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... To this end, the present study is investigating the effect of the shape of the cross section on time-dependent behavior, stability, and deformation of tunnels by numerical analysis. These cross sections are numerically modeled in FLAC and Burgers-creep viscous (CVISC) model [28] is used to investigate the time behavior of the tunnel. ...
... The visco-elastic and plastic strain-rate components are assumed to act in series. The properties needed for this constitutive model are: bulk modulus (K), Kelvin shear modulus (G k ), Kelvin viscosity (ɳ k ), Maxwell shear modulus (G M ), Maxwell viscosity (ɳ M ), cohesion (c), internal angle of friction (φ), dilation angle (ψ), and tension limit (σt) [28]. In this model, the deviatoric behavior is given by: ...
... where g is the plastic potential function, 1 and 3 are the major and minor principal stresses, ψ dilation angle. λ * is a plastic multiplier that is nonzero during plastic flow only which is determined by the application of the plastic yield condition f=0 [28]. ...
Time-dependent behaviors of the tunnel have challenged researchers for recent years. In this study, time-dependent behaviors of two types of tunnel shapes including the D-shaped and circular tunnel which are most common in tunnel design are investigated by numerical modelling. To this end, the finite difference software FLAC 2D and the Burger creep visco-plastic (Cvisc) model are employed. The results revealed that ground squeezing in terms of tunnel displacement of the D-shaped tunnel is much larger than the displacement of the circular tunnel in 2000 days after excavation. By comparing the convergence of the tunnel wall and roof of both sections in the hydrostatic stress state condition, it is found that the displacement of the D-shaped tunnel wall is 1.3 times larger than the displacement of the D-shaped tunnel roof, however, this ratio is about 0.96 in the circular tunnel. When the different lateral pressure is modeled, both tunnels behave differently and the ratio of the displacement of the tunnel wall to the displacement of the tunnel roof vividly is changed. In the present study, an equation is also developed to predict the time behavior of tunnels which takes both the lateral earth pressure effect and shape of tunnels into account.
... The current study is restricted to the plane-strain case of a long void using the FDM program 2DFLAC (Itasca 2011). The veracity of the general numerical approach is first examined by comparing FDM numerical results with measured results from a field test reported by Villard and Briançon (2008). ...
... Before carrying out the suite of numerical experiments that are the main outcome of the current study, the general FDM numerical approach using program 2DFLAC (Itasca 2011) was checked against the results of a full-scale test reported by Villard and Briançon (2008) and Villard et al. (2009). Lessons learned to achieve a good match between the FDM model of their test and the measured performance were then carried over to the numerical models used later in the current study. ...
... The numerical grid points were spaced at 0.02 m and the reinforcement was composed of 500 FLAC cable elements. The model was executed in large-strain mode (i.e., mesh updating) (see Itasca 2011) and solved to reach force equilibrium. The numerical grid was wished in place (i.e., modelling the fill construction sequence was not necessary). ...
The problem of a reinforced fill over a void has been the subject of much research in the geosynthetics literature. Previous studies have mainly focused on finding closed-form solutions to predict the tensile loads and strains in the reinforcement layer once a void develops below the fill. In this paper, a 2D finite difference (FLAC) model that implements the hyperbolic isochronous load-strain model for the reinforcement by Bathurst and Naftchali (2021) is used to investigate the influence of the rate-dependent properties of polymeric geosynthetic reinforcement materials on reinforcement tensile strains and load, and overall system performance including vertical deformation at the reinforcement elevation and at the fill surface. The paper also investigates the influence of fill soil properties and constitutive model type, foundation condition, void geometry and fill height on system performance. The results of numerical modelling are compared to predictions made using the closed-form solution of Giroud et al. (1990) and in the BSI 8006-1 (2010) design code. The results of numerical modelling demonstrate that the choice of fill height to void width and the stiffness of the rate-dependent geosynthetic reinforcement layer are important to ensure that the maximum reinforcement strain, allowable strength and fill surface settlement criteria are not exceeded.
... Dynamic analyses in total stress conditions has been carried out by using some of the most popular computer codes: STRATA (Kottke et al. 2018), which adopts the equivalent linear approach, DEEPSOIL (Hashash et al. 2020) and FLAC (Itasca, 2020) which perform nonlinear analyses in the time domain. ...
... Effective stress dynamic analyses according to the fully coupled approach have been performed by adopting the critical state compatible, stress ratio-based, bounding surface plasticity constitutive model (PM4Sand), in the last released 3.2 version (Boulanger and Ziotopoulou 2022), implemented in the commercial finite difference platform FLAC (Itasca 2020). For further comparison, and only for the 16 m soil column model, effective stress analyses according to the loosely coupled approach have been also performed by adopting simplified pore water pressure models. ...
The capability to correctly predict the liquefaction occurrence with numerical models is fundamental for the adequate design or verification of strategic structures and infrastructures under seismic conditions. Earthquake records provided by vertical liquefaction arrays constitute a powerful tool to verify the goodness and limitations of constitutive models. In this context, the recorded motions of the 1995 Kobe earthquake carried out by the instrumented vertical array located in Port Island (Japan) were used to assess the performance of several constitutive models able to predict the occurrence of liquefaction in the last three decades. This paper tries to retrace the history of the Port Island vertical array and the main contributions derived from the interpretation and modelling of the seismic records of the 1995 Kobe earthquake. Then, the study focuses on the on the simulation of the seismic response of the instrumented soil column of the array by using some of the most popular numerical models according to a loosely coupled and fully coupled approach for effective stress analysis. Also total stress analyses are performed for comparison. Special attention is devoted to model the dynamic behaviour of the man-made gravelly deposit that liquefied during the seismic event, and the related model calibration, which is based on the results of in-situ and laboratory tests. The results enrich the discussion on the numerical reproducibility of the seismic behaviour of gravelly soils which are largely adopted in man-made geo-structures, such as reclaimed ports and embankment dams.
... This study aims to numerically investigate the influence of ground motion parameters such as peak ground acceleration (PGA), Arias intensity (Ia), total duration (TD) and significant duration (TSD) on pipe uplift for shallow-buried pipes in loose, saturated sand deposit subjected to both synthetic, harmonic and recorded earthquake input motions. A well-calibrated 2D numerical framework is developed employing the numerical platform FLAC v8.1 (Itasca 2016) and the constitutive model PM4Sand v3.1 (Boulanger and Ziotopoulou 2017) considering Fraser River sand (called FRS hereafter), abundantly found in the Lower Mainland region of British Columbia, Canada, as the soil material for the study. BC Lower Mainland is situated in an active seismic zone underlain by soils that are susceptible to liquefaction, and many buried pipelines traverse the region. ...
