A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

The existence of saturated vapors in the deep source region of 2017Pohang earthquake evidenced from seismic tomography

Geothermal resources are a promising approach to clean renewable energy;90%of them are deep reservoirs of hot dry rock that require hydraulic fracturing to create a network of connections among wells to enable efficient heat exchange,known as an Enhanced Geothermal System(EGS).The Pohang EGS project in south Korea led to a devasting Mw5.5 earthquake,triggered by the reservoir's EGS stimulation,the largest earthquake known to have been induced by EGS development.Detailed investigations have been conducted to understand the cause of the Pohang earthquake;the conclusion has been that overpressurized injected fluids migrated into an unknown fault triggering this large earthquake.Detailed velocity images for the source zone of the 2017 Pohang earthquake,which could be helpful for further understanding its inducing mechanism,are unavailable.However,we have assembled detailed aftershock data recorded by 41 local stations installed within about three months after the Mw5.5 Pohang earthquake,and have then applied the V_(p)/V_(s)model's consistency-constrained double-difference seismic tomography method to determine the high-resolution three-dimensional Vp(compressional wave velocity),Vs(shear wave velocity),and V_(p)/V_(s)models of the source region that we report here,as well as earthquake locations within the source region.The velocity images reveal that the deep source area of the 2017 Pohang earthquake is dominated by low Vp,high Vs,and low V_(p)/V_(s)anomalies,a pattern that can be caused by overpressurized vapors due to high temperatures at these depths.Based on aftershock locations and velocity features,our studies support the conclusion that the 2017Pohang earthquake was triggered by injected EGS fluids that migrated into a blind fault.

Vertical distribution characteristics of soil saturated hydraulic conductivity under different land use patterns in the Mu Us sandy land

Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s) characteristics and the factors that inf luence this key parameter in the Mu Us sandy land(MUSL).Quantifying the impact of changes in land use in the Mu Us sandy land on K_(s) will provide a key foundation for understanding the regional water cycle,but will also provide a scientific basis for the governance of the MUSL.Materials and methods In this study,we determined K_(s) and the basic physical and chemical properties of soil(i.e.,organic matter,bulk density,and soil particle composition)within the first 100 cm layer of four different land use patterns(farmland,tree,shrub,and grassland)in the MUSL.The vertical variation of K_(s) and the factors that influence this key parameter were analyzed and a transfer function for estimating K_(s) was established based on a multiple stepwise regression model.Results The K_(s) of farmland,tree,and shrub increased gradually with soil depth while that of grassland remained unchanged.The K_(s) of the four patterns of land use were moderately variable;mean K_(s)values were ranked as follows:grassland(1.38 mm·min^(-1))<tree(1.76 mm·min^(-1))<farmland(1.82 mm·min^(-1))<shrub(3.30 mm·min^(-1)).The correlation between K_(s) and organic matter,bulk density,and soil particle composition,varied across different land use patterns.A multiple stepwise regression model showed that silt,coarse sand,bulk density,and organic matter,were key predictive factors for the K_(s) of farmland,tree,shrub,and grassland,in the MUSL.Discussion The vertical distribution trend for K_(s) in farmland is known to be predominantly influenced by cultivation,fertilization,and other factors.The general aim is to improve the water-holding capacity of shallow soil on farmland(0-30 cm in depth)to conserve water and nutrients;research has shown that the K_(s) of farmland increases with soil depth.The root growth of tree and shrub in sandy land exerts mechanical force on the soil due to biophysical processes involving rhizospheres,thus leading to a significant change in K_(s).We found that shallow high-density fine roots increased the volume of soil pores and eliminated large pores,thus resulting in a reduction in shallow K_(s).Therefore,the K_(s) of tree and shrub increased with soil depth.Analysis also showed that the K_(s) of grassland did not change significantly and exhibited the lowest mean value when compared to other land use patterns.This finding was predominantly due to the shallow root system of grasslands and because this land use pattern is not subject to human activities such as cultivation and fertilization;consequently,there was no significant change in K_(s) with depth;grassland also had the lowest mean K_(s).We also established a transfer function for K_(s) for different land use patterns in the MUSL.However,the predictive factors for K_(s) in different land use patterns are known to be affected by soil cultivation methods,vegetation restoration modes,the distribution of soil moisture,and other factors,thus resulting in key differences.Therefore,when using the transfer function to predict K_(s) in other areas,it will be necessary to perform parameter calibration and further verification.Conclusions In the MUSL,the K_(s) of farmland,tree,and shrub gradually increased with soil depth;however,the K_(s) of grassland showed no significant variation in terms of vertical distribution.The mean K_(s) values of different land use patterns were ranked as follows:shrub>farmland>tree>grassland;all land use patterns showed moderate levels of variability.The K_(s) for different land use patterns exhibited differing degrees of correlation with soil physical and chemical properties;of these,clay,silt,sand,bulk density,and organic matter,were identified as important variables for predicting K_(s) in farmland,tree,shrub,and grassland,respectively.Recommendations and perspectives In this study,we used a stepwise multiple regression model to establish a transfer function prediction model for K_(s) for different land use patterns;this model possessed high estimation accuracy.The ability to predict K_(s) in the MUSL is very important in terms of the conservation of water and nutrients.

