voz v.9 based on the FLAC algorithm (Cundall, 1989). This lawmaking allows for explicit testing of ductile, brittle, and elastic rheology laws. The models presume a gratuitous upper surface and a hydrostatic boundary condition at the lower surface (depicted past springs in the figure). (a) The stability exam was based on a mountain range of top 5   km and width 200   km that is initially in isostatic equilibrium with a zero-summit 36   km thick crust. The isostatic residuum has been disturbed past applying a horizontal compression to the edges of the lithosphere at a charge per unit of 5   mm   yr⁻¹. The displacements of both the surface topography and Moho were and so tracked through time. (b) The collision exam was based on a continent/continent collision initiated by subduction of a dense, downgoing, oceanic plate. Causeless a normal thickness oceanic chaff is seven   km, a total convergence rate of lx   mm   yr⁻¹, and a serpentinized subducted oceanic crust (Rupke et al., 2002). Rheological backdrop and other parameters are as given in Tables 2 and iii .

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Fundamentals of Discrete Element Methods for Stone Engineering

Lanru Jing , Ove Stephansson , in Developments in Geotechnical Technology, 2007

12.2.4.1 Instance report – Corvara Cliff in Italy

The stability status of the calcareous cliff of Corvara in the Abruzzo Region of Italian republic is used to illustrate a two-dimensional DEM analysis of a natural rock slope (Lanaro et al., 1996). The cliff at Corvara extends for nearly 4   km in the North–S direction, is about 500   m in width and is cutting by a sub-vertical error system that determines a stepped-line shape of the slope, with steep dipping faces and rock battlements. The stone mass consists of calcarenitic, micritic and bioclastic limestones with sub-horizontal bedding and breccias, overthrusted on top of a sandy dirt formation with chalk layers. In addition to the mistake structures, five sets of fractures with boilerplate spacing of 0.1–1.vii   m intersect the cliff. Since the early 1900s, the village, located on the northern corner of the massif, was alleged unstable and moved. From that fourth dimension on, some express toppling and rock falls have occurred in the vicinity of provincial and municipal roads sixty   chiliad below the old town. The predominant instability phenomena of the Corvara cliff are due to the presence of wedge-shaped blocks and tabular prisms defined by major mistake zones and a network of fractures dipping against the slope face. Moreover, the clay germination at the toe of the cliff is subject to creep. Extensive field investigations and laboratory testing have been conducted.

For the numerical modeling of the Corvara cliff, both a discrete element model with deformable blocks using the UDEC lawmaking and a continuum model using the FLAC lawmaking were performed ( Lanaro et al., 1996). A vertical department, oriented Eastward–W, that intersects the meridian of the cliff and the toe of the high face of the slope and encounters the boreholes drilled for field investigations was called for the model constructions (Fig. 12.12). The section comprises faults and traces of the most important sets of fractures that affect the rock mass stability. A aeroplane strain analysis was performed where vertical sides of the model have zero horizontal displacement, the bottom has goose egg vertical deportation and the top surface is gratuitous. To represent in situ conditions, the model was subjected to specified boundary velocity constrains and gravity acceleration. For that purpose the model was given depression deformability (linear elastic) and high strength (Mohr–Coulomb) for both rock materials and fractures. For the FLAC model a ubiquitous cloth model was used to correspond the rock mass with a series of embedded weak zones. On one mitt, the presence of well-defined, weak major faults justifies the distinct cake assumption and use of the DEM and the UDEC code. On the other hand, the big number of fracture sets of small spacing justifies application of an equivalent continuum approach with a ubiquitous material model. In add-on, the results of the discrete modeling are highly conditioned by the blocky structure, so that large blocks may go loose and produce rockslide, raveling and rock fall.

Fig. 12.12. Numerical model of Corvara Cliff, Italy; (a) discrete element model for UDEC analysis; (b) finite difference model for FLAC analysis (Lanaro et al., 1996).

