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Computational Geomechanics With Special Reference to Earthquake Engineering
... The u-p set of equations, comprising the set of the total mass of fluid and equilibrium of the momentum of the soil with Darcian porous behaviour, with the relations acquiring for the soil boundaries and the constitutive law of the stresses and strains is a stable calculating scheme compared to the Biot problem.The u-p set of equations is conducted hereinafter as static loads are subjected to the clayey soil mass. In most structured geomaterials the u-p scheme is appropriate in most of the physical load cases as proven in ( [60]). The discrete setup of u-p numerical scheme is given with the Galerkin method and the set of equations are: [61,62]: ...
A collection of feed forward neural networks (FNN) for estimating the limit pressure load and the according displacements at limit state of a footing settlement is presented. The training procedure is through supervised learning with error loss function the mean squared error norm. The input dataset is originated from Monte Carlo simulations for a variety of loadings and stochastic uncertainty of the material of the clayey soil domain. The material yield function is the Modified Cam Clay model. The accuracy of the FNN’s is in terms of relative error no more than $$10^{-5}$$ 10 - 5 and this applies to all output variables. Furthermore, the epochs of the training of the FNN’s required for construction are found to be small in amount, in the order of magnitude of 90,000, leading to an alleviated data cost and computational expense. The input uncertainty of Karhunen Loeve random field sum appears to provide the most detrimental values for the displacement field of the soil domain. The most unfavorable situation for the displacement field result to limit displacements in the order of magnitude of 0.05 m, that may result to structural collapse if they appear to the founded structure. These series can provide an easy and reliable estimation for the failure of shallow foundation and therefore it can be a useful implement for geotechnical engineering analysis and design.
... where is the total stress tensor. The contribution of the terms ̈ and ̈ is assumed negligible in this study following Zienkiewicz et al. (1999) and many others. ...
This study introduces an advanced finite element model for the light weight deflectometer (LWD), which integrates contact mechanics with fully coupled models. By simulating LWD tests on granular soils at various saturation levels, the model accurately reflects the dependence of the LWD modulus on dry density, water content, and effective stress. This model addresses and overcomes the limitations of previous finite element models for this specific problem. Simultaneously, this research presents the first experimentally validated fully coupled contact impact model. Furthermore, the research provides a comparative assessment of elastoplastic and nonlinear elastic models and contrasts an enriched node-to-segment method (developed in this study) with the more precise mortar technique for contact mechanics. These comparisons reveal unique advantages and challenges for each method. Moreover, the study underscores the importance of careful application of the LWD modulus, emphasising the need for sophisticated tools to interpret soil behaviour accurately.
... Definition of J 2 and J 3 is shown in Eqs. (17), refer to [56]. ...
This study presents a novel formulation for incorporating anisotropy into the generalized plasticity constitutive model. Generalized plasticity is a hierarchical framework allowing for extensibility, in order to encompass new phenomena and improve its predictive capabilities. Anisotropy formulation is based experimentally on the phase transformation state and considers explicitly the direction of the maximum principal stress and the magnitude of the intermediate principal stress, through an anisotropy state variable that contributes to the state parameter. Additionally, the model incorporates the fabric using an evolving fabric variable that reflects initial fabric due to sample preparation method for granular soils. The formulation is simple and introduces three constitutive parameters, allowing for straightforward implementation into the constitutive model and direct application in finite element analysis. The model is validated with undrained triaxial tests conducted on Toyoura sand, covering a wide range of initial conditions with a unique set of constitutive parameters, and yielding overall satisfactory results despite some limitations.
... Parameters 0 and 1 are adopted to calculate the plastic modulus during the loading period, and the parameter is adopted to calculate the plastic modulus during the unloading period. Detail of model parameters is shown in Table 2 and have been fully explained by Zienkiewicz et al. (1998). ...
It is important to determine dynamic tunnel behaviour under cyclic loading for the seismic underground structural design. The dynamic response of tunnels can be further complicated when considering the interaction with surface buildings. A series of 2D saturated plane-strain numerical analyses has been conducted to study the dynamic response of a shallow cut-and-cover rectangular tunnel in loose, cohesionless soil. Input motion is adopted as a sinusoidal wave with 10 cycles of shaking. A raft foundation with a 50 kPa structural surcharge is adopted to simulate the effect of the surface building. Soil displacements, wave propagation, and tunnel lining structural response are determined. These results show that the soil liquefaction due to accumulated excess pore pressures causes the attenuation of horizontal acceleration in the soil, reduction of soil effective stresses, and promotes tunnel flotation. In addition, the existence of the nearby building substantially reduces the liquefaction ratio of sub-surface soil below the foundation. The numerical results form a basis for further dynamic centrifuge testing to investigate the dynamic response of the tunnel-soil-building system subjected to cyclic loading.