Assessing the impact of concurrent high-fructose and highsaturated fat diets on pediatric metabolic syndrome:A review

High-saturated fat(HF)or high-fructose(HFr)consumption in children predispose them to metabolic syndrome(MetS).In rodent models of MetS,diets containing individually HF or HFr lead to a variable degree of MetS.Nevertheless,simultaneous intake of HF plus HFr have synergistic effects,worsening MetS outcomes.In children,the effects of HF or HFr intake usually have been addressed individually.Therefore,we have reviewed the outcomes of HF or HFr diets in children,and we compare them with the effects reported in rodents.In humans,HFr intake causes increased lipogenesis,hypertriglyceridemia,obesity and insulin resistance.On the other hand,HF diets promote low grade-inflammation,obesity,insulin resistance.Despite the deleterious effects of simultaneous HF plus HFr intake on MetS development in rodents,there is little information about the combined effects of HF plus HFr intake in children.The aim of this review is to warn about this issue,as individually addressing the effects produced by HF or HFr may underestimate the severity of the outcomes of Western diet intake in the pediatric population.We consider that this is an alarming issue that needs to be assessed,as the simultaneous intake of HF plus HFr is common on fast food menus.

Nested Saturated Control of Uncertain Complex Cascade Systems Using Mixed Saturation Levels

This study addresses the problem of global asymptotic stability for uncertain complex cascade systems composed of multiple integrator systems and non-strict feedforward nonlinear systems. To tackle the complexity inherent in such structures, a novel nested saturated control design is proposed that incorporates both constant saturation levels and state-dependent saturation levels. Specifically, a modified differentiable saturation function is proposed to facilitate the saturation reduction analysis of the uncertain complex cascade systems under the presence of mixed saturation levels. In addition, the design of modified differentiable saturation function will help to construct a hierarchical global convergence strategy to improve the robustness of control design scheme. Through calculation of relevant inequalities, time derivative of boundary surface and simple Lyapunov function,saturation reduction analysis and convergence analysis are carried out, and then a set of explicit parameter conditions are provided to ensure global asymptotic stability in the closed-loop systems. Finally, a simplified system of the mechanical model is presented to validate the effectiveness of the proposed method.

Strength characteristics of dry and saturated rock at different strain rates

The strength of rock materials is largely affected by water and loading conditions, but there are few studies on mechanical properties of saturated rocks at high strain rates. Through compressive tests on dry and saturated sandstone specimens, it was found that the dynamic compressive strength of both dry and saturated sandstone specimens increased with the increase of strain rates. The saturated rock specimens showed stronger rate dependence than the dry ones. The water affecting factor （WAF）, as the ratio of the strength under dry state to that under saturated state, was introduced to describe the influence of water on the compressive strength at different strain rates. The WAF under static load was close to 1.38, and decreased with the increase of strain rate. When the strain rate reached 190 s^-1, the WAF reduced to 0.98. It indicates that the compressive strength of saturated specimens can be higher than that of dry ones when the strain rate is high enough. Furthermore, the dual effects of water and strain rate on the strength of rock were discussed based on sliding crack model, which provided a good explanation for the experimental results.