... A soil-pipe interface friction angle of 23 º (2/3 rd of the critical state friction angle, ′ ) was used that was similar to what Chian et al. (2014) used in their pipe uplift study. The normal and shear stiffnesses for the interface were set to 3.1 GPa, which was approximately equal to 10 times the stiffness of the neighboring soil, as recommended in the FLAC User Manual (Itasca 2016). ...
Soil liquefaction occurring due to earthquakes poses severe risk to both above-ground structures as well as buried structures such as pipes, manholes etc. During liquefaction, the shear strength of the soil above and around the pipeline could decrease due to build-up of excess pore pressures and, subsequently, resulting in buoyancy forces that could cause the pipelines to displace and potentially “float up” towards the ground surface. Limit-equilibrium based procedures allow for prediction of uplift occurrence, but predicting the magnitude of uplift is a complex task with a number of components such as soil type, pipe diameter (D) and burial depth (H), pipe boundary constraints, and earthquake motion contributing to this mechanism. This study utilizes a well-calibrated and validated 2D numerical model to investigate the effects of input motion characteristics on pipe uplift for a steel pipe buried in a saturated, loose, and homogeneous deposit of Fraser River sand. The commercially available finite difference FLAC software and soil constitutive model PM4Sand were utilized. The influence of input motion amplitude and duration on uplift behavior of pipe was examined and discussed.
... Numerical modeling simulates the comprehensive interaction of structure, rock rupture, and fluid flow in a hydrothermal mineral system by a series of partial differential equations (Zhang et al., 2007;Gessner, 2009;Chi and Xue, 2011;Itasca, 2012). Such modeling can improve quantitative understanding of these processes, provide new insights into ore deposit genesis, and further contribute to predicting sites of exploration targets . ...
... The finite difference code FLAC 3D (Fast Lagrangian Analysis of Continua in Three Dimensions; Itasca, 2012) was used to investigate the response of rock changes and fluid flow to regional tectonic deformation (McLellan and Oliver, 2008). FLAC 3D is a 3D explicit Lagrangian finite-volume code, capable of simulating tectonic deformation, thermal convection, fluid flow, and the coupling between these processes in various ore-forming systems (Oliver et al., 2006;Leader et al., 2012;Zhang et al., 2013;Wilson and Leader, 2014;Li et al., 2017aEldursi et al., 2018Eldursi et al., , 2021. ...
Hydrothermal disseminated gold mineralization in the Sanshandao gold belt, Jiaodong Peninsula, China, is closely associated with regional NE–NNE fault zones. To investigate the structural controls on this mineralization, we conducted 3D numerical modeling of coupled heat transport, tectonic deformation, and fluid flow, of which two sets of models, designed simple models and actual models, were involved. The simple models were used to examine how general fault geometries (fault bend length, fault bend angle, and fault dip) influenced dilation (positive volume strain) and fluid flow and further influenced hydrothermal mineralization. In contrast, actual modeling was carried out to further understand the structural controls and mineralization localization in a specific geological condition at Sanshandao. Following this, numerical simulation experiments with variable paleo-stresses on these two models were carried out in FLAC3D platform. The simulation results of the simple models showed that long fault bend lengths, large absolute fault bend angles, and large changes in fault dip were more likely to promote dilation in the fault zone. The dilation zones are related to the small intersection angle of maximum principal stress and fault dip. The simulation results of the actual model illustrate that the gold mineralization distribution at Sanshandao was controlled by the coupling of fault strike–dip bends. Specifically, the discontinuous mineralization in the vertical direction was caused by local fluid focusing due to fault dip changes, particularly where the bend length was long. In addition, the oblique orientation of ore shooting depended on the variable strain orientations relative to the fault, which appeared to be fault strike variations. The results further determined the NNW–SSE-directed compression as the paleo-stress regime at Sanshandao during the ore-forming period. Our data also illustrated the deep fluid flow pathways in the Sanshandao gold belt and the Xinli S–SSE deep and the Sanshandao and Beibuhaiyu E–NE deep areas deserve to be the focus of the next gold exploration.
... In this study, the cable element available in the library of FLAC is employed for modeling the geogrid reinforcements. The incremental axial load in the cable element at each timestep is calculated: (Itasca 2011) where E denotes the elastic modulus; L = length; A r = area of the cross-section; ∆u t = incremental axial displacement; J t (ε,t) = Tangent stiffness; t = time; ε = strain. Since the tangential stiffness of the geogrid J t (ε,t) is the function of strain and time, the following hyperbolic constitutive law that is a strain-time dependent model was used to simulate the response of geogrids: where χ (t) is empirical fitting parameter; J 0 (t) = initial tangent stiffness. ...
... In FLAC, the shear and normal spring-slider systems are used to simulate the interface elements. The Coulomb shear-strength criterion (Itasca 2011) is used for determining the maximum shear force along all interfaces. Table 3 lists the interface parameters used in the validation model. ...
This paper evaluates the back-to-back MSE (BBMSE) walls’ performance under the action of self-weight and railway loading. To reach this aim, the two-dimensional finite difference method (FDM) was implemented to mimic the performance of the geogrid-soil system. For representing the material behavior of geogrid reinforcement, the hyperbolic time-strain-dependent constitutive model was adopted. Concerning the soil constitutive relations, the modified Duncan-Chang (D-C) model along with Mohr–Coulomb (M-C) failure criterion was used. The numerical model was initially validated in comparison with measured data from the instrumented full-scale laboratory wall. Subsequently, a parametric investigation was done to assess the effect of some contributing factors, including connecting the reinforcements of two opposite walls, the vertical space of the reinforcements, and reinforcement stiffness. The results obtained from the simulation of BBMSE walls under self-weight loading indicated that the geogrid connection reduces the horizontal facing displacements. The maximum geogrid strains distribution along the height of the wall, in both unconnected and connected cases, was found to be almost the same. The simulation results also revealed that connecting the reinforcements, as a cost-effective and safe method, improved the behavior of BBMSE walls under railway loading, including reducing the horizontal facing displacements and ballast settlements. The findings of the various parametric studies revealed that the reinforcement connection reduced horizontal facing displacements by 21 to 29% and reduced the ballast settlements by the amount of 18 to 26%, depending upon geogrid stiffness and vertical spacing of the reinforcements.