Figure 12.13a shows the block movements by shear forth fractures and plastic yielding indicators from the UDEC model. The layer situated deeper down in the cliff displaces more than slowly, mainly because of retentiveness by the clay formation at the toe of the cliff. The vector of displacements and the contour of the horizontal displacement in the clay formation by the FLAC model are illustrated in Fig. 12.13b. At the contact between the stiff limestone in the cliff and the soft clay formation at the toe, high compressive stresses are generated in the clay formation. The vertical extension of the yielding zones (Fig. 12.14) and the contour of horizontal displacements in the clay formation (Fig. 12.13b) by the FLAC model indicate the formation of circular failure modes. Sliding along the sub-vertical faults is limited and the surface of the cliff is deformed because of differential displacements along the fractures. These observations are in understanding with the observed damage of the old houses in the town of Corvara and at the toe of the cliff.

Fig. 12.thirteen. Deportation results of Corvara cliff, Italy: (a) block movement along fractures by UDEC model; (b) deportation vectors by FLAC model (Lanaro et al., 1996).

Fig. 12.14. Plasticity indicators in modeling the stability of Corvara cliff, Italian republic; (a) shear displacement of joints and yielding zones for the UDEC model; (b) plasticity indicator at yield for the continuous FLAC model (Lanarao et al., 1996).

The computed displacements from the continuous FLAC model are full-bodied at the top of the cliff and almost linearly diminish with depth. Relatively large shear displacements of 4.0 and four.six   cm were obtained along the mistake at the peak of the cliff and at the toe, respectively. Slip and tensile failure along ubiquitous fractures and extension of the plastic yield zone in the dirt germination are illustrated in Fig. 12.14. The absenteeism of a final stable land in the model is governed past the presence of unbalanced forces still acting on the system at the cease of the ciphering.

Information technology may be concluded that both the detached UDEC model and the continuous FLAC model gave reasonable and uniform results and satisfactorily captured the failure modes of the Corvara cliff. Both computations point that the meaning role, which controls the stability of the cliff, is the force and deformability of the clay formation at the toe of the cliff.

The sensitivity of the modeling results for slight variations in fabric properties suggests that the slope is in a limiting equilibrium condition and that pocket-sized amending of the geometry, material properties and groundwater condition tin can have significant effects on the stability. Sliding phenomena are localized at the meridian of the cliff and extend behind it for well-nigh 50   m. Housing located in this zone is invariably subjected to differential movements at the foundation level with severe harm.

I of the characteristics of natural stone slopes is their ability to remain intact at a stage of limited equilibrium. Minor changes in geometry, forcefulness of intact rocks and fractures due to rainfall, snow, water ice, frost heaving, groundwater fluctuation and weathering can crusade instability and result in failure. Consequently, the modeling exercises have to be performed at the very limit of stability and therefore should include sensitivity analyses on the geometry and governing parameters. In addition, the modeler has to solve the trouble of selecting relevant textile properties of intact rocks and fractures for large rock masses, including the scale furnishings. For certain natural rock slopes in mountainous terrain, the loading from the virgin stress field has to be included every bit well. For the majority of cases because gravity loading and consolidation may be sufficient.

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Natural and Engineered Clay Barriers

Jonny Rutqvist , in Developments in Clay Science, 2015

9.4 Coupled THM Evolution of Engineered and Natural Clay Barriers in a Nuclear Waste Repository

In this section, recent simulation results are presented related to a generic repository case bold an EBS blueprint with waste emplacement in horizontal tunnels back-filled with Bent every bit a protective buffer (Figure 9.12). This simulation study was part of the ongoing US Department of Energy, Office of Nuclear Energy's Used Fuel Disposition (UFD) campaign, to investigate current modeling capabilities and to identify problems and knowledge gaps associated with repositories hosted in clay-rock (Rutqvist et al., 2014a ). The modeling was conducted with the TOUGH-FLAC simulator, which, every bit mentioned, is based on linking the multiphase menses and heat transport code TOUGH2 ( Pruess et al., 2011) with the geomechanical simulator FLAC3D (Itasca, 2009). TOUGH-FLAC was originally developed and applied for modeling coupled THM processes in unsaturated fractured tuff (Rutqvist et al., 2002). Information technology has more recently been modified for modeling bentonite and clay host rocks, especially within the United states DOE's UFD campaign. For the modeling of bentonite, the BBM, and most recently, the BExM have been implemented into TOUGH-FLAC (Rutqvist et al., 2011, 2014b).