... In the dynamic simulations, the bottom of the model has been assumed rigid (as recommended by Ref. [97] when the depth of the recorded ground motions matched the depth of the profile base). Tied-nodes boundary conditions have been imposed along the lateral sides of the mesh to effectively absorb the energy induced by the seismic action, as demonstrated by Zienkiewicz et al. [98]. This approach prevents spurious wave reflections into the FE model. ...
Extensive documentation and research have highlighted the destructive impact of near-field earthquakes on underground structures, while the effects of far-field earthquakes remain relatively less explored. In regions such as Bangkok and Singapore, where active seismic faults are located at a significant distance, the influence of far-field motions on tunnels tends to be ignored. However, far-field earthquakes are generally less destructive than near-field motions due to their low peak ground acceleration, peak ground velocity, and Arias intensity, resulting in lower energy. Conversely, far-field earthquakes tend to have a longer duration than near-field and a higher probability of containing long-period waves, which can lead to higher responses in the low-frequency region of the response spectrum. When these far-field ground motions are applied to thick layers of soft natural clays, a common geological feature in Bangkok, they can undergo significant amplification in the long-period range, resulting in large soil displacements and shear strains. Consequently, this induces significant forces in the tunnel lining comparable to those generated by near-field earthquakes. This paper presents a comprehensive study of this rarely investigated topic, using advanced numerical simulations to analyse the seismic behaviour of a shallow circular tunnel in Bangkok soft clays subjected to long-period earthquakes. The results show that far-field earthquakes have the potential to generate forces in the tunnel lining that are equally destructive as those induced by near-field motions. Therefore, these far-field effects should be accounted for in the seismic design of tunnels.
... Herein, the soil-water coupled system is idealized as a saturated porous medium composing of a deformable solid skeleton and connecting voids fully filled by water. For earthquake related analysis, the u-p formulation, with two primary unknowns being solid displacement u and pore pressure p, is often adopted for the governing equation of the dynamic soil-water coupled system (Zienkiewicz et al., 1999), based on the Biot's theory (Biot, 1941). , with s K and n K being the compression moduli of solid grain and pore fluid, respectively. ...
Liquefaction-induced shear strain localization and delayed failure occur when a low permeability overlying soil layer impedes the dissipation of excess pore water pressure generated by the underlying sand. When this phenomenon is simulated by classical finite element method (FEM), the predicted strain localization and lateral deformation are mesh-size dependent. In this study, the nonlocal peridynamics theory is introduced as a novel regularization technique for modeling such phenomenon. The computational model is based on coupling the non-ordinary state-based peridynamics (NOSBPD) and FEM for the solid and pore fluid phases, respectively. The liquefiable sand is modelled using a plastic model for large post-liquefaction shear deformation of sand (CycLiq) in the NOSBPD layer and the fluid flow is solved in the FEM layer. After validation of the proposed method via a VELACS centrifuge model test, the seismic response of an idealized one-dimensional sloping site with a low-permeability interlayer is analyzed using various discretization resolutions. The results show that the proposed method for liquefaction-induced strain localization analysis is insensitive to spatial discretization density. Finally, the Lower San Fernando dam failure case is revisited. The localized sliding and delayed failure of the dam observed in the field is achieved in the simulation. The results demonstrate the potential of the proposed method in assessing realistic cases associated with liquefaction-induced shear strain localization.
One effective technique for mitigating the earthquake-induced liquefaction potential is the installation of stone columns. The permeability coefficients of stone columns are high enough to cause a high seepage velocity or expedited drainage. Under such conditions, the fluid flow law in porous media is not linear. Nevertheless, this nonlinear behavior in stone columns has not been evaluated in dynamic numerical analyses. This study proposes a dynamic finite element method that integrates nonlinear fluid flow law to evaluate the response of liquefiable ground improved by stone columns during seismic events. The impact of non-Darcy flow on the excess pore pressure and stress path compared to conventional Darcy law has been investigated numerically in stone columns. Furthermore, the effects of different permeability coefficients and stone column depths have been studied under near and far field strong ground motions. The results indicate that the non-Darcy flow increases the excess pore water pressure as high as 100% in comparison to the Darcy flow.