... As part of the foundation design of an offshore wind farm primarily underlain by sequences of dense sands and silty sands, a series of 3D cyclic time history numerical analyses were performed to provide insights on the soil behavior and the potential conservatisms or uncertainties included in the simplified approaches widely used in practice. The analyses employed the finite difference code FLAC3D v7.0 (Itasca, 2019) in combination with the Ta-Ger constitutive model Gerolymos, 2016a, 2016b). Aiming to explore the effects of drainage, analyses were performed for different stratigraphies and assumptions regarding pore fluid flow. ...
... The analyses were performed with the finite difference code FLAC3D v7.0 (Itasca, 2019). FLAC3D employs an explicit solution algorithm that is more efficient for highly nonlinear problems and advanced constitutive models as it does not require the assembly of a global stiffness matrix. ...
... The examples used in this paper are based on the SR-18 geogrid MSE walls reported by Allen and Bathurst (2014a,b;Bathurst and Allen 2021). These walls were chosen because the properties of the component materials are well documented and good agreement was demonstrated between measured wall deformations and reinforcement loads at end of construction, and numerical model predictions by Yu et al. (2016) using the finite difference method program FLAC 2D (Itasca 2011). The measured and numerical predicted load values were also judged to be in good agreement with the stiffness method predictions for Tmax using Equation 1. ...
... Numerical analyses were carried out using the program FLAC 2D (Itasca 2011). Figure 3 shows the numerical domain. ...
... An interface friction angle of = 0.67 tan , and zero cohesion was assigned to the soil-foundation interface. The shear and normal stiffness of the interface were set to ten times the equivalent stiffness of the stiffest soil zone (Itasca, 2008). The equivalent stiffness is calculated as ...
... The cables in FLAC 3D interact with the grid through grout material, the behavior of which is controlled by four parameters. These parameters are: (i) the grout stiffness ( ), a value of 1 MPa, selected from previous works (Chen et al., 2021;Yu and Bathurst, 2017), was assigned to ; (ii) the grout cohesive strength ( ), which was calculated using the formula (Chen et al., 2021;Itasca, 2008), where is the exposed perimeter of cable element, and is soil cohesion; (iii) the grout friction angle ( ) determined using the formula = 0.67 ; and (iv) the effective confining stress, ( ), which is computed internally by the software. ...
The use of geogrid reinforcement has proven to be an effective measure to improve the anchor uplift capacity. However, previous studies are limited to analyzing the axial pullout capacity of plate anchors. In comparison, the anchor foundations employed in field are compelled to resist both uplift and lateral forces. In most cases, the foundation's safety against lateral forces dictates the design criteria for tall structures. Therefore, improving the foundation's lateral load-bearing capacity is of utmost importance. This paper presents a three-dimensional numerical analysis of anchor foundations in geogrid-reinforced sand under uplift and lateral forces. The results highlight the benefits of geogrid reinforcement on the anchor's uplift and lateral load response. The geogrid reinforcement is modelled using cable elements capturing the actual apertures responsible for tensile force mobilization along the geogrid ribs. A significant reduction in the displacements of the anchor foundation is observed in geogrid-reinforced sand, both in horizontal and vertical directions, when combined loads are applied on the anchor. However, the maximum reduction is found in the case of vertical uplift forces for higher values of the applied load. The practical implication of this study is demonstrated using a performance-based design example of transmission tower foundations in geogrid-reinforced sand.
... where ψ is the dilation angle, elastic guess of principal stresses σ I 1 , σ I 3 are computed by adding to the stress components, increments calculated by application of Hooke's law to the total strain increments during the implementation of the Mohr-Coulomb model in FLAC3D (Itasca, 2020), α 1 and α 2 are material constants defined in terms of the shear modulus G and bulk modulus K, as ...
... To achieve thermo-mechanical coupling, both the mechanical model and the thermal isotropic model are assigned to each element. The equations provide the thermal strain increments (Δε mn ) associated with the free expansion due to temperature changes and the stress change (Δσ mn ) in a given zone as follows (Itasca, 2020): ...
Understanding thermo-mechanical behavior of granite under triaxial stress and ultrahigh heating rates is essential for advancing the flame-assisted drilling technique in geothermal systems. To address the challenge of real-time crack observations at high temperatures, we have developed a finite difference model that replicates grain-scale heterogeneities and incorporates a modified strain-softening law of granite subjected to various triaxial pressures (ranging from 10 to 90 MPa) and temperatures (from 25 to 300 • C). Using the calibrated model, we investigated the thermo-mechanical coupling mechanism of granite under high temperatures and triaxial pressures, along with the impact of ultrahigh heating rates (up to 600 • C/min) through a series of numerical simulations. Our simulation results, supported by laboratory observations, reveal that the combined effects of sample dimensions, heating rates, and confining pressures intricately shape the resulting patterns of cracking and internal structural modifications in the samples. Among the studied factors, confining pressure plays a central role in influencing thermal-induced cracking behaviors, contributing to the modification of crack patterns. These findings provide a fundamental understanding that can help address challenges related to thermal-assisted rock breaking techniques, thus holding great significance for the new and efficient well construction technologies in geothermal engineering.
... Nonlinear dynamic analyses of a 1D column were performed using the finite difference program FLAC 8.1 (Itasca 2019) and the user-defined constitutive models PM4Silt (Boulanger and Ziotopoulou 2019) and PM4Sand (Ziotopoulou and Boulanger 2016). ...
This paper presents a numerical investigation of the impacts of post-peak strength loss on ground motion amplification and reduction for a soil column with a layer of strain-softening clay. Stress attenuation and amplification were modeled with a one-dimensional soil column using the finite difference program FLAC 8.1 with the PM4Silt constitutive model. Three calibrations of an idealized soil were developed consisting of different rates and magnitudes of post-peak strength loss. Alternative column geometries were devised, each with different clay layers thicknesses to establish how ground surface motions were affected. Impacts were quantified using both a cumulative ground motion intensity (Arias Intensity) as well as different spectral components (base to surface transfer function). The results illustrate that the thickness of the clay layer surface and strength loss in the layer have an impact on the magnitude and frequency content of the earthquake motion measured at the ground surface. The impact of these results on practice and future research needs are presented.
... The Ta 3D time-history analyses were performed to evaluate single bucket performance under the application of a sustained cyclic tension load in FLAC 3D (Itasca, 2020). Fully -coupled effective stress numerical analyses were performed, where the full coupling between the deformable porous soil skeleton and the viscous fluid flowing within the pore space is modeled. ...