Figure 9.12. Model domain, numerical filigree, monitoring points, and estrus power function for an assumed bentonite dorsum-filled horizontal emplacement drift at 500m depth in clay host rock (Rutqvist et al., 2014a).

In the study presented here, the geomechanical behavior of the bentonite was modeled with the BBM, using properties corresponding to the FEBEX Bent, whereas dirt host stone backdrop were derived from the Opalinus clay at Mont Terri (Gens et al., 2007). The simulations were conducted in a second airplane strain model every bit shown in Figure 9.12. Because of the repetitive lateral symmetry, the model extends horizontally to the mid-altitude between two emplacement tunnels. In the 2D model, the heat load was scaled and applied as an initial rut load per meter tunnel of 200W. A complete description of the model, input parameters, and results are given in Rutqvist et al. (2014a).

THM simulation results are shown in Figure 9.xiii, including development of temperature, saturation, fluid pressure level, and stress within the buffer. The canister surface temperature peaks at about 91°C afterwards 50 years, whereas the top temperature at the buffer and stone interface is about 77°C (Figure 9.13(a)). The time to full resaturation of the buffer is 25 years, precedes the thermal peak (Figure 9.13(b)). The fluid pressure increases with temperature and peaks at 8.0MPa, significantly higher up the estimated 4.5MPa hydrostatic pressure level (Figure 9.13(c)). This excess fluid force per unit area above hydrostatic is caused past thermal pressurization, as a effect of thermal expansion of the pore fluid that cannot escape in the relatively low-permeability host rock. The backlog pressure is initially dissipated through radial and vertical outflow and inflow of water, which lasts for up to x 000 years until hydrostatic equilibrium pressure level is finally attained after well-nigh 100 000 years. The magnitude and duration of this excess pressure pulse depends on parameters such equally stone permeability, and compressibility of water and rock.

Figure 9.13. Simulated evolution of thermo-hydro-mechanical (THM) processes in the buffer: (a) temperature, (b) liquid saturation, (c) fluid pressure level, and (d) full and effective (or cyberspace) stress in the radial direction. See Figure 9.12 for locations of V1, V2, V3, and V6 (Rutqvist et al., 2014a).

The development of total and effective stress in the vertical management in points V1 and V2 within the buffer, i.e., equivalent to the radial stress at both points is presented in Effigy nine.thirteen(b). The development of total stress in Effigy 9.13(d) results from iii components: (1) swelling stress caused by saturation changes, (2) poroelastic stress from fluid pressure changes under saturated conditions, and (3) thermal stress. During the early on time, the stress in the buffer increase is mainly a result of swelling stress that occurs as a result of reduced suction during saturation of the buffer and is governed by the BBM. In improver, thermal stress is induced within the buffer along with the temperature increase, and after the buffer is fully saturated, poroelastic stress with increasing liquid fluid pressure in the rock causes a substantial stress increment both in the stone and in the buffer. The fact that the stress development in the buffer is strongly afflicted by the thermal pressurization in the rock, shows that in that location is a strong interaction between the buffer and the rock coupled THM processes, and thus, the buffer and stone coupled THM processes cannot be analyzed independently.

The model simulation also shows a complex mechanical evolution of the buffer involving a strong variation in the bulk modulus with stress and suction changes (Effigy nine.xiv(a)). The initial bulk modulus is about 2MPa and peaks at about 200–300MPa (0.2–0.3GPa), i.eastward., more than a 100-fold increase in stiffness. This complex development resulted in a permanent nonuniformity of porosity and buffer density (Figure 9.14(b)). The final porosity of nigh 0.35 at the inner parts of the buffer (V1) corresponds to a dry density of ane.72 kg/dm³, whereas the concluding porosity of about 0.44 at the outer office of the buffer (V2) corresponds to a dry density of i.48 kg/dm^three. This nonuniformity occurred as a result of thermo-hydro-elastic responses in the buffer governed by the BBM.

