Uncoupled state space solution to layered poroelastic medium with anisotropic permeability and compressible pore fluid

This paper presents an uncoupled state space solution to three-dimensional consolidation of layered poroelastic medium with anisotropic permeability and compressible pore fluid. Starting from the basic equations of poroelastic medium, and introducing intermediate variables, the state space equation usually comprising eight coupled state vectors is uncoupled into two sets of equations of six and two state vectors in the Laplace-Fourier transform domain. Combined with the continuity conditions between adjacent layers and boundary conditions, the uncoupled state space solution of a layered poroelastic medium is obtained by using the transfer matrix method. Numerical results show that the anisotropy of permeability and the compressibility of pore fluid have remarkable influence on the consolidation behavior of poroelastic medium.     

透明土与标准砂压缩变形特性对比试验研究

人工合成透明土模拟天然土体,以研究土体内部位移场和渗透场等问题的可视化模型试验方法逐渐得到相关工程技术人员的认可与应用;然而,针对不同类型人工合成透明土的压缩变形特性的研究却相对较少。基于熔融石英砂和无定形二氧化硅这两种固体颗粒材料,开展不同孔隙液体、粒径范围及相对密实度等情况下的单向压缩试验;分析不同制配方法和制配材料所制配成的透明土材料的压缩变形特性,并与福建标准砂、Toyoura砂的单向压缩试验进行对比分析。同时,针对典型透明土土体在载荷板作用下的土体内部位移场进行了简要对比分析。试验结果表明,本文试验条件下,由蔗糖溶液制配的熔融石英砂透明土压缩性相对于由混合油及溴化钙溶液制配的压缩性更接近天然砂土;熔融石英砂相对于无定型二氧化硅更适合模拟天然砂土;与福建标准砂相比,透明土材料的压缩性相对较大,且目前模型试验中常用的0.5~1.0 mm粒径制配成的透明土压缩性相对更大,值得相关研究人员重视。     

地下水位波动下基坑周围地基土的孔压响应半解析解

水位波动条件下的基坑性状研究是随工程实践产生的新课题,而基坑周围的孔压响应机制是该课题的关键问题。将基坑渗流场分区,假设土体总应力不变,将固结方程解耦,利用Laplace、Fourier变换推导了浅层含水层内地下水位波动时板式支护基坑周围地基土孔压响应的二维近似半解析解。利用该解答,对综合系数θ（与土体固结系数、海床厚度、水位波动周期相关）、孔隙流体压缩系数与围护墙插入深度的影响进行分析。结果表明：孔压波动幅值沿基坑最短渗流路径不断衰减,滞后相位不断增大;θ越大,基坑周围地基土的相对孔压波动幅值越小,滞后相位越大,稳态渗流时的相对孔压为地下水位波动条件下不同θ值相对孔压波动幅值的极大值;孔隙流体压缩系数越大,基坑周围的波动孔压响应幅值越小,滞后相位越大;围护墙插入深度越大,主动侧相对超孔压波动幅值越大,被动侧波动幅值则越小。     

孔隙流体可压缩各向异性土体三维固结半解析数值模拟

 基于满足边界条件的位移和超孔隙水压力试探函数,利用半解析数值原理建立考虑孔隙流体可压缩性各向异性层状土体三维Biot固结问题的有限层求解格式,由三角函数系的正交性实现加权余量方程按不同级数项的解耦。在编制相应计算程序实现有限层方程求解的基础上,进行算例数值分析,通过计算结果和经典解答的对比验证半解析数值方法的有效性,同时说明渗透各向同性、孔隙流体可压缩性、横观各向同性以及土体层状分布对三维固结行为的影响。     

考虑孔隙流体压缩性的土体平面应变固结 半解析数值分析

针对 Biot 固结基本方程的特点,在构建满足边界条件的位移和超静孔压试探函数的基础上,由 Galerkin 法 建立了考虑孔隙流体可压缩性渗透 各向异性 层状 土体中平面应变固结问题的半解析数值求解格式,并利用三角函数系的正交性实现了加权余量方程按不同级数项的解耦。在此基础上,编制相应计算程序实现了半解析数值方程的求解。通过算例对比分析验证了半解析数值方法的正确性,并说明了其处理渗透各向同性、孔隙流体可压缩性和土体层状的能力。     

