Thermoelastic and thermoplastic response of a double-layer porous space containing a decaying heat source

Solutions are presented for the behaviour of a layered porous space which contains a decaying heat source. Such a problem arises when high-level nuclear waste is placed in deep underground depositories in deep clayey formations of sedimentary basins. The geometry of the problem is one dimensional and the porous space is constituted by two layers: a deep low permeability layer which contains the nuclear waste disposal and a superficial layer. The solution is used to examine the effects of contrasts of permeability, thermal conductivity and specific heat capacities between the two layers on the large-scale behaviour of the porous space. Results are presented, using realistic data, for the pore pressure and temperature evolution at the heat source centre, and for the vertical displacement of the ground level. The superficial layer has no significant effects on pore pressure, temperature and stress evolution near the heat source centre. The vertical displacement of the ground level is mainly due to the thermal dilatation of the pore water, so it decreases with an increasing of permeability of the superficial layer. The solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical methods to invert the transformed solutions. Comparisons with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass are presented. © 1998 John Wiley & Sons, Ltd.     

Consolidation around a spherical heat source with a decaying power output

When a heat source such as a cannister of radioactive waste is placed in a saturated soil the temperature of both the soil and the pore water will rise. The coefficient of expansion of the pore water is greater than that of the soil skeleton and so there will be a tendency for a differential volume change and a consequent increase in pore pressure. This will in turn lead to a reduction in effective stress and so if the temperature is too great cracking of the surrounding soil may occur.If the soil is sufficiently permeable the temperature generated pore pressures will dissipate during consolidation and so the severity of these effects will be reduced. A further reduction will also occur because the power output of the radioactive waste will decrease with time due to radioactive decay.This paper develops an analytic solution for the temperature and pore pressure field around a rigid impermeable spherical heat source which takes account of the reduction of power output due to radioactive decay.     

The behaviour of layered soil or rock containing a decaying heat source

Solutions are presented for the behaviour of layered soil or rock deposits which contain a heat source. Such a problem arises when high level nuclear waste is placed in deep underground depositaries, as the waste continues to generate heat for many years after placement. This heating of the surrounding soil or rock may lead to expansion and cracking with subsequent contamination of ground water. Results are presented for heat soureces with different decay rates and for heat sources in layers of material with different coefficients of expansion. An example using realistic data for rock is also given. The solution method involves applying Fourier or Hankel transforms to the field quantities and this reduces the two-dimensional or axisymmetric problem to one involving a single spatial dimension. In cases where the soil or rock is horizontally layered, the method has great advantages over other numerical methods such as finite element or finite difference techniques, since little computer storage and data preparation time is required. Solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical means to invert the transformed solutions. This enables easy solution of problems involving time-dependent (i.e. decaying) heat sources.     

Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Presentation of an analytical solution

The thermoelastic response due to a time-dependent rectangular heat source in a semi-infinite medium is analyzed. The problem originates from studies of nuclear waste repositories in rock. Canisters containing heat-emitting nuclear waste are deposited over a large rectangular area deep below the ground surface. The solution for a time-dependent heat source is obtained from the corresponding instantaneous heat source by superposition. The thermoelastic problem for the instantaneous rectangular heat source in a infinite surrounding is solved exactly. An important step is the introduction of so-called quadrantal heat sources. The solution for the rectangle is obtained from four quadrantal solutions. The solution for the quadrantal heat source depends on the three dimelasionless coordinates only. Time occurs in the scale factors only. The condition of zero normal and shear stresses at the ground surface is fulfilled by using a mirror heat source and a boundary solution. The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple solution is obtained. The final analytical solution is quite tractable considering the complexity of the initial problem. The solution may be used to test numerical models for coupled thermoelastic processes. It may also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three-dimensional global process.     

Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source

This paper presents an analytical layer element solution to axisymmetric thermal consolidation of multilayered porous thermoelastic media containing a deep buried heat source. By applying the Laplace–Hankel transform to the state variables involved in the basic governing equations of porous thermoelasticity, the analytical layer elements that describe the relationship between the transformed generalized stresses and displacements of a finite layer and a half‐space are derived. The global stiffness matrix equation is obtained by assembling the interrelated layer elements, and the real solutions in the physical domain are achieved by numerical inversion of the Laplace–Hankel transform after obtaining the solutions in the transformed domain. Finally, numerical calculations are performed to demonstrate the accuracy of this method and to investigate the influence of heat source's types, layering, and the porous thermoelastic material parameters on thermal consolidation behavior. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermo-mechanical coupling response of a layered isotropic medium around a cylindrical heat source

Based on the governing equations of the thermo-elastic problem, the analytical layer-elements of a finite layer and an underlying half-space are obtained using the Laplace-Hankel transform and the characteristic value method. The cylindrical heat source is divided into several micro cylindrical heat sources, which can be approximately simulated by plane heat sources. Then, the global stiffness matrix for the problem is assembled and solved in the transformed domain, and a Laplace-Hankel transform inversion is taken to obtain the real solution. Finally, the influence of heat source types, division numbers, embedded depths and layered properties on the thermo-mechanical coupling response is investigated.     

地埋点热源作用下层状半空间的热-力耦合响应

采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发,利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元;然后结合有限单元法原理组装得到总刚度矩阵,结合边界条件,得到其在变换域内的解答,最后应用拉普拉斯-傅里叶积分逆变换技术,得到物理域内的解。编制了相应的计算程序,算例分析表明：该结果与已有文献吻合较好,该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度;层状岩土介质体系中,热扩散系数对温度及地表隆起的变化过程影响显著,但对其初始值和最终稳定值影响不明显;分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。     

Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties

A solution is derived for the heat flow and consolidation which occur when a heat source is buried deep in a porous thermoelastic soil having anisotropic flow properties. This solution is used to examine the pore pressure generation and dissipation near both point and cylindrical heat sources. An increase in temperature will tend to generate an increase in excess pore pressure. However, the pore water will tend to flow from regions of high excess pore pressure to regions of low excess pore pressure, and so consolidation will occur, and temperature-generated excess pore pressures will tend to dissipate. Many natural soils exhibit horizontal layering and so have a higher horizontal than vertical permeability. It is shown that in soils the excess pore pressure generated by a heat source is significantly less than that in an isotropic soil having an equal vertical permeability.     

Consolidation around a point heat source

When a heat source such as a canister of radioactive waste is buried in a saturated soil the temperature changes that occur will cause the pore water to expand a greater amount than the voids of the soil. The temperature change will thus usually be accompanied by an increase in pore pressure. If the soil is sufficiently permeable these pore pressures will dissipate. This paper develops an analytic solution for the fundamental problem of a point heat source buried deep in a saturated soil.     

Dynamic response of an elastic and viscoelastic full-space to a spherical source

The dynamic response due to a spherical source of radius a embedded in an elastic and viscoelastic full-space is investigated at a distance R from the source. Previous solutions to the elastic case are extended to incorporate realistic source pressure functions. The elastic solution is then cast in a scale independent form in order to generalize the application. The results show that the near-field of the spherical source may be defined by R/a < 5. For this region the particle velocity and displacement decrease as R^?2, and the risetime decreases as R^?1. However. in the far-field region (R/a > 5) the particle velocity and displacement decrease as R^?1, and the risetime is independent of R. A non-constant Q model is developed to model viscoelastic attenuation and a complete analytical solution for wave propagation is obtained by cascading the separate mechanisms of geometric attenuation and viscoelastic attenuation. A comparison of our analytical model with the results of dynamic finite element modelling shows excellent agreement. This suggests that the method of cascading the separate transfer functions is a valid approach for wave propagation in viscoelastic media.     

Analysis of a point sink embedded in a porous elastic half space

Closed-form solutions are presented for the steady-state distributions of displacement, pore pressure and stress around a point sink embedded in a homogeneous, isotropic elastic half space. These solutions have been evaluated for a typical case of a sink (pump) buried in sand and the magnitude of the settlement of the ground surface has been estimated.     