The Effective stress path (σ′_one vs σ′₃) at point V3 at the summit of the tunnel, as is the yield surface for the rock matrix is presented in Figure 9.fifteen. Actually, most of the rock failure around the tunnel has already occurred during the excavation, both along bedding planes and in the rock matrix betwixt bedding planes. The stress states move along the yield surface, causing some additional plastic yield until i year has elapsed. Afterward one year, the stress state moves abroad from the yield surface every bit a upshot of increasing minimum principal stress (σ′_iii). This minimum principal stress is the radial stress normal to the tunnel wall, which increases as a result of swelling and the associated increment in buffer stress. The stress country and so remains within the elastic region over the unabridged 100 000 year simulation fourth dimension and no further plastic yield takes place.

Effigy 9.15. Effective stress path at indicate V3 located in the rock just above the tunnel with comparing to the yield surface of a Mohr–Coulomb model (Rutqvist et al., 2014a).

The modeling indicated some failure not just on elevation of the tunnel, simply likewise around the entire tunnel wall, in both the intact rock matrix and forth the horizontal bedding planes. The failure zone forth bedding planes extends to nigh 0.4m into the rock at the top and bottom of the tunnel, whereas there is a 0.15m thick zone effectually the entire periphery of the tunnel with both matrix and bedding aeroplane shear failure (Figure 9.16). All the same, despite an anisotropic failure zone developing every bit a consequence of bedding plane orientation, the mechanical response in terms of plastic yield and volumetric strain is compatible around the periphery of the tunnel, with a 2% maximum strain at the tunnel wall. This reflects, first, the fact that the rock can only expand toward the free surface (i.e., the tunnel wall) and 2nd, the fact that the in situ stress was assumed isotropic. Consequently, an EDZ forms as defined in the model simulations every bit the zone in which more meaning plastic strain occurs, in this case 0.15m into the rock. However, the simulation showed that the buffer swelling had the positive effect of increasing the circumscribed stress on the rock wall and thereby prevents farther failure development during the thermal phase.

Effigy ix.sixteen. Volumetric strain profile and extent of failure zones related to horizontal bedding planes and rock matrix (Rutqvist et al., 2014a).

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Numerical modelling of faults

Andreas Henk , in Understanding Faults, 2020

4.2 Numerical methods for hydromechanical fault zone modelling

Several numerical techniques have been used for hydromechanical modelling of fault zones and incorporation of faults into larger models, respectively. The various methods can be grouped in iii main categories, i.due east., continuum- and discontinuum-based numerical techniques also as hybrid (continuum/discontinuum) methods. Each approach has its pros and cons, which will be discussed in the post-obit paragraphs.

At kickoff glance, continuum methods – past the proper name – appear to contradict modelling of a detached discontinuity like a error, but discretization schemes and special element types like contact or interface elements offering possibilities to represent localized deformation and even differential slip, respectively. Among these continuum approaches, the Finite Difference Method (FDM) is a well established numerical method for solving the partial differential equations (PDE'due south) describing hydromechanical processes, i.e., fluid flow and deformation, in rocks (e.g., Smith, 1986; Ramsay and Lisle, 2000; Anderson et al., 2015). Thereby, the differential equations are replaced past difference equations over a sure interval in space and – for time-dependent solutions – also over a sure time interval. This approach requires to subdivide the domain of interest into a filigree of calculation points, so-chosen nodes, which – at to the lowest degree for the standard FDM – take to be distributed regularly (Fig. four.1A). This leads to an important drawback of this method as information technology implies that irregular subsurface geometries and/or lithological distributions cannot be properly represented. Advancements like the full general FDM and special numerical solution schemes too equally further developments similar the Finite Book Method (FVM) can overcome these shortcomings and likewise allow for irregular node distributions (e.1000., Perrone and Kao, 1975; Leveque, 2002). Nonetheless, a limitation remains as the continuity requirement adhered to FDM does non allow for modelling of new discrete fracture formation and fault propagation, respectively. Worked examples of fault zone modelling with FDM take been presented past Cappa (2009) and Zhang et al. (2016), for instance. An established software combination for hydromechanical simulations based on FDM/FVM – but past no means the only i – is the coupling of codes TOUGH (developed at Lawrence Berkeley National Laboratory, U.s.a.) for modelling of multiphase catamenia and of FLAC (Itasca, USA) for geomechanical calculations ( Rutqvist, 2011; Jeanne et al., 2014). Among others, information technology offers the incorporation of several faulting-related features like, strain-softening Coulomb failure and slip-weakening besides equally fault permeability changes (Rutqvist, 2011).