Geological materials such as Opalinus Clay show complex coupled hydro-mechanical behavior at laboratory and field scales. In the context of radioactive waste disposal, in-situ excavations might remain open for ventilation and operation for decades and, consequently, be susceptible to environmental changes such as desaturation. The saturation changes can then lead to mechanical deformation and desiccation cracks. To account for desiccation cracking at field scale, this study proposes an unsaturated hydro-mechanical model combined with the phase-field approach. Using laboratory and in-situ experimental data as input in the numerical model, the modeling framework is applied for simulating the hydro-mechanical effects and desiccation cracks reported in the Cyclic Deformation (CD-A) experiment carried out in the Opalinus Clay formation at the Mont Terri Rock Laboratory in Switzerland. Simulations with homogeneous and heterogeneous material properties generated from experimentally obtained ranges are carried out. Crack initiation and propagation show a good correlation with the monitored relative humidity range of the experiment. Practical information is summarized to motivate the application of the proposed formulation at different setups. Finally, possibilities to improve the framework and to reason simplification of more abstract models are indicated.
Purpose: Underground structures such as lifelines, tunnels, and pipelines are vital structures that may object damage during an earthquake. This damage may cause economic and life loss. So the behavior of liquefaction potential soils around the tunnels under dynamic loads gets more importance. The purpose of this study is to investigate the soil behavior with structure under earthquake loads. Study design/methodology/approach: In this study, two-dimensional (2D), nonlinear, fully coupled, effective stress, dynamic finite-element (FE) analyses were performed in Open Source Earthquake Engineering System (OpenSees). The saturated sandy soil was simulated by using Pressure Dependent Multi Yield Material (PDMY02) constitutive model. UP element type was used for modeling the soil based on Biot's Dynamic consolidation theory, where "u" is the displacement and "p" is pore-water pressure. To check the reliability of the results obtained from numeric study, the verification was done at the first step. Within this framework, results of the experimental Cyclic Shear Stress test were used and modeled for a single element and analyzed under cyclic loading by using OpenSees. A comparison of experimental and simulation results proved the applicability of constitutive soil material. To study the effect of relative density, the relative densities of Dr= 63%, 50%, and 30% of Nevada sand layers were used for analyses. For searching the effect of ground motion, two ground motions were used. The first one was the time history of the North-South component of the Izmit earthquake with Mw=5.8 magnitude and the maximum acceleration of a=46.4 cm/sec 2 that occurred on 13.09.1999 which was the aftershock of the 1999 Kocaeli earthquake. The second one was the time history of the East-West component of the Arsuz earthquake with Mw=6.4 magnitude and maximum acceleration of a=336 cm/sec 2 occurred 20.02.2023 within the 6.02.2023 Maraş earthquake series. The effect of the structure was studied by placing a square steel tunnel with dimensions of 4x4 m 2 in a model which is covered with the same soil type. The geometry of the model was simulated with the GiD program for different relative densities and GWT elevations. The free field boundary conditions and ground motion were applied to the model then a tunnel was added to the model and analyses were continued. In all cases, results of acceleration, displacements in vertical and horizontal directions, and excess pore pressure ratios were obtained at a set of the same reference nodes. In conditions with placed tunnel two sets of reference nodes were studied. The first set of reference nodes was near the location of the tunnel (near the structure) and the second set was far from the tunnel (free field). Findings: Results of the simulation showed that, for both the ground motions displacements happened in all studied cases. As the sandy soil got looser displacements and excess pore water pressure increased. Liquefaction did not occur in any studied case when Izmit ground motion was applied, but liquefaction phenomena were observed up to the depth of 15m when Arsuz input motion was used as it was stronger than the previous ground motion. Originality/value: The purpose of this study is to provide insights into the behavior of sandy soil with liquefaction potential under dynamic loads, predict the possible damages and find solutions for preventing damages. Soil improvement methods may be effective choice.
هدف از اين تحقيق، تحليل خاك بر اساس فرمولبندي تنش مؤثر با بكارگيري مكانيك محيط متخلخل اشباع براي بررسي اثر جريان غير دارسي و توپوگرافي نامنظم لايه بندي بر روي روانگرائي مي باشد. اين که قانون دارسي براي عدد رينولدز بسيار پايين صادق است، موضوعي کاملاً شناخته شده است. قانون جريان در محيط متخلخل براي سرعت تراوش بالا غيرخطي است. با اين وجود، جريان غيرخطي در معادلات اندرکنش خاک- سيال حفرهاي و مکانيک خاک مرسوم استفاده نشده است. در اين تحقيق روش اجزاء محدود ديناميکي جهت تحليل محيط متخلخل اشباع بر پايه فرمولاسيون اوليه ارائه شده توسط بيوت (1962-1941) براي جريان غيردارسي توسعه داده شده است. رفتار ارتجاعي- خميري سيکلي خاک تحت بارگذاري لرزهاي با استفاده از نظريه پلاستيسيته عمومي منتج شده از مفهوم سطح تسليم همراه با قانون جريان غير همراه شبيه سازي شده است. براي بررسي اثر حرکت غيردارسي سيال، نرم افزاري به زبان برنامه نويسي فورترن نوشته شده است. شبيه سازي هاي عددي محيط متخلخل با نفوذپديري بالا و زلزلههاي ورودي فرکانس بالا نشان ميدهد که اختلاف قابل ملاحظه اي در نتايج تحليل روانگرائي بين محيط دارسي و غير دارسي وجود دارد. در ادامه تحقيق اثر توپوگرافي نامنظم لايه بندي بر روانگرائي براي دو لايه از خاک نيز بررسي شده است. در کليهي روشهاي ساده شده براي شناسايي پتانسيل روانگرائي، خاک به صورت لايه هاي همگن مسطح فرض شده است، اما در واقع لايه هاي خاک داراي نامنظمي در توپوگرافي است. نتايج بدست آمده حاکي از آن است که لايه بنديهاي نامنظم در بسياری از موارد بر پاسخ ديناميکي خاک اثر گذار بوده که اين امر مي تواند در ارزيابي روانگرائي تاثير داشته باشد.