Effect of the volume of the drainage system on the measurement of undrained thermo-poro-elastic parameters

For evaluation of the undrained thermo-poro-elastic properties of saturated porous materials in conventional triaxial cells, it is important to take into account the effect of the dead volume of the drainage system. The compressibility and the thermal expansion of the drainage system, along with the dead volume of the fluid filling this system, influence the measured pore pressure and volumetric strain during an undrained thermal or mechanical loading in a triaxial cell. The correction methods previously presented by Wissa [Pore pressure measurement in saturated stiff soils. ASCE J Soil Mech Found Div 1969;95(SM 4):1063–73], Bishop [Influence of system compressibility on observed pore pressure response to an undrained change in stress in saturated rock. Geotechnique 1976;26(2):371–5] and Ghabezloo and Sulem [Stress dependent thermal pressurization of a fluid-saturated rock. Rock Mech Rock Eng 2009;42(1):1–24], only permit one to correct the measured pore pressures during an undrained isotropic compression test or an undrained heating test. An extension of these methods is presented in this paper to correct the measured volumetric strain, and consequently the measured undrained bulk compressibility and undrained thermal expansion coefficients, during these tests. Two examples of application of the proposed correction method are presented for an undrained isotropic compression test and an undrained heating test performed on a fluid-saturated granular rock. A parametric study has demonstrated that the porosity and the drained compressibility of the tested material, and the ratio of the volume of the drainage system to the one of the tested sample, are the key parameters that most influence the error induced by the drainage system.     

Effect of water salinity on Atterberg limits of El-Hodna sabkha soil

Sabkha soils are recent saline sediments widely distributed in Algeria and other countries. As they are characterised by low strength and high compressibility, they are considered to be difficult foundation soils that pose special problems for design and construction engineering. This study deals with the effect of salts on the determination of the water content and Atterberg limits of sabkha soils. The tests were performed using distilled water, natural sabkha brine and saline solutions with different salt concentrations. The results indicate that the liquid and plastic limits decrease with pore fluid salinity when the conventional water content procedure is used, but increase when the fluid content method is used. Also, the results revealed that the oven-drying time of saline soils is highly affected by the size of soil clods and surface salt precipitation.     

饱和城市固废一维降解固结解析解

填埋后的城市固废因降解产生固相质量损失,从而造成在外力作用下的固结是一个相当复杂的过程。为研究饱和城市固废的降解固结特性,建立了一维降解固结普遍模型;基于已有城市固废降解、压缩和渗透特性研究,获得了考虑可降解固相水解、胞内水释放为孔隙水及降解导致压缩性衰变的一维降解固结简化模型;基于简化模型,针对饱和城市固废填埋层底部淤堵不透水和顶部自由排水工况,获得了一维降解固结解析解。针对国内填埋场新鲜城市固废的计算结果表明:在瞬时常荷载作用下,固结初期,填埋层底部的超静孔压值会超过初始值,这主要是因为降解引起固相质量损失导致骨架疏松、压缩性增大;固结后期,整个填埋层出现负的超静孔压,这是因为后期填埋层孔隙比因固相质量损失而增大,而压缩性衰变相对较小。参数敏感性分析表明:降解引起的次压缩速率越大,固结初期超静孔压越大;增加填埋层的先期固结压力会延缓超静孔压的消散。     