Suction buckets supporting a tripod jacket structure can be subjected to sustained tension loading during storm loading. The long-period content of the storm loading combined with its cyclic nature, can lead to partial drainage conditions where generation of excess pore pressure competes with dissipation during loading, resulting in complex response mechanisms. These mechanisms, associated with sand-like behavior, are rarely considered in design which are typically based on binary assumptions regarding drainage, fully undrained or fully drained, and unity checks comparing an estimated degraded capacity to peak storm loads. In this paper, numerical time-history, effective-stress, coupled-flow analyses of a single suction bucket under storm loading were performed in the finite-difference code FLAC3D. The irregular load time history applied corresponds to a 600-second window where the highest tension loads are observed. The Ta-Ger constitutive model was used for the cohesionless soils, calibrated against undrained CDSS tests. Sensitivity analyses on drainage conditions and model calibration parameters affecting the drained response showed that drainage effects are important for design optimization. Moreover, it was shown that the sequence of the pulses within a time-history can have a significant impact on system deformations.
... To obtain the ground motion database related to the slope sites, 760 two-dimensional slope models are established using the finite-volume code FLAC 7.0 (Itasca 2011). The schematic diagram, boundary conditions and dimensions of the slope models are shown in Fig. 1. ...
Slopes have a significant impact on the ground motion characteristics, which can aggravate the damage degree of building structures during a strong earthquake. However, many studies have focused on the design response spectra under flat site conditions and fewer researchers have investigated the impact of slope topography on the design response spectra. In this study, the numerical simulation is used to obtain the seismic response of slopes and the differential evolution algorithm is used to obtain the standardized response spectra of the acceleration time histories along the ground surface behind the slope crest. The impacts of slope height (H), slope gradient (i), average shear wave velocity in the top 30 m (VS30) and distance from the slope crest (x) on the characteristic parameters of the design response spectra are then investigated. The results show that H, i, VS30 and x have a little influence on the normalized second inflection point period (mean(Tg/Tg,ff)) but a great influence on the normalized plateau value (mean(αmax/αmax,ff)). Specifically, both mean(Tg/Tg,ff) and mean(αmax/αmax,ff) show a trend from increasing first to decreasing and stabilizing finally as x increases; the mean(αmax/αmax,ff) shows an increasing trend as H increases, but a decreasing trend as i or VS30 increases. Finally, to provide some guidance for the seismic design of building structures near slopes, two approximate relationships are proposed: (1) between mean(Tg/Tg,ff) and x, and (2) between mean(αmax/αmax,ff) and H, i, VS30, x. The main innovation of this paper is that the relationship between the characteristic parameters of the design response spectra and the slope site characteristic parameters is clearly summarized and quantified for the first time.
... Tv=mQi Ovv=t l=N QO`tW MU=B 'u= Q=mty w Q=mQU [23] "OvOQm |UQQ@ = Qov=wQ l=N QO`tW |m}t=v}O u=Wv j}kLD u}= G}=Dv "OvOQm |UQQ@ u}tR hrDNt C=mQL QF= CLD = Q = Qov=wQ l=N ?; Q=Wi ?} Q[ R= |Y=N Q}O=kt QO`tW QO xOW O=H}= |wQ}v QFm =OL xm O=O |Oa@ xU |R=UpOt R= xO=iDU= =@ 'j}kLD u}= QO [24] "OwW|t p=ta= Ru |=xQiL QF= |UQQ@ x@ '`tW l=N VvmQOv= uDiQo Q_v QO =@ w FLAC 3D Q= Ri=sQv =@ xDN=OQB = Qov=wQ l=N QO`tW MU=B Q@ l}ORv xRwL |=yxrRrR R= |W=v |=yTr=B u=tR COt QO O=}R |SQv= p=ta= p}rO x@ Tr=B QF= xm CU= Qm P x@ sRq "CU= xOW "CU= |O=}R C}ty= |= Q=O sm |OOa |R=UpOt "2 xNUv FLAC 3D Q= Ri=sQv w OwOLt p[=iD VwQ R= xO=iDU= =@ |OOa |R=UpOt w l=N VN@ wO pt=W xOW xDiQo Q_v QO |OOa pOt [25] "OW s=Hv= 7.0.142 xOW s=Hv= 'VELACS xSwQB R= 1 xQ=tW Sw}i}QDv=U pOt V}=tR; QO xm CU=`tW QO |OOa pOt x@ \w@Qt O=a@= w C=YNWt "CU= xOW xO=iDU= ' [26] [27] uUr} w j}kLD QO xOW xDiQo Q_v QO O=a@= '=DU= Q u}= QO "OvQ}ov Q= Qk VvD Q}F -=D [28] "DM04 w P2Psand pOt wO \@=wQ xU}=kt "1 pwOH ...
... The explicit finite-difference software FLAC 3D [29] was used to execute both the deterministic and probabilistic analyses of the problem. The square and rectangular footings (having B = 1 m) were considered to be rough and rigid, resting on the surface of the granular soil deposit. ...
The present study explores the effect of rotational anisotropy on the bearing capacity responses of the square and rectangular footings using the random finite difference method (RFDM) and Monte Carlo simulation (MCS) technique. Three different aspect ratios (i.e., L/B = 1, 2, and 3) are considered in this study. The lognormal distribution is chosen for the spatial distribution of the tangent of the friction angle. The probabilistic bearing capacity response (μNγ) and the failure probability (pf) of the footings are obtained for different angles of rotation of the soil strata (β) considering different orientations of the footings. The probabilistic results are presented in the form of PDF and CDF for different β and L/B ratios of the footing. The desired safety factors (FSr) corresponding to a specific target failure probability (say pft = 0.01%) are also evaluated for different β. It is found that the orientation of the rectangular footings with respect to the strike direction of the soil strata has significant effects on the μNγ and pf of the footings.
... The data for the artificial neural networks is acquired via numerical simulations carried out with FLAC3D [74], an explicit Lagrangian finite-volume program for engineering mechanics computation, widely adopted in geotechnics. ...
Tunnelling-induced settlement is usually estimated based on field data. However, the data are representative of the local study area only depending on such parameters as geology setting and tunnel geometry. Moreover, the number of training data samples is also limited. In this study, surrogate models are developed to account for the variation of the tunnel parameters, so that they are representative of many types of conditions. The data is generated with numerical simulations by employing the Hardening Soil Model and considering various stress reduction factors. Exploiting their pattern recognition capabilities, single and multi-output artificial neural networks are trained to predict the maximum settlement and the trough width. The networks employ only 10 features and return very accurate predictions with a coefficient of determination generally higher than 90%. The network architecture, activation functions and weight initialisers are optimised by grid search. The relative importance of the various features is also studied. A computer script is provided to predict the settlement and trough width with custom input data based on the trained networks.
