竖向简谐荷载下二维层状饱和地基的解析层元解

基于Biot固结理论,运用解析层元方法求解竖向简谐荷载作用下二维层状饱和地基的动力响应问题。从直角坐标平面应变问题控制方程出发,通过Fourier-Laplace变换将偏微分方程组转化为常微分方程组,求解得到单层饱和地基的解析层元。结合层间连续条件和边界条件,组装得到多层饱和地基的总刚度矩阵方程,进而求得变换域内的解。借助Fourier-Laplace逆变换的数值积分方法,获得平面应变动力问题在物理域内的解,编制了相应的计算程序,其计算结果与已有文献结果吻合较好。通过算例分析了荷载圆频率、荷载作用深度及地基成层性对地基竖向位移的影响。计算结果表明：随荷载圆频率的增大,地基竖向位移先增加后减小;地基竖向位移在荷载作用点处呈现波峰,且受表层土性的影响较大。     

具有不规则界面的层状地基三维动力响应的薄层法

天然地基通常含有不规则的分层界面。对此,提出了一种计算具有不规则界面的层状地基三维动力响应的薄层法,推导了简谐点源作用下不规则分层半空间三维动力问题的基本解。基于双重Fourier变换,获得弹性介质在频域-波数域内的薄层单元系统控制方程;利用模态叠加原理,推导了半无限长和有限长薄层单元的刚度矩阵,引入完美匹配层模拟波向底层半无限空间的传播,从而构建可考虑土层界面沿横向不规则分布的三维层状地基计算模型,获得了简谐点源作用下不规则分层地基三维动力问题的基本解;通过与既有方法的对比分析,验证了新方法的正确性。最后,利用该方法计算了具有倾斜分层界面的双层地基在简谐荷载作用下的动力响应,结果表明：界面倾斜导致的动力响应差异大,且随着倾斜度以及荷载频率的增加而变大。在进行天然地基的动力分析时,需考虑地基的不规则分层特性导致的振动响应差异。     

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。     

基于传递-反射矩阵法的层状公路结构动力响应研究

利用传递-反射矩阵方法和叠加原理推导了双轮胎振动荷载作用下弹性层状公路结构的动力响应解,并利用Hankel数值逆变换技术进行了数值求解。弹性层状结构的传递-反射矩阵同时具有单个矩阵尺寸小、矩阵元素只含有负指数项2个优点,计算结果不受土层单元厚度与荷载频率大小的影响,可以大幅提高计算效率和精度。通过将数值计算与室内模型试验结果进行比较,验证了方法的正确性。在此基础上,分析了面层厚度及模量对层状公路结构动应力、动位移的影响程度和规律,得出了一些有意义的结论。研究结果可为公路路面、路基结构设计提供参考。     

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.     

Thermal stresses in borehole heat exchangers

The backfilling materials of borehole heat exchangers (BHE), particularly the grout material, must provide a suitable thermal contact and ensure durability to the induced thermal stresses because of the heat loading. In this paper, the thermal stresses that occurred in BHEs because of heat injection or extraction is investigated with an analytical solution of a hollow cylinder model that is adapted for time‐dependent heat loading, the geometry of a BHE, and the thermo‐mechanical properties of surrounding ground conditions. Firstly, the hollow cylinder model is solved with the considered boundary conditions in 2D plane stress. Secondly, the temperature differences at the inner and outer circles of the cylinder are evaluated with the heat line source models for continuous and discontinuous loading to observe the impact of the heat loading schedule. The developed analytical solution for thermal stress investigation is validated with numerical models. It is demonstrated that the analytical solutions agree well with numerical results for two types of BHE configurations (co‐axial and single U‐shaped pipes). Furthermore, the calculated maximum stresses are compared with the tensile strength of grout materials obtained from Brazilian tests. It is predicted that the thermal contraction of the grout, partially constrained by the surrounding rock, generates tensile stresses that may lead to cracking in the BHE. According to the results, the stiffness of rock has a primary role on the developed tensile stresses, and the relationship between the thermal conductivity of the ground and of the grout induces a proportional impact on the magnitude of thermal stresses. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupled consolidation and heat flow analysis of layered soils surrounding cylindrical heat sources using a precise integration technique

The engineering applications of energy piles, geological radioactive waste disposals, and mining wells of geothermal and petroleum are usually associated with strong coupled behaviour of consolidation and heat flow. This paper aims to present an efficient precise integration technique (PIT) for the analysis of such behaviour within layered saturated soils surrounding cylindrical heat sources (ie, with a cross section as a point, ring, or disc). Each soil layer, together with its embedded part of heat source, is divided into 2^N layer elements with equal thickness. Then any pair of adjacent two layer elements are merged into a heat source on the interface. With the aid of Taylor series expansion and recurrence formula for adjacent layer elements combination, such problems can be solved by means of an improved PIT. Typical examples are performed to examine the effects of heat source type and soils layered properties on the coupled consolidation and heat flow responses. The elevation of the clay surface increases with time because of thermal expansion and reaches a peak value before showing a tendency of getting stabilised because of the dissipation of pore pressure becoming dominant. Such a peak cannot be achieved in sand case because of no accumulation of pore pressure. The influencing area of the heat source was found to be limited to near the source. These quantitative results serve as good verification of the presented technique, which proves to be remarkably efficient and several orders more accurate than traditional numerical techniques in that it ideally reaches the accuracy limit of the hardware of the computers used.     

