The disturbances in an infinite inhomogeneous medium due to transient forces and twists on the surface of a buried spherical source

Summary In this paper the disturbances in an inhomogeneous medium due to two types of forces (i) transient normal forces, (ii) transient twists in presence of a buried spherical source has been considered. The material of the inhomogeneous medium is assumed to be transversely isotropic. The results are in terms of modified Bessel functions. In a particular case, the equation reduces to an ordinary differential equation of second order.     

On the disturbances in an infinite viscoelastic medium due to transient normal forces and transient twists on the surface of a spherical cavity

Summary In this note the disturbances in an infinite viscoelastic medium ofViogt type with a spherical cavity have been considered. The problem has been solved separately for (1) transient radial forces and (2) transient twist acting on the inner spherical surface of the cavity. Exact solutions have been obtained in both cases.     

Dynamic analysis of large 3-D underground structures by the bem

An up to date literature survey on the dynamics of underground structures is presented briefly. The dynamic response of large three-dimensional underground structures to external or internal dynamic forces or to seismic waves is numerically determined by the frequency domain boundary element method. This method is used to model both the structure and the soil medium, which are assumed to behave as linear elastic or viscoelastic bodies. The full-space dynamic fundamental solution is employed in the formulation and this requires a free soil surface discretization, confined to a finite portion around the area of interest, in addition to soil—structure interface and free structural surface discretizations. The dynamic disturbances can have a harmonic or a transient time variation. The transient case is treated with the aid of numerical Laplace transforms with respect to time. Various numerical examples involving lined cavities and long lined tunnels buried in the full- or the half-space subjected to harmonic or transient external forces or seismic waves are presented to illustrate the method and demonstrate its advantages.     

On the effective seismic input for non-linear soil-structure interaction systems

Two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately. The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free-field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil-structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil-structure interface of the complete system. It is shown, further, that the free-field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free-field ground motion at a site is usually specified at a single reference point.     

Disturbances produced in a visco-elastic medium by transient torsional body forces

Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above.     

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.     

Dynamic response of 3-D rigid surface foundations by time domain boundary element method

The dynamic response of three-dimensional rigid surface foundations of arbitrary shape is numerically obtained. The foundations are placed on a linear elastic, isotropic and homogeneous half-space representing the soil medium and are subjected to either external dynamic forces or seismic waves of various kinds and directions, with a general transient time variation. The problem is formulated in the time domain by the boundary element method and the response is obtained by a time step-by-step integration. Two examples dealing with three-dimensional rectangular foundations are presented in detail, together with comparisons with other methods, in order to document the accuracy of the method. The main advantages of the proposed method are that, unlike frequency domain techniques, it provides directly the transient response and forms the basis for extension to the case of non-linear behaviour.     

A coupled computational method for multi-solver, multi-domain transient problems in elastodynamics

This work presents an efficient and stable methodology for the coupling of Finite Element Methods (FEM) and Boundary Element Methods (BEM) that is independent of the particular solver and allows for independent temporal discretizations among solvers. The approach satisfies explicitly compatibility conditions and equilibrium of forces at the contact interfaces. Although the proposed approach has been developed in view of the soil-rail-vehicle dynamic interaction problem in High Speed Rail applications, it is expressed in a general form applicable to any multi-domain, multi-phase transient problem. The method development and formulations are presented in detail. Verification and application studies demonstrate the accuracy, efficiency and versatility of the method for the direct time domain solution of dynamic problems including structure-structure interaction and soil-structure interaction. The proposed approach demonstrates high accuracy and efficiency to that of direct coupling solutions and more rigorous methods.     

DYNAMIC CROSS-INTERACTION BETWEEN FLEXIBLE SURFACE FOOTINGS BY COMBINED BEM AND FEM

A combined boundary and finite element method is developed and applied to study the dynamic behaviour of a system of flexible surface footings of arbitrary shape bearing on an elastic half-space. The proposed method employs the frequency domain Green's function for the surface of the elastic half-space while a layered plate model is used for the flexible footing. Both the footing and the surface of the half-space are discretized by 8-noded quadratical isoparametric elements, and the meshes are identical. Thus, the compatibility of displacements and equilibrium of forces between the footing and the half-space are fully satisfied. This model provides a better approximation of the stress concentration at edges of relatively rigid footings. Numerical examples demonstrating the effects due to the excitation frequency, the relative rigidity and the distance between footings on the interaction between two square footings are presented. The external forces can be either harmonic or transient.     

Transient response of a group of rigid strip surface foundations

A numerical procedure is proposed to investigate the transient response of a group of rigid strip foundations resting on an elastic, homogeneous half-space subjected to either external forces or seismic motions. A fundamental solution is presented for uniform strip loadings with Heaviside function time-dependence applied on the half-space. In the procedure, each of the foundations is discretized into subelements. The tractions between the half-space and the subelements are assumed constant at every time step. The through-soil coupling effects between the foundations are studied numerically.     