Creep experiment and rheological model of deep saturated rock

By the methods of uniaxial single-stage loading and graded incremental cyclic loading, the creep experiments were performed on the deep saturated rock from Dongguashan Mine, and the creep curves of saturated rock under different loading stresses were obtained. By comparing with the creep rule of dry rock in the same location, the creep rule of deep saturated rock was analyzed. Based on the united rheological mechanical model, the rheological model of deep saturated rock was recognized, and the parameters of the model were determined. The results show that the creep curves are very smooth under low stress, but the phenomena of wave and catastrophe turn up under high stress, and the bearing capacity of rock is weakening over time. The rheological properties of saturated and dry rocks are very different under tlie condition of deep high stress, especially when unloading, degradation and damage of rock quality is more serious, and the effect of water cannot be neglected. The H--HIN--NJS model （Schofield-Scott-Blair model） was selected to represent the rheology rule of deep saturated rock, and the fitting curves of model agree well with the experiment data, so the selected model is reasonable.

Distinctive roles of unsaturated and saturated fatty acids in hyperlipidemic pancreatitis

AIM: To investigate how the saturated and unsaturated fatty acid composition influences the susceptibility of developing acute pancreatitis. METHODS: Primary pancreatic acinar cells were treated with low and high concentrations of different saturated and unsaturated fatty acids, and changes in the cytosolic Ca2+ signal and the expression of protein kinase C(PKC) were measured after treatment. RESULTS: Unsaturated fatty acids at high concentrations, including oleic acid, linoleic acid, palmitoleic acid, docosahexaenoic acid, and arachidonic acid, induced a persistent rise in cytosolic Ca2+ concentrations in acinar cells. Unsaturated fatty acids at low concentrations and saturated fatty acids, including palmitic acid, stearic acid, and triglycerides, at low and high concentrations were unable to induce a rise in Ca2+ concentrations in acinar cells. Unsaturated fatty acids at high concentrations but not saturated fatty acids induced intra-acinar cell trypsin activation and cell damage and increased PKC expression.CONCLUSION: At sufficiently high concentrations, unsaturated fatty acids were able to induce acinar cells injury and promote the development of pancreatitis. Unsaturated fatty acids may play a distinctive role in the pathogenesis of pancreatitis through the activation of PKC family members.

Dietary saturated fatty acid and polyunsaturated fatty acid oppositely affect hepatic NOD-like receptor protein 3 inflammasome through regulating nuclear factor-kappa B activation

AIM: To investigate the effect of different dietary fatty acids on hepatic inflammasome activation.METHODS: Wild-type C57BL/6 mice were fed either a high-fat diet or polyunsaturated fatty acid (PUFA)-enriched diet. Primary hepatocytes were treated with either saturated fatty acids (SFAs) or PUFAs as well as combined with lipopolysaccharide (LPS). The expression of NOD-like receptor protein 3 (NLRP3) inflammasome, peroxisome proliferator-activated receptor-&#x003b3; and nuclear factor-kappa B (NF-&#x003ba;B) was determined by real-time PCR and Western blot. The activity of Caspase-1 and interleukine-1&#x003b2; production were measured.RESULTS: High-fat diet-induced hepatic steatosis was sufficient to induce and activate hepatic NLRP3 inflammasome. SFA palmitic acid (PA) directly activated NLRP3 inflammasome and increased sensitization to LPS-induced inflammasome activation in hepatocytes. In contrast, PUFA docosahexaenoic acid (DHA) had the potential to inhibit NLRP3 inflammasome expression in hepatocytes and partly abolished LPS-induced NLRP3 inflammasome activation. Furthermore, a high-fat diet increased but PUFA-enriched diet decreased sensitization to LPS-induced hepatic NLRP3 inflammasome activation in vivo. Moreover, PA increased but DHA decreased phosphorylated NF-&#x003ba;B p65 protein expression in hepatocytes.CONCLUSION: Hepatic NLRP3 inflammasome activation played an important role in the development of non-alcoholic fatty liver disease. Dietary SFAs and PUFAs oppositely regulated the activity of NLRP3 inflammasome through direct activation or inhibition of NF-&#x003ba;B.