... We exported the "within" acceleration Geo-Congress 2024 GSP 349 400 time history at a depth of 10 meters below the contact between the lower alluvium and the soft bedrock, consistent with the location of seismic loading application in the numerical model. Kuhlemeyer and Lysmer (1973) showed that for accurate representation of wave transmission though a model, the spatial element (zone) size, Δl, must be smaller than approximately one-tenth to one-eighth of the wavelength associated with the highest frequency component of the input wave (Itasca 2016). Given the dimensions of the model, approximately 680 meters in width, 108 meters in depth, and the ground motion band-pass filtering higher bound of 25 Hz of the recordings, approximately 50,000 zones would be needed in the model, which would render the analytical effort impractical. ...
... The calibration of PM4Sand was completed for apparent relative densities ranging from 20% to 80% in increments of 5%. For each value of apparent DR and corresponding Go, an automated optimization algorithm was used to obtain the contraction rate parameter (hpo) that results in the desired CRR at 15¼ cycles using a direct simple shear simulation driver coded in FISH, the coding language of FLAC (Itasca, 2019). Figure 8 summarizes results of the calibration process, with the calibrated contraction rate parameter being plotted as a function of apparent relative density. ...
... The experimental data selected to perform the investigation on, are those obtained from the centrifuge model test number 10 of the Liquefaction Experiments and Analysis Project, performed at the Rensselaer Polytechnic Institute (RPI) centrifuge facility (RPI-10). Respectively, numerical data were obtained from the simulation of the same test in FLAC 8.1 (Itasca, 2019), and with the constitutive model PM4Sand (Boulanger and Ziotopoulou, 2022) applied to the liquefiable sands. ...
... This simplified model is implemented in the one-dimensional non-linear code SCOSSA (Tropeano et al. 2019), which can perform both total (TS) and effective (ES) stress analyses, neglecting or considering the generation of excess pore pressure, respectively. The advanced model used in the fully coupled approach is a critical state compatible, stress ratio-based, bounding surface plasticity constitutive model (PM4Sand), in the last released 3.2 version (Boulanger and Ziotopoulou 2022), implemented in the commercial finite difference platform FLAC (Itasca 2020). For further comparison, total stress (TS) analyses have been also performed by adopting the equivalent linear code STRATA (Kottke et al. 2018). ...
The assessment of the seismic performance of geo-structures via numerical modelling is crucial for ensuring their safety and serviceability. While the capability of numerical models to predict liquefaction in uniform clean sands has been widely studied, less attention has been given to reproducing the behavior of well-graded gravels using recorded seismic events. To this aim, this study simulates the dynamic behavior of a well-graded gravelly soil instrumented in the vertical array of Port Island, Japan, in response to the 1995 Kobe earthquake, utilizing both total and effective stress analyses according to both fully-coupled and loosely-coupled approaches. The calibration of the models is based on the results of site investigations, with a focus on laboratory tests collected in previous studies. The comparison between simulated and observed soil response contributes to improving the reproducibility of the nonlinear behavior of man-made gravelly soils, with potential implications for the design and verification of geo-structures.
... It is a 3D numerical analysis code that was developed based on continuous medium theory and explicit FDM. FLAC3D is especially well suited for dealing with FEM difficult-to-solve complex geotechnical subjects, typically such as complex multiconditions, large deformation, nonlinear material behavior, occurrence, and development of destabilization damage [38]. Therefore, FLAC3D is a well-suited numerical simulation software for underground subterranean works. ...
Appropriate simulation set parameters are the precondition to obtain accurate results; while the simulation results are affected by multiple factors, it is thus crucial to investigate the sensibility of different factors. This paper first analyses the application situation of numerical simulation software in the field of geotechnical engineering and finds that Fast Lagrangian analysis of continua in three dimensions (FLAC3D) has been widely used on roadways or tunnels. Then, taking the roadway excavation process as the engineering background, FLAC3D was used to create 171 schemes of different simulation parameters and analyze the influence of different factors on the simulation results. The findings show that there is a considerable difference in the degree of effect of different parameters on the simulation results. Most of the factors have a remarkable effect on the numerical simulation results (displacement and stress), and only some factors (parameter uniformity and density) have almost no effect on the results. Meanwhile, the trend of displacement and stress is opposite in most cases. In addition, some neglected factors can also have a considerable effect on the simulation results, such as the zone amount; therefore, it is necessary to avoid the variation of nonstudy factors as possible when carrying out the numerical simulation. This study may significantly assist concerned engineers and technicians in developing a more organized and thorough grasp of the impacts of various parameters on simulation outcomes.
... These geotechnical inputs to the economic analysis of earthworks interventions and failures were obtained from detailed modeling of an earthworks cutting slope subjected to changing seasonal weather representative of the current climate of the southern UK. The modeling adopted a commercial finite difference code, FLAC (Fast Lagrangian Analysis of Continua) with Two Phase Flow [23] and made use of a meteorological surface boundary flux derived from an external soil water balance model. The geotechnical model was used to perform coupled consolidation analysis whereby deformations causing changes in material volume would drive pore fluid flow or pore pressure changes and vice versa. ...
Transport and other infrastructure systems are supported on, adjacent to and retained by extensive systems of earthworks of varying (and increasing) age, and of variable original construction quality. These earthworks are subject to natural deterioration, which can be accelerated and complicated by the effects of climate change. The ACHILLES research program is providing improved understanding of earthworks behavior, performance and deterioration. It is also developing methods and tools to analyze and provide decision support for the construction, maintenance and renewal of earthworks, with particular emphasis on the management of existing, deteriorating assets. The work described here aims to identify the most cost-effective timing and means of extending earthworks asset lives and maintaining their safety and serviceability. Conventional cost-benefit analysis methods, of the type used for new infrastructure projects, do not directly provide the decision support needed for the maintenance and renewal of existing earthworks assets. An alternative approach is proposed and applied to a modeled example, demonstrating the potential asset management benefits of early, pre-emptive intervention, the economic attraction of deferred intervention, and the means of identifying an intermediate whole-life cost ‘sweet spot’, based on a timely assessment of intervention options. The handling of the uncertainty associated with earthworks behavior, deterioration rates and times to failure is also considered, as is the extension of the single-asset approach to the management of multiple earthworks assets.
... The analyses listed in Table 3 were executed on continuum coupled models (see Fig. 2f) generated in the 2D finite difference code FLAC ver. 7.0 [47]. Fig. 5 shows the numerical model for the squat structure (slenderness ratio h/b = 1), as an example. ...