Fig. iv.i. Sketches showing characteristics of the diverse numerical methods with respect to the discretization of the model domain. (A) Application of the standard finite difference method is based on a rectangular grid geometry. (B) The finite element method also offers the use of irregular grids. In addition, contact elements (in gray) tin can be defined at discrete discontinuities, which allows for differential sliding betwixt independently meshed parts of the model. (C) A variant of the detached element method uses private elements with regular shape (e.g., circles in 2d, spheres in 3D) to draw the model geometry. Optionally, these elements tin be bonded together initially (in grey) but can break autonomously during the course of the numerical simulation.

The other nigh normally-used continuum technique for hydromechanical modelling is the Finite Chemical element Method (FEM). Its strengths are the ability to describe complex model geometries and heterogeneous fabric distributions also every bit non-linear material beliefs (due east.one thousand., Zienkiewicz et al., 2013; Simpson, 2017). The principle is to divide or to discretize the entire model domain into numerous elements (Fig. 4.1B). Joint corner points – and boosted mid-side points in case of higher-society elements – ensure the continuity requirement. For each chemical element, so-called ground or trial functions are formulated that represent a local approximation of the underlying PDE'due south. Subsequently, these equations are combined in to a global gear up of equations comprising the unabridged model domain. Boundary weather condition are applied and the entire set of equations is solved based on the principle of minimum potential energy (Zienkiewicz et al., 2013). The upshot is an judge solution for the unabridged model. The quality of the approximation depends – beside the convergence criteria selected – on the ground function used for the chemical element equations (linear vs. higher-order) and the element size and model resolution, respectively. As a continuum method, FEM has similar restrictions regarding modeling of fracturing processes as FDM. Even so, an interesting extension of the classical FEM, also relevant for fault modeling, is the use of so-called interface or contact elements to stand for existing discontinuities, e.g., fractures and/or faults (depending on model scale). These elements tin transmit shear and normal stresses according to the frictional properties (cohesion and angle of friction) assigned to them. Their use allows for differential displacement between independently-discretized parts of the model. However, contact elements have to be incorporated into the initial model geometry at sites of existing discontinuities or where fracturing and relative displacements are expected to occur in the course of the modeling (Fig. 4.1B). Thus, they cannot account for arbitrarily oriented fracture formation. Recent developments like FEM with embedded discontinuities (ED-Fe; e.g., Ibrahimbegovic and Melnyk, 2007) and extended FEM (XFEM; e.thousand., Fries and Belytschko, 2010; Prevost and Sukumar, 2015) aim to overcome these limitations. Some recent examples of fault zone modelling studies based on FEM tin be plant in Pereira et al. (2014) and Schuite et al. (2017).

A discontinuum arroyo that is suitable for error modelling is the Discrete Chemical element Method (DEM). Initially designed for mechanical problems, it has been expanded to also embrace hydromechanical simulations. The basic principle is to separate the model geometry into numerous private elements with regular (e.g., circles in 2D, spheres in 3D) or irregular (e.one thousand., polygons in 2D, polyhedra in 3D) shapes that interact with each other on the basis of contact laws and equations of movement (Fig. 4.1C; e.thou., Cundall, 1971; Lisjak and Grasselli, 2014). The forcefulness of the approach is that the elements tin move relative to each other and that fifty-fifty the contact of elements initially bonded together can break during the class of the simulation. Thus, this numerical technique is well suited for modelling of fractured rock masses as well as of new fracture formation and fault propagation. However, as the discrete elements cannot break internally, fracturing is still controlled by the geometry of the element edges. In addition, the properties derived from standard rock mechanical tests cannot exist used directly but have to be transferred to specific parameters for utilise in the DEM model, which depend on element size and bonding. Examples of hydromechanically-coupled fault modelling based on DEM are provided past Yoon et al. (2015, 2016).

