Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the halfspace is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Predhohn integral equations of the second kind and solved by numerical procedures. In the numerical extortples, the dynamic colnpliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

Steady-state response of a saturated half-space with an overlying dry layer subjected to a moving load

In this paper,the steady-state response of a saturated half-space with an overlying dry layer subjected to a moving rectangular load is investigated.The governing partial differential equations are solved using the Fourier transform.The solutions in time-space domain are expressed in terms of infinite Fourier type integrals,which can be evaluated only by numerical quadrature.Numerical results show that the influence of a drained or undrained interface on the response is related to the permeability of the underlying saturated soil.Moreover,the effect due to the upper dry layer is associated with the thickness of the layer.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.

Amplification of in-plane seismic ground motion by group cavities in layered half-space (Ⅱ): with saturated poroelastic soil layers

As the continuation study on amplification of in-plane seismic ground motion by underground group cavities in layered half-space, this study extends to the case of poroelastic half-space with dry poroelastic and saturated poroelastic soil layers. The influence of poroelastic layers on the amplification of seismic ground motion is studied both in frequency domain and time domain using indirect boundary element method （IBEM）. It is shown that for the example of a saturated poroelastic site in Tianjin under the excitation of Taft wave and E1 Centro wave, the amplification of seismic ground motion in poroelastic case is slightly smaller than that in the elastic case, and the amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum）.. can be increased up to 38.8% and 64.6%; the predominant period of response spectra in poroelastic case becomes shorter to some extent compared with that in the elastic case. It is suggested that the effect of underground group cavities in poroelastic half-space on design seismic ground motion should be considered.

Dynamic Stress and Pore Pressure Around Circular Cavity in Saturated Porous Elastic Half-space Under Harmonic Plane Dilatational Waves

Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot’s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.

Solution of a Green's function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green＇s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters （permeability, frequency, etc.） under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner＇s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two- phase saturated medium in engineering.

Soil pressure and pore pressure for seismic design of tunnels revisited: considering water-saturated, poroelastic half-space

This paper describes a systematic study on the fundamental features of seismic soil pressure on underground tunnels, in terms of its magnitude and distribution, and further identifi es the dominant factors that signifi cantly infl uence the seismic soil pressure. A tunnel embedded in water-saturated poroelastic half-space is considered, with a large variety of model and excitation parameters. The primary features of both the total soil pressure and the pore pressure are investigated. Taking a circular tunnel as an example, the results are presented using a fi nite element-indirect boundary element(FE-IBE) method, which can account for dynamic soil-tunnel interaction and solid frame-pore water coupling. The effects of tunnel stiffness, tunnel buried depth and input motions on the seismic soil pressure and pore pressure are also examined. It is shown that the most crucial factors that dominate the magnitude and distribution of the soil pressure are the tunnel stiffness and dynamic soil-tunnel interaction. Moreover, the solid frame-pore water coupling has a prominent infl uence on the magnitude of the pore pressure. The fi ndings are benefi cial to obtain insight into the seismic soil pressure on underground tunnels, thus facilitating more accurate estimation of the seismic soil pressure.

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.

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.

A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

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.

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.

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.

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.

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.

3-D DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED SOILS

A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot＇s theory for fluid- saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface, were presented.

Anti-plane deformations around arbitrary-shaped canyons on a wedge-shape half-space:moment method solutions

The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.