A significant amount of damage and casualties induced by several strong-motion earthquakes which recently
stroke South-East Mediterranean area is due to the major seismic vulnerability of residential buildings. In small
villages and mid-size towns, those buildings very often consist of two- to four-story, unreinforced masonry (URM)
structures not designed for earthquake resistance, with direct foundations usually corresponding to an in-depth
extension of load-bearing walls. For such structures, especially when founded on soft soils, site amplification and
soil-foundation-structure interaction (SFSI) can significantly affect the seismic performance; conversely, such
phenomena should be investigated through methods that allow a trade-off between accuracy and computational
effort, hence encouraging their implementation in engineering practice. This paper provides a comprehensive
updated description of the studies carried out in the last years by the authors, which are based on both linear and
nonlinear, parametric, dynamic analyses of complete soil-foundation-structure (SFS) models representative of
existing residential building configurations on different soils. Specifically, the parametric study investigated SFS
models with different masonry types, aspect ratios, and code-conforming homogeneous and heterogeneous soil
profiles. The methodology and analysis results allowed for reaching the following objectives: (i) predicting the
elongation of the fundamental period and the variation of equivalent damping of the SFS system with respect to
fixed-base conditions, through a simplified approach based on an equivalent simple oscillator; and (ii) estimating
the probability of exceeding increasing damage levels associated with out-of-plane overturning of URM walls,
through fragility functions that take into account SFS interaction. The effectiveness of these simplified tools was
successfully validated against well-documented case studies, at the scales of both single instrumented buildings
and urban area.
... A numerical simulation is constructed based on the computer program FLAC3D [15] to study the stability of the retained roadway and stress distribution when the coal pillar width varies. FLAC3D is a computer program for the numerical modelling of continuum media to investigate the stress-strain state of a rock mass. ...
... Simulations were performed using both free-field (baseline) and periodic boundary conditions along the lateral sides of the model. The free-field boundary condition seeks to approximate a 1D response along the sides of the model, and is described by Itasca (2016). A linear elastic constitutive model was assigned to the elements forming two columns on either edge of the section, with properties identical to those from the adjacent columns that utilized the PM4Sand model. ...
Assessment of earthquake-induced liquefaction is an important topic in geotechnical engineering due to the significant potential for damage to infrastructure. Some of the most significant infrastructure damage occurs due to differential settlement of the ground, including due to liquefaction. Post-liquefaction deformations commonly are assessed using one-dimensional empirical models, which inherently assume laterally homogeneous soil layers. Numerical models offer the potential to examine the effects of ground motion variability and spatially variable soil properties on liquefaction-induced deformations. This study explored the post-liquefaction reconsolidation settlement for a site in Hollywood, South Carolina, which was characterized using a three-dimensional (3D) geostatistical model and simulated using the numerical platform FLAC and constitutive model PM4Sand. The effects of ground motion characteristics on mean and maximum differential settlements are investigated. The physical mechanisms associated with postliquefaction responses such as excess pore pressures, shear strains, and volumetric strains also were examined. The efficacy of uniform models assuming representative percentile soil properties to represent the stochastic mean settlement was investigated. The inherent inability of uniform models to capture differential settlements and therefore the need for using stochastic models is discussed.
... The finite difference program -FLAC [30] was used to simulate the performance of the MSE wall with the same dimensions as the full-scale model in section 2. The wall's height was 3 m and the length of the reinforcement bars was 2.1 m. The geometric details of the MSE wall in FLAC are shown in Figure 6. ...
The study examines the behavior of the Mechanically Stabilized Earth (MSE) wall using available reinforcement materials in Danang, Vietnam. The MSE was reinforced by the self-fabricated galvanized steel grids using CB300V steel with 3 cm ribs. The backfill soil is a sandy clay soil from the local area with a low cohesion. A full-scale model with full instrumentation was installed to investigate the distribution of tensile forces along the reinforcement layers. The highest load that caused the wall to collapse due to internal instability (reinforcement rupture) was 302 kN/m2, which is 15 times the design load of 20 kN/m2. The failure surface within the reinforced soil had a parabolic sliding shape which is similar to the theoretical studies. At the failure load level, the maximum lateral displacement at the top of the wall facing was small (3.9 mm) which is significantly lower than the allowable displacements for the retaining wall. Furthermore, a numerical model using FLAC software was applied to simulate the performance of the MSE wall. The modeling results are in good agreement with the physical model. Thus, the self-fabricated galvanized steel grids could be confidentially used in combination with the local backfill soil for the MSE walls.
... 2. Regarding the dissipation energy, according to the user help manual [41], the incremental solution program is used in the FLAC3D, that is, the equation of motion and stress-strain calculation are solved at each steps. There are a variety of plastic models available in FLAC3D that can be used to describe the deformation capacity of the region. ...
The time and space of the support structure applying is related to the overall stability of the roadway after excavation directly. Designed twenty-four groups of roadway support schemes with time and space dimensions, and studied the stability characteristics of roadway in different schemes by using Fast Lagrangian Analysis of Continua in Three Dimensions. The main conclusions are as follows: the influence of energy dissipation (time) and support position (space) on the stability of the roadway is not a linear relationship, and supporting at the appropriate opportunity can be beneficial. Established the "displacement-dissipation energy" curve, founding that there is an obvious "jump" phenomenon in the dissipation energy of surrounding rock during the process of gradually increasing displacement. A novel method for determining the optimum supporting opportunity of roadway based on energy dissipation was proposed, based on the above finding. This study can provide an original idea for the determination of roadway supporting opportunity.
Earthquake-induced soil liquefaction can lead to significant structural damage, due to excessive foundation settlement and rotation. The numerical modelling of this phenomenon is challenging, demanding both an advanced constitutive model and a hydro-mechanically coupled calculation. The PM4sand constitutive model can be calibrated in a straight-forward manner, and has been shown to reasonably approximate complex soil response. The model is currently available in both the commercial numerical analysis codes FLAC 2D and PLAXIS 2D. While FLAC 2D offers the possibility of a fully-coupled dynamic analysis, PLAXIS 2D recently released a ‘‘quasi’’ coupled hydro-mechanical calculation. Aiming to assess their reliability and robustness, the two numerical analysis codes are comparatively assessed by simulating published plane strain centrifuge model tests (conducted at the University of Cambridge) of a SDOF structure resting on a liquefiable layer of loose Hostun sand. PM4sand has been calibrated against element tests on Hostun sand conducted at the laboratory of the Institute for Geotechnical Engineering (IGT) of ETH Zurich. The numerical models are assessed based on their ability to capture the excess pore-water pressures, the accelerations within the soil, and the rotation-displacement response recorded during the centrifuge model tests.