非饱和土受压变形的简化计算研究

非饱和土的固结问题是岩土工程研究中非常复杂的热门课题。本文拟将非饱和土受压后的固结过程简单地分为压密和固结两个阶段。在压密过程中,与饱和土固结不同是,由于非饱和土的孔隙水、气来不及排出,与骨架共同承担荷载,产生了超孔隙气压和超孔隙水压,这个阶段土体变形主要是压缩孔隙气产生的压缩变形;固结阶段,土体在恒定荷载作用下,超孔隙气压和超孔隙水压逐渐消散而固结。对于饱和度较高的地基土,将水、气可看作混合流体,并考虑残留混合流体的压缩性,建立平衡微分方程和混合流体的连续方程,求出有效应力和混合流体压力;土体中水压力可通过水连续方程求出,继而求出气压力、吸力等。最后算例表明:加载过程中,有效应力、混合流体压力、水压力不断增大,吸力不断减小;竣工后,混合流体压力、水压力还在增长;由加载产生变形以荷载压密变形为主,之后变形增量逐渐减小。这与路堤填筑过程中的监测结果相一致,说明本文的简化方法是合理的。因此本文的非饱和土固结研究对于促进了非饱和土固结变形计算走向实用化,具有重要的工程意义。     

混凝土孔体积分形维数及其与氯离子渗透性和强度的关系

采用压汞法对含不同掺合料混凝土的孔分形结构进行了试验研究,测定了其孔体积分形维数,探讨了含不同掺合料混凝土的孔体积分形维数与氯离子渗透性能及强度的关系。结果表明:混凝土孔体积分形维数越大氯离子渗透系数越大;含不同掺合料混凝土的孔体积分形维数与氯离子渗透系数相关性由高到低依次为:粉煤灰矿渣石灰石水泥;含不同掺合料的混凝土的孔体积分形维数与强度相关性由高到低依次为:粉煤灰矿渣水泥石灰石。     

孔隙压力变化对岩石强度特性的影响

 在油气开采过程中,注采制度的改变必然会引起孔隙压力的波动,进而影响到储层岩石的力学性质。通过三轴抗压实验研究不同孔隙压力下的岩石强度特性及周期性孔隙压力作用下的岩石变形特征,结果表明,围压恒定,随孔隙压力下降,岩石的三轴抗压强度、弹性模量、体积模量、剪切模量都呈现增大趋势,泊松比整体呈下降趋势。对采用降压方式开发的油气藏,随着孔隙压力降低,岩石体积模量增大,体积压缩系数减小,岩石的可压缩性逐渐减弱。孔隙压力周期性加、卸载过程中岩石的轴向应变、径向应变和体积应变都将随循环周期逐渐累积,在加、卸载初期变化较大,随循环次数增加逐渐趋于稳定。岩石强度及变形规律随孔隙压力的变化规律表明,油气藏开发初期的压力降落对储层物性的影响和损害大,在储层开发前期若不采取有效措施稳定地层压力,到储层开发后期,再通过注入流体来改变地层的渗透率不会产生明显的效果,而且岩石变形的累计还可能诱发、诱导地层破坏甚至灾害性事件发生。     

Mechanical characterization of small shale samples subjected to fluid exposure using the inclined direct shear testing device

The mechanical strength, elastic moduli, and other properties of shale are known to be highly sensitive to any variation in pore fluid content and pore fluid chemical composition. To date, all existing rock mechanics testing procedures and studies attempting to quantitatively quantify these changes employ standard methods and techniques, i.e., shale testing under hydrostatic confinement, triaxial tests, or direct shear tests, which require very long fluid circulation time due to the intrinsic low hydraulic permeability and low solute diffusivity of shale rocks and large sample size recommended by these conventional methods. Moreover, standard-size samples for conventional rock testing methods are not always available, and the use of non-conventional size samples is sometimes required. In this work, shale testing and results on rock sample the size and shape of a stack of a few pennies are presented. The inclined direct shear test, an innovative patent-pending testing method for small and thin rock specimens, has been developed to facilitate mechanical strength characterization under variable confining pressure, with tested material exposed to different fluids at any desired exposure time, while dynamic elastic moduli can be simultaneously monitored as functions of applied stress state. This device has been compared to standard triaxial test with excellent results. Practical applications using the inclined direct shear testing device (IDSTD^TM) for three shale rocks of different natures are also presented herein.     