The Combined Finite Discrete Element Method (FEM/DEM) is a rather new development and intends to make employ of the advantages of both numerical techniques (e.thou., Munjiza, 2004; Lisjak and Grasselli, 2014). The approach allows to insert cracks in a formerly continuous model domain based on a failure benchmark and the local stress weather. Thus, information technology is ideal for modelling of fracture formation and propagation independent of any pre-defined contacts or element shapes. In combination with flow simulations the arroyo has been used for modelling of hydraulic fracturing processes (e.g., Profit et al., 2016) and reactivation of faults due to pore pressure reduction (Ferguson et al., 2016), amongst others.

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Slope Failure Machinery and Monitoring Techniques

S.One thousand. Chaulya , G.M. Prasad , in Sensing and Monitoring Technologies for Mines and Chancy Areas, 2016

1.nine.2.two Numerical Modeling

To sympathize the causes of instability of these three dumps, numerical modeling study was carried out. Just details of the report related to Mudidih overburden dump take been presented here. This dump was surveyed past electronic altitude meter for measuring dump geometry. A digital terrain model of the dump was established as shown in Fig. 1.49. The methodologies adopted for the field and laboratory studies are systematically presented in Fig. ane.l.

Fig. 1.49. Three-dimensional view of Mudidih dump.

Fig. 1.50. Menstruation chart of the methodologies adopted for the study.

ane.9.ii.two.1 Modeling Software

Numerical modeling written report was carried out by finite divergence method (FDM). In this method, the whole domain was discretized into pocket-sized 2-dimensional zones (elements) that were interconnected with their grid points (nodes) (Naylor, 1982; Soren et al., 2014 ). Over each zone, the differential equation of equilibrium was approximated. This resulted in a system of simultaneous equations which were solved past iteration methods. A two-dimensional FDM package FLAC version ii.27 (developed by Itasca Consulting Group Inc., USA) was utilized for the analysis.

one.9.2.2.2 Constitutive Model

Mohr Coulomb plasticity constitutive model was used to stand for the behavior of dump materials. This model assumes an rubberband, perfectly plastic solid in airplane strain that conforms to a Mohr-Coulomb yield condition and nonassociated menstruation rule.

The yield surface (f) is given by:

(ane.2) $f={\sigma }_{\mathrm{i}}-N_{\varphi }{\sigma }_2+2c{\left(N_{\varphi }\right)}^{\mathrm{one}/2}$

and the plastic potential function (thou) is given by:

(i.3) $g={\sigma }_{\mathrm{i}}-{\mathrm{Northward}}_{\psi }{\sigma }_2+\mathrm{ii}c{\left(N_{\psi }\right)}^{\mathrm{one}/2}$

where, N_ξ   =   (i   +   sin ξ)/(1   −   sin ξ) $\left[\xi =\varphi \mathrm{or}\psi \right]$ , c  =   cohesion (positive sign), ϕ is friction bending, ψ is dilation bending, σ ₁ is major main stress, σ ₂ is minor primary stress.

