Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

Application of headed studs in steel fiber reinforced cementitious composite slab of steel beam-column connection

Steel fiber reinforced cementitous composites （SFRCC） is a promising material with high strength in both compression and tension compared with normal concrete. The ductility is also greatly improved because of 6% volume portion of straight steel fibers. A steel beam-column connection with Steel fiber reinforced cementitous composites （SFRCC） slab diaphragms is proposed to overcome the damage caused by the weld. The push-out test results suggested that the application of SFRCC promises larger shear forces transferred through headed studs allocated in a small area in the slab. Finite element models were developed to simulate the behavior of headed studs. The failure mechanism of the grouped arrangement is fiarther discussed based on a series of parametric analysis. In the proposed connection, the SFRCC slab is designed as an exterior diaphragm to transfer the beam flange load to the column face. The headed studs are densely arranged on the beam flange to connect the SFRCC slab diaphragms and steel beams. The seismic performance and failure mechanism of the SFRCC slab diaphragm beam-column connection were investigated based on the cyclic loading test. Beam hinge mechanism was achieved at the end of the SFRCC slab diaphragm by using sufficient studs and appropriate rebars in the SFRCC slab.

A New Mixed Finite Element Method for Biot Consolidation Equations

In this paper,we study a new finite element method for poroelasticity problem with homogeneous boundary conditions.The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity,i.e.,the stress tensor,displacement and pressure are unknown variables in the weak form.For the linear elasticity formula,we use a conforming finite element proposed in[11]for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow.We will show that the newly proposed finite element method maintains optimal convergence order.

New artificial boundary condition for saturated soil foundations

Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves （S-waves） are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra＇ is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves （fast-P-waves and slow-P-waves） are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.

DYNAMIC INTERACTION BETWEEN ELASTIC THICK CIRCULAR PLATE AND TRANSVERSELY ISOTROPIC SATURATED SOIL GROUND

A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.

Seismic wave equations in tight oil/gas sandstone media

Tight oil/gas medium is a special porous medium,which plays a significant role in oil and gas exploration.This paper is devoted to the derivation of wave equations in such a media,which take a much simpler form compared to the general equations in the poroelasticity theory and can be employed for parameter inversion from seismic data.We start with the fluid and solid motion equations at a pore scale,and deduce the complete Biot’s equations by applying the volume averaging technique.The underlying assumptions are carefully clarified.Moreover,time dependence of the permeability in tight oil/gas media is discussed based on available results from rock physical experiments.Leveraging the Kozeny-Carman equation,time dependence of the porosity is theoretically investigated.We derive the wave equations in tight oil/gas media based on the complete Biot’s equations under some reasonable assumptions on the media.The derived wave equations have the similar form as the diffusiveviscous wave equations.A comparison of the two sets of wave equations reveals explicit relations between the coefficients in diffusive-viscous wave equations and the measurable parameters for the tight oil/gas media.The derived equations are validated by numerical results.Based on the derived equations,reflection and transmission properties for a single tight interlayer are investigated.The numerical results demonstrate that the reflection and transmission of the seismic waves are affected by the thickness and attenuation of the interlayer,which is of great significance for the exploration of oil and gas.

Numerical Analysis on Cnoidal Wave Induced Response of Porous Seabed with Definite Thickness

Severe water waves can induce seabed liquefaction and do harm to marine structures. Dynamic response of seabed with definite thickness induced by cnoidal water waves is investigated numerically. Biot＇s consolidation equations are employed to model the seabed response. Parametric studies are carried out to examine the influence of the air content in the pore water and the soil hydraulic conductivity. It is been shown that the air content and soil hydraulic conductivity can significantly affect the pore pressure in seabed. An increase of air content and/or a decrease of soil hydraulic conductivity can change the pore pressure gradient sharply.