Film-pore diffusion model for the fixed-bed sorption of copper and cadmium ions onto bone char

The sorption of copper and cadmium ions onto bone char in single component systems has been studied using fixed-bed column adsorbers. The effects of solution flowrate, initial metal ion concentration and bone char particle size have been studied. A film-pore diffusion model has been developed to predict the fixed-bed breakthrough curves for the two metal ions. A sensitivity analysis has been carried out to investigate the influence of the external mass transfer coefficient (film resistance), the effective diffusion coefficient (pore diffusion) and the solid phase loading capacity. It is found that under the experimental conditions employed in the study, film diffusional resistance was low and the Biot numbers were relatively high. Furthermore, a constant effective pore diffusivity was not sufficient to correlate the breakthrough curves accurately and a variable dependent effective diffusivity was required; suggesting a possible contribution from surface diffusion. Since the metal ion-bone char systems take a long time to reach equilibrium, the solid phase loading capacity, as predicted by the "best-fit" equilibrium isotherm, was not suitable for use in the diffusional mass transport model and the mass balance solid phase loading was utilised instead.     

Buckling analysis of thin circular FG plates made of saturated porous-soft ferromagnetic materials in transverse magnetic field

This study presents the buckling analysis of soft ferromagnetic FG circular plates made of poro material. Equilibrium and stability equations of a poro circular plate in transverse magnetic field are derived. This study analyzes the poroelastic instability of clamped edge ferromagnetic plates subjected to magnetic loadings. The geometrical nonlinearities are considered in the Love–Kirchhoff hypothesis sense. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are being investigated.     

考虑温度效应的固结问题有限元分析

研究热固结问题需考虑诸多因素、试验条件不易控制且所需时间长从而难以实现,因此辅以数值计算手段具有十分重要的意义。本文根据饱和土体热固结问题中温度、渗流及应力之间的复杂耦合关系,系统地探讨了二维有限单元方法的求解过程,并在FORTRAN语言环境下研制了相应的计算机分析程序APOSE-T。文中选取一典型算例并进行适当改编,应用APOSE-T程序分析研究土体热固结问题的主要规律,同时也考证了程序的正确性。研究表明,水和土颗粒的压缩性一般对孔压的变化速度有延缓作用,但对固结效果影响不显著,故一般的固结分析时可以忽略;在不考虑自身发热条件下,研究域内经历先升温然后降温的过程,但在升温前的短时间内有微小的降温,且温度对固结的影响时间不长。本文的研究成果为分析热固结过程提供了一条有效途径。     

Consolidation and creep of soil layer of limited width under a local load

Expressions in the form of series are derived for determination of the stress distribution, deformations, and displacements in a soil region subject to local loading under plane deformation and various conditions on the lateral boundaries. A comparison of the stress and strain state was made between the region under consideration and the mass of soil in the form of a half-space. Expressions in the form of series are derived for determination of pore-pressure distribution in the soil region under consideration, and also the settlement of any point of the surface over time with allowance for the compressibility of the pore water and the creep of the soil skeleton. Secondary consolidation in the soil mass under conditions of the plane problem is discussed. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 2, pp. 2–6, March–April, 1998.     

Probabilistic nature of cyclic load pore pressure in cohesive soil

The probability distribution of cyclic-load-induced pore pressure in contractive cohesive soil is derived based on its dependence on the compressibility of voids. The gamma distribution is established to be the most appropriate by summing exponential changes in the soil compressibility resulting from changes in the condition of the voids. However, since the pore pressure in this soil type is bounded, the upper limit being equal to the undrained strength of the soil and the lower limit near zero, the distribution can be approximated by beta for specified limits.It is established also that the normal distribution can be adopted for the cyclic load pore pressure without loss of accuracy because the gamma distribution approaches the unit normal distribution as the gamma parameter becomes very large. Besides, the gamma distribution has been derived by considering contributions from an infinite number of voids. Therefore the normal distribution, which is generally known as the probability model for sums of random variables when the number of variables is infinitely large, is a fairly reliable approximation of the pore pressure distribution for purposes of practical application.     