A three-dimensional heat transfer and thermal cracking model considering the effect of cracks on heat transfer

A simple three-dimensional heat transfer model is developed to consider the hindering effect of cracks on heat transfer. The 3D heat transfer model can also be applied to numerical methods such as the combined finite-discrete element method (FDEM), discrete element method (DEM), discontinuous deformation analysis (DDA), the numerical manifold method (NMM), and the finite element method (FEM) to construct thermo-mechanical coupling models that allow these methods to solve thermal cracking problems and dynamically consider the hindering effect of cracks on heat transfer. In the 3D heat transfer model, the continuous-discontinuous medium is discretized into independent tetrahedral elements, and joint elements are inserted between adjacent tetrahedral elements. Heat transfer calculations for continuous-discontinuous media are converted to heat conduction in tetrahedral elements and the heat exchange between the adjacent tetrahedral elements through the joint element. If the joint element between adjacent tetrahedral elements breaks (ie, a crack generates), the heat exchange coefficient of the joint element is reduced to account for the hindering effect of cracks on heat conduction. Then the model and the FDEM are combined to build a thermo-mechanical coupling model to simulate thermal cracking. The thermally induced deformation, stress, and cracking are investigated by the thermo-mechanical coupling model, and the numerical results are compared with analytical solutions or experimental results. The 3D heat transfer model and thermo-mechanical model can provide a powerful tool for simulating heat transfer and thermal cracking in a continuous-discontinuous medium.     

套管式地埋管换热器热短路及换热性能

套管式地埋管换热器是深层地源热泵系统常用的换热装置。基于流体流动换热方程,建立套管式地埋管换热器与周围岩体之间的传热模型。以第一个供暖季为例,分析内管导热系数和循环水流量对换热性能的影响,并引入换热器效能对热短路现象进行评估,研究结果显示：内管导热系数越大,热短路现象越显著;热短路使内外管中循环水温差降低,管内出现热堆积,导致换热器换热功率降低;套管式地埋管换热器的换热功率随循环水流量的增大逐渐增大;内外管之间存在热短路时,出口水温随循环水流量的增大先升高后降低,随着流量增大,换热器效能增大。研究成果可为深层地源热泵系统中地埋管换热器的设计提供借鉴。     

用弹性板理论分析顺层岩质边坡的失稳

根据弹性板的稳定理论，利用能量法对缓倾角顺层岩质边坡的弯曲失稳机理进行了探讨，特别考虑了边坡长度的影响，推导了相应的计算公式，并通过计算实例，将文中的方法与用平面应变问题的弹性梁分析得出的结果做了对比，验证了文中方法的可行性。     

水平层状场地自振频率的剪切质点系法研究

场地土层的自振频率是场地土的重要动力特性之一。为避免结构物与场地地基的共振效应,工程设施的固有频率应尽量避开地基的固有频率。在传统的基于集中质量矩阵的剪切质点系法（集中质量法）的基础上,发展了基于一致质量矩阵的剪切质点系法。在此基础上,对利用剪切质点系法求解水平层状场地自振频率的精度的影响因素进行了分析,主要考虑了土层分层特性、质量矩阵形式以及材料阻尼3个影响因素,分析表明：分层数越多,计算结果越接近真实解,从实际工程角度出发,分层数超过三层时可不再细分;在层数相等的情况下,层厚对计算结果精度的影响甚微;一致质量法的计算结果要优于集中质量法,且表现出上限解性质;在通常小阻尼情况下,阻尼对自振频率的影响很小。     

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.     

基于现场热响应测试方法的地下岩土热物性分析

目前获取导热系数的主要方法是现场热响应试验,但该方法缺乏统一的技术标准,导致计算结果可比较性差,难以应用。笔者开展了不同热响应试验设备的原位热物性测试系列试验,分析了测试与数据处理方法对测试结果的影响,探讨了试验过程中需要注意的问题。结果显示：为减少试验误差,两次热响应试验测试的时间间隔不应少于10 d;应尽量避免循环水与岩土介质以外的其他介质产生热量交换;对于恒热流热响应试验,导热系数值与舍弃时间（1.0~12.0 h）成正相关关系;而对于定进回循环水温差的热响应试验,导热系数值与舍弃时间（0.0~12.0 h）成负相关关系;舍弃时间大于12.0 h时,导热系数变化趋于稳定。按统一标准舍弃前12.0 h的测试数据进行导热系数计算,6家单位的导热系数计算值都在2.2～2.8 W/(m·℃)范围内,测试结果合理可靠。