Transient responses of girder bridges with vertical poundings under near‐fault vertical earthquake

Previous studies on pounding responses of bridge structures mainly focus on the horizontal pounding between adjacent structures. However, the vertical pounding responses of bridge are rarely studied. The aim of this paper is develop a theoretical approach to investigate the transient behavior of continuous bridge under near‐fault vertical ground motions. The transient behavior of bridge manifests as the earthquake‐induced response wave and pounding‐induced response wave travel throughout bridge. Based on a new continuous model of beam–spring–rod, the theoretical solution of bridge responses involving multiple vertical poundings is derived by the expansion of transient wave functions in a series of eigenfunctions. A new theoretical solving approach of the multiple vertical pounding forces is presented based on the transient internal force on the contact surface of the girder and bearing. The numerical results show that the present method can reasonably capture the propagations of the earthquake‐induced response wave and pounding‐induced response wave. The calculations of pounding force by the present method are convergence of the time‐step size and truncation number of wave modes. As the effect of transient wave is taken into account, the numerical results show several transient phenomena involving the vertical pounding, the high pounding force, the multiple‐pounding phenomenon, the vertical separation of girder from the bearing, the dependence of poundings on earthquake period and the narrow period window of poundings. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic analysis of a beam resting on an elastic half-space with inertial properties

This work gives a semi-analytical approach for the dynamic analysis of beams and plates resting on an elastic half-space with inertial properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, this paper presents a detailed analysis of Green's function defining surface displacements of such a space in the contact zone with structures, which allows determination of reactive forces and other physical magnitudes. The obtained solutions can be applied to (i) study dynamic interaction between soil and structures, (ii) determine transient wave fields caused by a seismic source, and (iii) assess numerical computations with different numerical methods programs. Natural frequencies, natural shapes, and the dynamic response of a beam due to external harmonic excitation are determined. Eigenfrequencies and Eigenshapes are presented. Validation with a Boussinesq problem illustrates the inertia effect on the results of the dynamic analysis.     

Origin of tectonic stresses in the Chinese continent and adjacent areas

Based on data of principal stress orientation from focal mechanism and of geological features in China, we made pseudo-3D genetic algorithm finite element (GA-FEM) inversion to investigate the main forces acting on the Chinese continent and adjacent areas which form the Chinese tectonic stress field. The results confirm that plate boundary forces play the dominant role in forming the stress field in China, as noticed by many previous researchers. However, we also find that topographic spreading forces, as well as basal drag forces of the lower crust to the upper crust, make significant contribution to stresses in regional scale. Forces acting on the Chinese continent can be outlined as follows: the collision of the India plate to the NNE is the most important action, whereby forces oriented to the NW by the Philippine plate and forces oriented to the SWW by the Pacific plate are also important. Topographic spreading forces are not negligible at high topographic gradient zones, these forces are perpendicular to edges of the Tibetan Plateau and a topographic gradient belt running in the NNE direction across Eastern China. Basal drag forces applied by the ductile flow of the lower crust to the base of upper crust affect the regional stress field in the Tibetan Plateau remarkably, producing the clockwise rotation around the eastern Himalaya syntax.     

Lattice Boltzmann simulations of the transient shallow water flows

A two-dimensional lattice Boltzmann model (LBM) is presented for transient shallow water flows. The model is based on the shallow water equations coupled with the large eddy simulation model. In order to obtain accurate results efficiently, a multi-block lattice scheme is applied at the area where a local finer grid is needed for strong change in physical variables. The model is verified by applying to five cases with transient processes: (a) a tidal wave over steps; (b) a perturbation over a submerged hump; (c) partial dam break flow; (d) circular dam break flow; (e) interaction between a dam break surge and four square cylinders. The objectives of this study are to validate the two-dimensional LBM in transient flow simulation and provide the detailed transient processes in shallow water flows.     

A discontinuous Galerkin method for seismic soil–structure interaction analysis in the time domain

A technique for modeling transient wave propagation in unbounded media is extended and applied to seismic soil–structure interaction analysis in the time domain. The technique, based on the discontinuous Galerkin method, requires lower computational cost and less storage than the boundary element method, and the time‐stepping scheme resulting from Newmark's method in conjunction with the technique is unconditionally stable, allowing for efficient and robust time‐domain computations. To extend the technique to cases characterized by seismic excitation, the free‐field motion is used to compute effective forces, which are introduced on the boundary of the computational domain containing the structure and the soil in the vicinity of the structure. A numerical example on a dam–foundation system subjected to seismic excitation demonstrates the performance of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental study of charge vertical transfer in surface air layer

The variability of air–earth electric currents in the lower 3-m air layer is analyzed in a complex with measurement data on the physical parameters that affect charge transfer in the atmosphere. Three types of air–earth current density profiles have been revealed during experimental observations in summer in Rostov region: (1) the current density decreases with an increase in the distance from the Earth’s surface and then stabilizes (nighttime conditions); (2) the current density increases with altitude up to 1 m and then decreases as altitude increases (day hours); (3) transient between types 1 and 2 that are observed in the morning and evening hours. The intensity of charge transfer in the surface air layer under the action of mechanical forces under different stratifications is estimated on the basis of data on altitude variations in the air–earth current density in view of the stationarity of electric processes and the constancy in the altitude of the total air–earth current density. Thermodynamic conditions are estimated with the use of wind velocity measurements and calculations of the turbulence factor and vertical component of the air temperature gradient.     