孔隙液体对玻璃砂透明土强度特性影响研究

玻璃砂透明土由一种玻璃砂(或称熔融石英砂)和与之折射率相一致的孔隙液体制配而成的新型人工合成透明土,为岩土工程可视化模型试验方法提供技术支撑。开展混合油、溴化钙溶液、蔗糖溶液以及纯净水等不同孔隙液体所制配成的透明土的三轴固结排水(CD)试验,分析该新型透明土材料的应力–应变关系曲线、体积变形等力学特性以及推导其邓肯–张模型参数。试验结果表明,不同孔隙液体所制配成的透明土试样力学特性规律相似、数值上有所差异;由蔗糖溶液制配成的透明土强度最大、由混合油制配成的透明土强度最小、由溴化钙溶液制配成的透明土强度值与水样熔融石英砂的强度相对更接近。     

Microstructure-based modeling of water diffusivity in cement paste

In view of the crucial influence of water diffusion in cement paste on durability, it is necessary to predict the water diffusivity of cement-based materials. The main purpose of this paper is to present a computational approach to predict the water diffusivity in cement paste. A computer-based cement hydration model HYMOSTRUC3D is used to generate the 3D microstructure of cement paste. The simulated pore structure is compared with the experiments. Based on the generated microstructure, finite element method (FEM) is applied to simulate the diffusion process of tritiated water through the saturated cement paste. In the FE simulation, cement paste is modeled as a three-phase composite material, consisting of capillary pores, un-hydrated cement and hydration products. Un-hydrated cement is considered non-diffusible. The contribution of capillary pore phase and hydrating products phase to the diffusivity of tritiated water in cement paste are taken into account. Finally, the diffusivity modeling is applied for series of hardened cement paste with variations on water-to-cement (w/c) ratio and curing age. The simulations are validated with experimental data obtained from literature. The comparison between simulation and experiments indicate that the simulated and experimental data are of the same order of magnitude. Furthermore, the tendency of simulated relationship (diffusivity vs. w/c ratio, diffusivity vs. curing age) shows a good fit to the experiments.     

Impact of pore structure and morphology on flow and transport characteristics in randomly repacked grains with different angularities

The flow and transport behaviors in porous media are closely linked to the structure and morphology of the pore space. A fundamental objective of most studies of porous media is to link the pore structure to the hydraulic functions, such as the permeability, capillary pressure and diffusivity, which are necessary for engineering applications. In this paper, an attempt is made to build a direct link between the hydraulic functions and the morphological measures of diverse porous media. Porous columns with different structures and morphologies are generated by randomly packing grains with different shapes and sizes. The pore structure of the repacked porous media is visualized through X-ray computed tomography and quantified by a series of parameters, including the set of Minkowski functionals, diverse characteristic pore sizes, geometric tortuosity and fractal dimension. The intrinsic permeability, molecular diffusivity and apparent thermal conductivity of the repacked porous media are simulated numerically. The Minkowski functionals have the capacity to characterize the microscale complex pore domain of the porous media in a macroscale way. A good linear relationship is shown among the effective pore size, nominal opening dimension and critical pore neck size obtained from the morphological analysis regardless of the shapes and sizes of the grains. The three different pores may serve as the characteristic pore correlation to the intrinsic permeability. The Kozeny-Carman equation can be used to mimic the intrinsic permeability and to serve as a quality-control tool for porous media with different grain angularities. A topologically based model can generally provide a single relationship for porous media randomly repacked with grains of different angularities. The molecular diffusivity of angular grains is found to be larger than that of round ones. The molecular diffusivity is linearly related to the porosity and fractal dimension. Porous media repacked with round grains tend to attain denser packing, a higher number of contacts per unit volume and higher thermal conductivity than media packed with angular particles. The apparent thermal conductivity has a negative linear correlation to the porosity and fractal dimension of porous media with different grain morphologies.