Two new semiexplicit algorithms for the coupled soil–pore fluid problem are developed in this article. The stability of the new algorithms is much better than that of the previous algorithm. The first new scheme (H*-scheme) based on operator splitting before spatial discretization can avoid the restriction of mixed formulation in the incompressible (zero permeability) limit. The steady-state formulation is discussed to verify this argument. Several examples illustrate the article.
During the San Fernando, California earthquake of February 9, l97l, a major slide occurred in the upstream slope of the Lower San Fernando Dam. Based on data obtained from tests on undisturbed samples, a detailed dynamic analysis of the seismic stability of the embankment is presented. It is concluded that an analysis procedure incorporating: (1) Consideration of the initial static stresses in the embankment: (2) the use of a dynamic finite element analysis procedure to determine the dynamic stresses induced in individual elements of the embankment by the earthquake; (3) the use of cyclic loading triaxial compression test data to determine the response of the soil elements to the induced stresses; and (4) consideration of progressive failure effects provides a satisfactory basis for assessing the stability of the embankment. This type of analysis indicates the development of a zone of liquefaction along the base of the upstream shell that would be sufficiently extensive near the end of the earthquake shaking to lead to a condition of instability.
A laboratory test method for the determination of the coefficient of earth pressure at rest, Ko, in sandy soils is presented. In this method, initially, a series of undrained cyclic triaxial tests were made on high-quality undisturbed sand samples recovered by the in-situ freezing sampling method (FS sample), in order to obtain the relationship between the shear modulus at very small strain, Go, and the effective confining stress, σ'c. Next, the Go was also calculated based on elastic wave theory by using the shear wave velocity measured at a depth from which the undisturbed samples were recovered. By equalizing the Go values obtained from these two independent methods, the coefficient of earth pressure at rest, Ko, in the sandy soils, can be determined using the proposed simple method. The Ko-value of a diluvial sand obtained using this method is 0.84. Based on the test results on the sand samples obtained by the rotary type triple tube sampling method (TS sample), recovered from the same soil layer and the same depth, however, the Ko value obtained with this method was 1.44, which is considerably larger than that obtained from the FS sample. The larger Ko value of the TS sample compared with that of the FS sample is because the initial shear modulus of the TS sample is much lower than that of the FS sample for the same level of confining stress due to sample disturbance.
A triaxial shear test box equipped with six rubber pressure bags was constructed to test cubical specimens of sand with a dimension of 100 mm multiplied by 100mm multiplied by 100mm. A series of drained tests was carried out on loose sand specimens prepared by depositing the sand under water. The tests employed different radial stress paths in which the major, intermediate and minor principal stresses were oriented independent of the direction of the specimen sedimentation. A number of tests were also carried out on specimens rotated by 90 degree about the horizontal axis after the specimens had been prepared by deposition.
Five fundamental postulates are introduced as the bases on which a model of undrained deformation of sand under cyclic loading is to be established. The procedures for assessing pore pressures, shear strains and consequent occurrence of liquefaction during cyclic loading are illustrated on the diagrams based on the above postulates as well as actual data obtained in the static triaxial tests. The undrained performance of sand predicted by the proposed model were compared with several cyclic triaxial test results conducted under various conditions.
The theory of plasticity is applied to describe the behavior of granular materials. It is shown that the yield condition of the Granta-Gravel model corresponds to a very simple case of density hardening. When the second invariant of plastic strain deviator is considered in the yield condition, peaks in the stress-strain diagrams may be explained and the volumetric strains may be described in a way which includes the basic features of real behavior. To illustrate the behavior, the axially symmetric homogeneous stress is considered on the basis of two simple models.