It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristics. One-dimensional seismic site response analysis (SH1D) is the most common approach for investigating site response. This approach assumes that soil is homogeneous and infinitely extended in the horizontal direction. Therefore tying side boundaries together is one way to model this behavior, as the wave passage is assumed to be only vertical. However, SH1D cannot capture the 2D nature of wave propagation, soil heterogeneity, and 2D soil profile with inclined bedrock. In contrast, 2D seismic site response modeling can consider all of the mentioned factors to better understand local site effects on strong ground motions. The 2D wave propagation and considering that soil on two sides of the model is not identical in a soil profile clarifies the importance of a boundary condition on each side that can minimize the unwanted reflections from the edges of the model. Regarding site response, for the avoidance of wave reflections in the boundaries, the model size should be sufficiently large to minimize the wave reflection. However, due to computational limitations, increasing the model size is impractical in some cases. Another approach is to employ free-field boundary conditions (absorbing boundaries) to have a non-reflecting behavior in the boundaries while absorbing the wave energy by a factor. These boundary conditions must take into account free-field motion in the absence of the structure at the sides of the model. This research focuses on implementing free-field boundary conditions in OpenSees for 2D site response analysis with considering free-field 1D model results as input for 2D model.
Soil-structure interaction (SSI) is the relationship between soil response affecting structure movement and vice versa. SSI has long been thought to benefit a structure's seismic response. It is proposed that neglecting SSI in design results in conservative results. Various design standards either permit a decrease in the total seismic coefficient because of SSI or suggest that it be disregarded entirely to simplify the complexity of analyses. However, findings from prior seismic disasters, such as the 1989 Loma Prieta and the 1995 Kobe Earthquakes, reveal that SSI can be detrimental in some situations, especially in pile-supported structures. Although it is necessary in certain modeling cases to consider soil-pile-structure interaction (SPSI), there is a lack of knowledge detailing which approach to utilize for an SPSI problem and which approach does or does not include the effects that provide simplification or complexity in modeling. In this paper, modeling issues on SPSI are investigated in general, considering different approaches presented in the literature. It is predicted that the findings of this paper will provide invaluable knowledge for researchers in the geotechnical and structural engineering fields.
To investigate the effects of slope geometric parameters and soil stratigraphic properties on the topographic amplification of ground motions, a large number of 2-D horizontally layered slope models are constructed. First, the linear and nonlinear seismic responses of a slope model are compared, and the result shows that the nonlinear characteristics of soils should be considered when studying the amplifying effect of slope topography on ground motions. Then, the nonlinear seismic responses of these slope models are analysed from four aspects: the maximum shear strain in the slopes, the effects of geometry and stratigraphy on the seismic response, the distance between the maximum topographic amplification indicators and the slope crest, and the influence range of slope topography behind the slope crest. The results indicate that the amplifying effect of slope topography on ground motions increases with increasing slope height or decreasing average shear wave velocity of the overlying soil layers. Besides, the variation of the topographic amplification effect with slope gradient is significantly influenced by soil stratigraphic properties. The distance between the maximum topographic amplification indicators and the slope crest is mainly in the range of 0–60 m, and the influence range of slope topography behind the slope crest is mainly in the range of 0–150 m. Subsequently, approximate relations are derived based on regression analyses of simulation results, which can provide meaningful references for the seismic design and seismic retrofitting of engineering structures behind the slope crest. Finally, the effects of slope geometric parameters and soil stratigraphic properties on ground motion modifications are further evaluated according to the prediction curves provided by the approximate relations.
Seismic displacements are critical analysis components for evaluating the slope stability during earthquakes and essentially regulated by the yield acceleration of slopes. The conventional Newmark’s method applies the constant yield acceleration to estimate the seismic displacement of slopes, albeit disregarding the time-dependent nature of yield acceleration. This paper presents an efficient analytical method for determining the seismic displacement of Bedding Slopes stabilized with anchor Cables and Piles (BSCP) by considering the dynamic yield acceleration. The dynamic process of yield acceleration was achieved by updating the instantaneous elongation of anchor cables and rotation of piles at each time increment. This was then incorporated within the Newmark’s method to solve the seismic displacement of the BSCP. The results show that the proposed method can reliably predict the general trend of seismic displacement of the BSCP under earthquake loadings, and correlates well with the dynamic finite difference method. Notably, the yield acceleration increases dynamically during the excitation of seismic ground motion and is closely related to the type of earthquake waves. Ignoring the dynamic yield acceleration leads to an overestimation of the post-seismic displacement of the BSCP. Moreover, the proposed method allows for the multi-layer landslide with minor alternations in the formulation of each component of work rates. This study facilitates a better displacement-based seismic design of the BSCP.
The construction of earth dams on active faults presents a risk of instability. The Ourkiss dam, built 14 km south of the town of Ain Fakroun, is a heterogeneous type of dam made of clay and alluvial materials, with a watertight geo-membrane lining on the upstream face of the dam and on the dam flanks. Due to its location close to active faults, the dam could be damaged by instability in the event of a very strong earthquake. For this reason, in this article a comparison between two study approaches is made: one is quasi-static based on a failure analysis due to the effect of normal and reverse fault propagation. Different angles of inclination are applied by sliding through the Ourkiss dam at the end of construction and in the filled state. The other approach is based on the dynamic effect of the 2003 Boumerdes earthquake (magnitude 6.9 on the Richter scale), modeled with a sinusoidal propagation velocity applied to the model base in the horizontal direction. The results obtained for both approaches are presented in terms of shear deformations developed at the dam foundation and dike. They show that the deformation values found by the quasi-static method are greater than those found by the dynamic method.
In this research, the seismic behavior of the back-to-back MSE walls has been assessed in a probabilistic approach using the fragility curves and the effect of the overlapping length of the metal strips on the vulnerability of this type of walls has been investigated. To this end, the back-to-back MSE walls are simulated using FLAC2D finite difference program, and validated with a shaking table physical model test. So, using the results of nonlinear incremental analysis, fragility curves are analytically extracted based on PGA and PGV intensity measures under far-field and near-fault earthquakes. The obtained results, in addition to providing the possibility of predicting the vulnerability of the wall in different seismic intensities, indicate that increasing the length of the metal strips from 0.65 to 0.85 of the wall height (increasing the overlapping length from 0.3 to 0.7wall height), reduces the probability of seismic damage up to 35% in the far-field and by about 50% in the near-fault earthquakes, respectively.