Effects of microalgal polyunsaturated fatty acid oil on body weight and lipid accumulation in the liver of C57BL/6 mice fed a high fat diet

Dietary polyunsaturated fatty acids （PUFAs）, which are abundant in marine fish oils, have recently received global attention for their prominent anti-obesogenic effects. Among PUFAs, eicosapentaenoic acid （EPA; 20：5n-3） and docosahexaenoic acid （DHA; 22：6n-3）, which are n-3 long-chain PUFAs widely referred to as omega-3 oils, were reported to prevent the development of obesity in rodents and humans. In the present study, we evaluated the anti-obesity effects of microalgal oil on high-fat induced obese C57BL/6 mice, compared with commercial omega-3 fish oil and vegetable corn oil. Microalgal oil is an inherent mixture of several PUFAs, including EPA, DHA and other fatty acids produced from a marine microalgal strain of Thraustochytriidae sp. derived mutant. It was found to contain more PUFAs （〉80%） and more omega-3 oils than commercial omega-3 fish oil （PUFAs 〉31%） and corn oil （PUFAs 59%）. All three types of oils induced weight loss in high-fat-induced obese mice, with the loss induced by microalgal oil being most significant at 9 weeks （10% reduction）. However, the oils tested did not improve blood lipid levels, although microalgal oil showed an apparent inhibitory effect on lipid accumulation in the liver. These findings may be attributed to the higher PUFA content, including omega-3 oils of microalgal oil than other oils. Collectively, these findings suggest that microalgal oil, derived from Thraustochytriidae sp. derived mutant, is a prominent candidate for replacement of omega-3 fish oils based on its apparent anti-obesity effect in vivo.

Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam

Based on the three-dimensional Gurtin-type variational principle of the incompressible saturated porous media, a one-dimensional mathematical model for dynamics of the saturated poroelastic Timoshenko cantilever beam is established with two assumptions, i.e., the deformation satisfies the classical single phase Timoshenko beam and the movement of the pore fluid is only in the axial direction of the saturated poroelastic beam. Under some special cases, this mathematical model can be degenerated into the Euler-Bernoulli model, the Rayleigh model, and the shear model of the saturated poroelastic beam, respectively. The dynamic and quasi-static behaviors of a saturated poroelastic Timoshenko cantilever beam with an impermeable fixed end and a permeable free end subjected to a step load at its free end are analyzed by the Laplace transform. The variations of the deflections at the beam free end against time are shown in figures. The influences of the interaction coefficient between the pore fluid and the solid skeleton as well as the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam are examined. It is shown that the quasi-static deflections of the saturated poroelastic beam possess a creep behavior similar to that of viscoelastic beams. In dynamic responses, with the increase of the slenderness ratio, the vibration periods and amplitudes of the deflections at the free end increase, and the time needed for deflections approaching to their stationary values also increases. Moreover, with the increase of the interaction coefficient, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Timoshenko beam.

BISQ model based on a Kelvin-Voigt viscoelastic frame in a partially saturated porous medium

Taking into account three important porous media mechanisms during wave propagation （the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms）, we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt （BISQ） model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.

Design of artificial neural networks using a genetic algorithm to predict saturates of vacuum gas oil

Accurate prediction of chemical composition of vacuum gas oil （VGO） is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks （ANN） based on a genetic algorithm （GA） is developed for predicting VGO saturates. The number of neurons in the hidden layer, the momentum and the learning rates are determined by using the genetic algorithm. The inputs for the artificial neural networks model are five physical properties, namely, average boiling point, density, molecular weight, viscosity and refractive index. It is verified that the genetic algorithm could find the optimal structural parameters and training parameters of ANN. In addition, an artificial neural networks model based on a genetic algorithm was tested and the results indicated that the VGO saturates can be efficiently predicted. Compared with conventional artificial neural networks models, this approach can improve the prediction accuracy.