The strain increments are causeless to be composed of elastic and plastic parts:

(ane.4) $\mathrm{\Delta }{\mathrm{eastward}}_1={\mathrm{\Delta }e}_{\mathrm{one}}^{\mathrm{eastward}}+{\mathrm{\Delta }e}_1^{\mathrm{p}}$

(ane.v) $\mathrm{\Delta }{e}_2={\mathrm{\Delta }e}_{\mathrm{two}}^{\mathrm{e}}+{\mathrm{\Delta }e}_2^{\mathrm{p}}$

The plastic strain rates are given past the nonassociated menstruum dominion:

(1.6) $e_1^{\mathrm{p}}=\lambda \partial g/\partial {\sigma }_{\mathrm{ane}}=\lambda$

(1.7) $e_2^{\mathrm{p}}=\lambda \partial \mathrm{thou}/\partial {\sigma }_{\mathrm{ii}}=–\lambda {\mathrm{North}}_{\psi }$

where λ is the multiplier which is determined from the stress country.

ane.9.2.ii.three Shear Force Properties

Shear strength properties of dump material play a vital function in the dump stability. Determination of reliable shear strength values is a critical part of any dump slope design and a small-scale variation in it tin can upshot in significant change in the dump slope stability. For most of the evaluation regarding the stability on dump slope, information technology is necessary to utilize failure relationship, which is a direct line as shown in Fig. i.51 and is as well known every bit Mohr Coulomb failure law (Lambe and Whitman, 1979). Shear strength, which is defined as the maximum resistance to shear stress, is expressed as:

Fig. one.51. Relation between normal and shear stresses during sliding stage.

(1.8) $\tau =c+\sigma tan\varphi$

where τ is shear strength (kg/cm²), c is cohesive strength (kg/cmⁱⁱ), σ is normal stress (kg/cm²), and ϕ is angle of internal friction (degree).

Shear strength of spoil textile decreases with decrease of cohesive strength while normal stress and angle of internal friction remain same (Chaulya, 1993). This decrease in shear strength reduces stability of dump. Shear strength of spoil textile as well decreases equally the angle of internal friction decreases, which in turn reduces stability of the dump.

1.9.2.2.4 Gene of Safe

The critical approach for evaluating the stability of slopes is to make up one's mind the FOS, which is generally defined as the ratio of bachelor shear force of the dump material to the shear resistance required to maintain equilibrium. FOS may also exist defined every bit that cistron by which the shear strength parameters must be reduced in gild to bring the potential failure mass into a state of limiting equilibrium. When the material has both cohesion (c) and friction (ϕ), it is usual to apply the same factor to c and tan ϕ. Denoting the reduced parameters by an asterisk (*) and the factor by λ:

(1.9) $c⁎=\frac{c}{\lambda }$

(i.10) $tan\varphi ⁎=tan\varphi /\lambda$

λ  =   FOS, when c* and ϕ* are associated with incipient failure.

i.9.2.2.5 Physicochemical Properties of Dump Fabric

Field and laboratory studies were conducted to determine the physicomechanical properties of dump fabric by standard methods. X samples from different locations of the dump slope were collected and analyzed separately.

ane.9.ii.2.6 In Situ Jack Shear Test

In situ shear strength backdrop of the dump materials were found out by in situ jack shear test method as described past Anand and Rao (1967) and Haribar et al. (1986), and subsequently studied by Singh (1992), Chaulya (1997, 2011), and Chaulya et al. (1999, 2000, 2001). These tests were repeated v times. A block of known dimension (forty   cm in height, 80   cm in width, and 100   cm in length) was made and pushed gradually to fail by a fixed-reaction confront (Fig. 1.52). The observation was recorded at diverse stages of failure. The loading face of the block was kept at a altitude equal to the full length of the equipment assembly. The sides of the exam block were separated from the main soil mass by a narrow cutting of 15–20   cm width to the full depth and loosely backfilled by the excavated soil (Fig. 1.52). Both reaction faces of the pit and the test block were kept vertical so that the load applied was horizontal.

Fig. 1.52. In situ jack shear test diagram.