On the geometry of convergent plate boundaries

Previous studies of plate dynamics suggest that, at consuming plate boundaries, driving forces (negative buoyancy) acting on the slab are counterbalanced by viscous forces, proportional to the consumption velocity and resisting the downgoing motion into the mantle. New observations on the geometry of subduction zones may help test this equilibrium theory. A condition for local equilibrium of the driving and resistive forces is that the consumption velocity (V_⊥) remains constant along a given trench. From this condition, a geometrical property of the shape of trenches and island arcs on the sphere is inferred: the consuming margin of two plates should follow segments of helices about the axis of rotation of their relative motion. A comparison of the shape of island arcs and trenches with helices supports this inference.     

Dike emplacement and flank instability at Mount Etna: Constraints from a poro-elastic-model of flank collapse

Many volcanic edifices are subject to flank failure, usually produced by a combination of events, rather than any single process. From a dynamic point of view, the cause of collapse can be divided into factors that contribute to an increase in shear stress, and factors that contribute to the reduction in the friction coefficient μ of a potential basal failure plane. We study the potential for flank failure at Mount Etna considering a schematic section of the eastern flank, approximated by a wedge-like block. For such geometry, we perform a (steady state) limit equilibrium analysis: the resolution of the forces parallel to the possible basal failure plane allows us to determine the total force acting on the potentially unstable wedge. An estimate of the relative strength of these forces suggests that, in first approximation, the stability is controlled primarily by the balance between block weight, lithostatic load and magmatic forces. Any other force (sea load, hydrostatic uplift, and the uplift due to mechanical and thermal pore-fluid pressure) may be considered of second order. To study the model sensitivity, we let the inferred slope α of the basal surface failure vary between ?10° and 10°, and consider three possible scenarios: no magma loading, magmastatic load, and magmastatic load with magma overpressure. We use error propagation to include in our analysis the uncertainties in the estimates of the mechanics and geometrical parameters controlling the block equilibrium. When there is no magma loading, the ratio between destabilizing and stabilizing forces is usually smaller than the coefficient of friction of the basal failure plane. In the absence of an initiating mechanism, and with the nominal values of the coefficient of friction μ = 0.7 ± 0.1 proposed, the representative wedge will remain stable or continue to move at constant speed. In presence of magmastatic forces, the influence of the lateral restraint decreases. If we consider the magmastatic load only, the block will remain stable (or continue to move at constant speed), unless the transient mechanical and thermal pressurization significantly decrease the friction coefficient, increasing the instability of the flank wedge for α > 5° (seaward dipping decollement). When the magma overpressure contribution is included in the equilibrium analysis, the ratio between destabilizing and stabilizing forces is of the same order or larger than the coefficient of friction of the basal failure plane, and the block will become unstable (or accelerate), especially in the case of the reduction in friction coefficient. Finally, our work suggests that the major challenge in studying flank instability at Mount Etna is not the lack of an appropriate physical model, but the limited knowledge of the mechanical and geometrical parameters describing the block equilibrium.     

Driving mechanisms of nitrogen transport and transformation in lacustrine wetlands

As an essential component of proteins and genetic material for all organisms, nitrogen (N) is one of the major limiting factors that control the dynamics, biodiversity and functioning of lacustrine wetlands, in which intensified N biogeochemical activities take place. Reactive N loaded into wetland ecosystems has been doubled due to various human activities, including industrial, agricultural activities and urbanization. The main driving mechanisms of N transport and transformation in lacustrine wetlands are categorized to pushing forces and pulling forces in this study. Geomorphology, wetland age, N concentrations, and temperature are the main pushing forces (passive forces); whereas water table variation, oxygen concentration, other elements availability, oxidation-reduction potential (Eh) and pH, and microorganisms are the predominant pulling forces (active forces). The direction and kinetic energy of reactions are determined by pulling forces and then are stimulated by pushing forces. These two types of forces are analyzed and discussed separately. Based on the analysis of driving mechanisms, possible solutions to wetland N pollutions are proposed at individual, regional and global scales, respectively. Additional research needs are addressed to obtain a thorough understanding of N transport and transformations in wetlands and to reduce detrimental impacts of excessive N on such fragile ecosystems.     

Dynamic response of flexible strip-foundations by boundary and finite elements

A time domain Boundary Element-Finite method is employed to determine the dynamic response of flexible surface two-dimensional foundations under conditions of plane strain placed on an elastic soil medium and subjected either to transient external forces or to obliquely incident seismic waves. The elastic, isotropic, and homogeneous soil medium is treated by the time domain Direct Boundary Element Method, while the flexible foundation is treated by the Finite Element Method. The two methods are appropriately combined through equilibrium and compatibility considerations at the soil-foundation interface. Parametric studies examining the effect of the relative stiffness between the foundation and the soil and the spatial distribution of the dynamic disturbances on the foundation response are presented.