Test Investigation on Liquefied Deformation Structure in Saturated Lime-Mud Composites Triggered by Strong Earthquakes

Three identical model boxes were made from transparent plexiglass and angle iron. Using the method of sinking water and according to the sedimentary rhythm of saturated calcium carbonate （lime-mud） intercalated with cohesive soil, calcites with particle sizes diameters of ≤ 5 μm, 10–15 μm and 23–30 μm as well as cohesive soil were sunk alternatively in water of three boxes to build three test models, each of which has a specific size of calcite. Pore water pressure gauges were buried in lime-mud layers at different depths in each model, and connected with a computer system to collect pore water pressures. By means of soil tests, physical property parameters and plasticity indices （Ip） were obtained for various grain-sized saturated lime-muds. The lime-muds with Ip ranging from 6.3 to 8.5 （lower than 10） are similar to liquid saturated silt in the physical nature, indicating that saturated silt can be liquefied once induced by a strong earthquake. One model cart was pushed quickly along the length direction of the model so that its rigid wheels collided violently with the stone stair, thus generating an artificial earthquake with seismic wave magnitude greater than VI degree. When unidirectional cyclic seismic load of horizontal compression-tension-shear was imposed on the soil layers in the model, enough great pore water pressure has been accumulated within pores of lime-mud, resulting in liquefaction of lime-mud layers. Meanwhile, micro-fractures formed in each soil layer provided channels for liquefaction dewatering, resulting in formation of macroscopic liquefaction deformation, such as liquefied lime-mud volcanoes, liquefied diapir structures, vein-like liquefied structures and liquefied curls, etc. Splendid liquefied lime-mud eruption lasted for two to three hours, which is similar to the sand volcano eruption induced by strong earthquake. However, under the same artificial seismic conditions, development of macroscopic liquefied structures in three experimental models varied in shape, depth and quantity, indicating that excess pore water pressure ratios at initial liquefaction stage and complete liquefaction varied with depth. With size increasing of calcite particle in lime-mud, liquefied depth and deformation extent increase accordingly. The simulation test verifies for the first time that strong earthquakes may cause violent liquefaction of saturated lime-mud composed of micron-size calcite particles, uncovering the puzzled issue whether seafloor lime-mud can be liquefied under strong earthquake. This study not only provides the latest simulation data for explaining the earthquake-induced liquefied deformations of saturated lime-mud and seismic sedimentary events, but also is of great significance for analysis of foundation stability in marine engineering built on the soft calcium carbonate layers in neritic environment.

Torsional vibration of a pipe pile in transversely isotropic saturated soil

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot＇s poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated.A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils.The accuracy of the model is validated using a classic example in literature.The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils.The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model.The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy.The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model,which provides a weaker confining action to the underground structure.

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.

Impact of stretching-segment on saturated flow rate of signalized intersection using cellular automation

In order to analyze the impact of stretching-segment on the saturated flow rate of signalized intersection approach, an improved cellular automation model was proposed to estimate its saturated flow rate. The NaSch model was improved by adding different slow probabilities, turning deceleration rules and modified lane changing rules. The relationship between the saturated flow rate of stretching-segments and adjacent lanes was tested in numerical simulation. The length of stretching-segment, cycle length and green time were selected as impact factors of the cellular automation model. The simulation result indicates that the geometrics design of stretching-segment and the traffic signal timing scenario have major effects on the saturated flow rate of the intersection approach. The saturated flow rate will continually increase with increasing stretching-segment length until it reaches a threshold. After reaching the threshold, the stretching-segment can be treated as a separate lane. The green time is approximately linearly related to the threshold length of the stretching-segment. An optimum cycle length exists when the length of the stretching-segment is not long enough, and it is approximately linearly related to the length of stretching-segment.

LIQUEFACTION AND DISPLACEMENT OF SATURATED SAND UNDER VERTICAL VIBRATION LOADING

In order to investigate the influence of the vertical vibration loading on the liquefaction of saturated sand,one dimensional model for the saturated sand with a vertical vibration is presented based on the two phase continuous media theory.The development of the liquefaction and the lique- faction region are analyzed.It is shown that the vertical vibration loading could induce liquefaction. The rate of the liquefaction increases with the increase of the initial limit strain or initial porosity or amplitude and frequency of loading,and increases with the decrease of the permeability or initial modulus.It is shown also that there is a phase lag in the sand column.When the sand permeability distribution is non-uniform,the pore pressure and the strain will rise sharply where the permeability is the smallest,and fracture might be induced.With the development of liquefaction,the strength of the soil foundation becomes smaller and smaller.In the limiting case,landslides or debris flows could occur.

THE NON-AXISYMMETRICAL DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED POROELASTIC MEDIA

The Blot's wave equations of transversely isotropic saturated poroelastic media excited hy non-axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot's wave equations. The method of research on non-axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.