The paper presents a novel 3D numerical methodology validated against monotonic pullout centrifuge tests of suction buckets in dense sands. The tests considered suction buckets subjected to different loading rates (i.e., different drainage conditions) and simulated different water depths. The numerical meth-odology consistently accounts for the interaction between the foundation, the soil skeleton and the pore fluid while properly simulating the effects of both water depth and rate of loading. The Ta-Ger constitutive model is used to simulate the complex sand response under the variable loading paths that take place during pullout. The model parameters are calibrated against available drained and undrained monotonic tests performed as part of the centrifuge testing program. Special emphasis is placed on the accurate simulation of the interaction between the bucket lid and the underlying water as cavitation of the latter can be critical for the response. The results of the numerical analyses provide valuable insight regarding the governing failure mechanisms and their dependance on loading rate and water depth.
This paper re-evaluates the Edenville earth dam that failed in 2020 after a rapid rise in reservoir level caused by prolonged significant rainfall. The dam instability and possibility of static liquefaction-induced flow failure are assessed in the framework of critical state soil mechanics (CSSM). Both undrained loading and drained unloading stress paths are considered for flow liquefaction assessment. Using documented triaxial compression tests, the Norsand constitutive model is calibrated for finite-element numerical models. This study supplements the analyses conducted by an independent forensic team (IFT) in charge of failure investigation. The advances achieved by tailings dam practitioners are leveraged here to study flow liquefaction as recommended by the IFT. Multiple ways are employed to generate reasonable initial field stresses. Simulation of dam construction coupled with steady-state seepage analysis creates an appropriate starting condition for further flow liquefaction assessment. The numerical outputs confirm the result of the IFT's limit equilibrium analyses for an undrained boundary condition. Stress analyses with a drained boundary condition show that a major stress change with a constant-shear-drained (CSD) stress path develops below the dam crest due to a rising reservoir level. The results of our models with a CSD stress path and drained-to-undrained transition better explain the evolution of the Edenville dam failure. The current study provides a practical approach to earth dam design and evaluation.
Mildly sloped liquefiable sand deposits are susceptible to lateral spreading under earthquake ground motion. Geometry, material properties, and input motion are the high-level impacting factors on the slope displacements. The recently developed SANISAND-MSf, a two-surface sand plasticity model with memory surface and semifluidized state, is used in the finite difference-based platform FLAC3D to simulate the nonlinear behavior of the soil. A multi-layer system with different thicknesses of liquefiable layer, various sand relative densities, and a suite of ground motion intensities are considered to study the primary design variables affecting the slope response. The simulation results indicate that superficial lateral displacements increase significantly with increasing thickness of the liquefiable layer, decreasing relative density, and increasing cumulative absolute velocity of the ground motion. Furthermore, the lateral spreading obtained under bidirectional shaking may be smaller or larger than that under unidirectional, highlighting the importance of accounting for the former in predicting the response of liquefiable slopes. RÉSUMÉ Les dépôts de sable liquéfiable légèrement inclinés sont susceptibles de se propager latéralement sous le mouvement du sol sismique. La géométrie, les propriétés des matériaux et le mouvement d'entrée sont les facteurs d'impact de haut niveau sur les déplacements de pente. Le SANISAND-MSf récemment développé, un modèle de plasticité du sable à deux surfaces avec surface mémoire et état semi-fluidisé, est utilisé dans la plate-forme basée sur les différences finies FLAC3D pour simuler le comportement non linéaire du sol. Un système multicouche avec différentes épaisseurs de couche liquéfiable, diverses densités relatives de sable et une suite d'intensités de mouvement du sol sont considérés pour étudier la principale variable de conception affectant la réponse de la pente. Les résultats de la simulation indiquent que les déplacements latéraux superficiels augmentent de manière significative avec l'augmentation de l'épaisseur de la couche liquéfiable, la diminution de la densité relative et l'augmentation de la vitesse absolue cumulative du mouvement du sol. De plus, l'étalement latéral obtenu sous agitation bidirectionnelle peut être plus petit ou plus grand que celui sous unidirectionnel, soulignant l'importance de tenir compte du premier pour prédire la réponse des pentes liquéfiables.
Mechanically stabilized earth (MSE) walls have been widely applied in construction to maintain the stability of high embankments. In Vietnam, imported reinforcement materials are expensive; thus, finding locally available materials for MSE walls is beneficial. This study examines the behavior of an MSE wall using local reinforcement materials in Danang, Vietnam. The MSE was reinforced by self-fabricated galvanized steel grids using CB300V steel with 3 cm ribs. The backfill soil was sandy clay soil from the local area with a low cohesion. A full-scale model with full instrumentation was installed to investigate the distribution of tensile forces along the reinforcement layers. The highest load that caused the wall to collapse due to internal instability (reinforcement rupture) was 302 kN/m2, which is 15 times greater than the design load of 20 kN/m2. The failure surface within the reinforced soil had a parabolic sliding shape that was similar to the theoretical studies. At the failure load level, the maximum lateral displacement at the top of the wall facing was small (3.9 mm), significantly lower than the allowable displacement for a retaining wall. Furthermore, a numerical model using FLAC software 7.0 was applied to simulate the performance of the MSE wall. The modeling results were in good agreement with the physical model. Thus, self-fabricated galvanized steel grids could confidently be used in combination with the local backfill soil for MSE walls.
With the increasing depth of engineering in rock masses, the issue of significant rheological deformation becomes notably prominent. To accurately characterize the deformation and failure behavior of the surrounding rock near the goaf in deep small coal pillars, we have developed a viscoelastic–plastic constitutive model that takes into account the initial stress associated with creep. This model builds upon an existing viscoelastic–plastic constitutive framework and is implemented numerically using C++ in the FLAC3D. The Oedometer test method is used to check the creep components and the calculated parameter (η/G) ensure convergence of numerical operations. We conducted both pre‐improvement and post‐improvement tests of the constitutive model in a simple numerical analysis of roadways. The enhanced model demonstrates improved accuracy in deviational stress calculations and proves suitable for modeling deep, soft roadways. Furthermore, we applied the improved model to simulate actual working conditions at Zhaozhuang Mine, where mining operations near the working face induce a fracture zone of approximately 3 m in the small coal pillar located at the goaf's edge. The new model closely aligns with the observed results, further validating its suitability for tunneling along the goaf. Tunneling and mining activities result in significant deformation at various locations, including the shoulder socket of the working face, the top angle of the coal pillar, and the bottom angle of the floor. The crushing zone at the working face extends up to 4 m. Rheological effects transform the triangular elastic core, from its original high‐pressure elastic state to a fracture and plastic zone in the deep coal. Stress in deep coal is transmitted along the triangular elastic core. Numerical simulation results closely match the excavation profile of the tunneling, providing valuable insights into the impact of mining activities. This study can provide reference for deformation of similar geological conditions and engineering situation.
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