Analysis of subsidence due to a point sink in an anisotropic porous elastic half space

Analytical solutions of the long-term consolidation deformation and excess pore water pressure due to fluid withdrawal from a saturated anisotropic porous elastic half space are presented. In the analysis, both the permeability and the elastic properties are considered cross-anisotropic. Cases of pervious and impervious half-space boundary are studied. The consolidation settlements as effected by the anisotropy and boundary conditions for pore water are illustrated and discussed.     

Dynamic response of a pile embedded in a porous medium subjected to plane SH waves

In this paper, the frequency domain dynamic response of a pile embedded in a porous medium subjected to SH seismic waves is investigated. The surrounding porous medium of the pile is described by Biot’s poro-elastic theory, while the pile embedded in the porous medium is treated as a beam and described by a beam vibration theory. Using the Hankel transformation method, the fundamental solution for a half-space porous medium subjected to a horizontal circular patch load is established. According to the fictitious pile methodology, the second kind of Fredholm integral equation for the pile is established in terms of the obtained fundamental solution and free wave field. The solution of the integral equation yields the dynamic response of the pile to plane SH waves. Numerical results indicate that the parameters of the porous medium, the pile and incident waves have considerable influences on the dynamic response of the pile and the porous medium.     

某地源热泵场地浅层土壤分层热物性响应实验

浅层土壤导热系数的确定一直是地源热泵系统设计研究中的一个重点。为了获得更精确的土壤热物性,引入分布式光纤测温系统,并在原有柱热源测试模型方法的基础上提出分层热物性测试法并对测试数据进行分析。测试数据包括竖直方向上浅层土壤初始温度分布,稳定功率加热过程中竖直方向地埋管内流体温度随时间变化分布。结果表明:通过分层土壤热物性测试可以更直观地观察地下土壤温度分布,了解土壤中地下水分布情况。并得出竖直方向上不同深度土壤的导热系数、土壤密度与比热容乘积以及回填料热阻分布情况。     

同井回灌循环水方法在中央地温空调中的应用

文章分析了既环保又节能地利用地下水中热(冷)资源的有效途径,提出了同井回灌循环水方法的新思路,使砂土、粉土地层中地下水在中央地温空调中的应用实现突破,并成功地投入使用.同时与异井回灌方法进行了比较,提出了同井回灌法的优越性.     

考虑热-水-力耦合效应多孔弹性地基的动力响应

通过对Biot波动方程的修正,得到考虑热-水-力学耦合效应的多孔弹性介质动力响应的控制方程,研究了简谐均布荷载作用下地基土体的热-水-力耦合动力响应问题。利用Fourier变换技术,得到地基中的应力、位移和孔隙水压力积分形式的解答。利用Fourier逆变换得到数值结果,分析了热-水-力学耦合条件下地基土体中温度增量、应力、位移和孔隙水压力响应的分布,并讨论了热源输入的影响, 结果表明：应力、位移和孔隙水压力随 的增大而有一定的减小。     

Dynamic response to fluid extraction from a poroelastic half‐space

In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd.     

Heat-induced moisture transport in the vicinity of a spherical heat source

The present paper develops an analytical approach to the problem of heat-induced moisture movement in the vicinity of a spherical heat source embedded in an undeformable, moist porous solid of infinite extent. A transient-state distribution of temperature within the infinite medium is assumed to induce the moisture transport process. The numerical results, presented in the paper, illustrate the influence of the moisture transport characteristics on the time-dependent distribution of moisture within the porous medium. © 1998 John Wiley & Sons, Ltd.     

Short-crested wave-induced soil response in a porous seabed of infinite thickness

Waves reflecting obliquely from structures establish short-crested waves which are conducive to scour of the bed adjacent to them. The pore pressures and effective stresses induced by this wave system are derived analytically for an unsaturated, anisotropic soil matrix of infinite depth in a three-dimensional domain. Verification is available by the solutions being readily reduced to the two-dimensional cases of the progressive and standing wave, for which some closed-form solutions are available. It is shown that wave obliquity is coupled with soil permeability. The effects of wave obliquity, relative water depth, soil stiffness and soil permeability on wave-induced pore pressure are discussed in detail.