The shear jack assembly was lowered in the pit and put into the testing position. The load was applied in increments of 0.5   t. It was maintained for a period of 10–fifteen   min, afterward which the load was increased to the next phase. It was noticed that after the application of some load, the block of soil started moving up forth a sliding plane that exhibited cracks and heaving of the failed material. The application of load was continued until the examination block moved by a distance of approximately 10   cm horizontally. Loads at the commencement of movement (P _max) and at the time when block moved by 10   cm (P _min) were recorded. Subsequently the test, the assembly was taken out from the pit. The true shape of the sliding surface was determined past removing the soil that sheared off forth the sliding airplane. After the removal of failed soil, the depth of the failure surface was measured at three locations along the width of the block and at every 10   cm interval along the length of the block. The average value of the depth (h), which was measured at three locations, was used to determine the shear strength parameters [cohesion (c) and angle of internal friction (ϕ)]. These were determined as discussed beneath.

A cross section, every bit shown in Fig. 1.52, was drawn for all the pits tested by making utilise of the average depth of the sliding surface. Information technology was further subdivided into suitable number of slices. The weight of each slice (west) and length (I) along the sliding plane were adamant. Further, the weight of the whole sliding mass (W) was determined from following equations:

(ane.11) $\mathrm{due\; west}=\gamma h_{\mathrm{m}}xb$

(1.12) $\mathrm{Due\; west}={\displaystyle {\sum }_i^n{w}_{\mathrm{due\; north}}}$

where h _yard is mid-pinnacle of the slice (yard), γ is unit of measurement weight (t/grand³), x is width of the slice (m), b is width of the test block (ie, 0.8   m), and northward is number of slices.

Using the value of P _max, P _min, lengths, and weight of slices, the values of cohesion (c) and friction angle (ϕ) were calculated from the following equations:

(1.xiii) $c=\left(P_{\text{max}}–P_{\text{min}}\right)/\left(bX\right)$

where P _max is load at the start of the movement, P _min is load at the fourth dimension when the block moved by 10   cm

(i.14) $tan\varphi =\left\{\left(mA\right)–B–\left(cX\right)\right\}/\left\{\left(mB\right)+A\right\}$

where m  = P _max/(bW), A  = W cos θ _n, B  = W sin θ _n, $X={\displaystyle {\sum }_i^{\mathrm{due\; north}}{\mathrm{ten}}_{\mathrm{north}}}$ .

1.ix.2.2.7 Conception of Models

Mohr Coulomb plasticity constitutive model was used to represent the behavior of dump materials every bit discussed before. The whole domain was assigned with same properties equally measured in the respective field to simulate the natural dump material (Fig. 1.53).

Fig. i.53. Geometry of the dump used for numerical modeling with boundary conditions.

Slope angle and height of Mudidih dump were observed to be 35 degrees and 30   m, respectively. Base length of seventy   m was selected considering the geometry of the dump and influence of stress. Whole domain was discretized into two different sizes of two-dimensional elements. Fine elements of 0.v   ×   0.5   k size for the slope surface area and those of 0.v   ×   two   m size for rest of the expanse were selected. The boundary weather were applied equally roller boundary (ie, displacement in vertical management keeping horizontal management fixed) along the rear side of the dump and stock-still boundary (ie, no displacement past horizontal and vertical directions) along the base of operations (Fig. 1.53).

1.ix.two.ii.viii Results and Discussions

Results of in situ jack shear tests are presented in Table 1.twenty. Contours of Mohr Coulomb FOS are illustrated in Fig. 1.54, which shows minimum FOS is 1.2. Results of numerical modeling have indicated that maximum displacement of elements occurs most the crest of the dump, that is, meridian portion of slope (Figs. 1.55 and 1.56). Therefore, whatever dump deformation monitoring program should exist planned near the crest of the dump slopes, as dump failure mostly occurs later on meaning movement over a long time (British Columbia Mine Waste Rock Dump Research Committee, 1991a). Thus, for a large dump with long dump gradient and swell top continuous monitoring of dump deformation is essential.

Table 1.20. Results of In Situ Jack Shear Test

Parameters	Unit	Natural Dump Material
Cohesion (c)	kN/kii	64 (±   4)
Angle of internal friction (ϕ)	degree	32 (±   1.5)

Fig. 1.54. FOS of Mudidih dump.

Fig. 1.55. Displacement vector of different elements of dump.

Fig. i.56. Displacement in Y direction of different portions of the dump.

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