A fluid-pressure feedback model of dehydration reactions: experiments, modelling, and application to subduction zones

Dehydration and melting reactions generate large volumes of fluid in the crust and upper mantle, and play an important role in subduction zone seismicity. The fluid pathway must evolve from isolated pockets in low porosity, low permeability rock, coalescing to interconnected permeable pathways to the surface. When fluid pressures generated from a dehydration or melting reaction are sufficient to induce hydrofracture, then hydrofracture significantly influences the porosity–permeability structure within the dehydrating/melting horizon. If a low fluid-pressure boundary is introduced to the dehydrating rock, then fluid will be driven from the rock along the evolved permeable network toward that boundary. The resulting pressure reduction can then accelerate the dehydration reaction and further drive the flow. The sudden introduction of a low fluid-pressure boundary may occur by the co-seismic (dilatant) rupturing of a pressure seal that connects different fluid pressure states. This mechanism is invoked to explain the observed post-seismic evolution of wave velocities (V_p/V_s) following the 1995 Antofagasta, Chile earthquake. We show experimental results and introduce a conceptual and numerical model that reflects this scenario. The model couples the mechanical and thermodynamic effects of fluid pressure with devolitization kinetics, and is quantitatively consistent with experimental studies of the dehydration of gypsum and serpentine. The experimental results show that dehydration is controlled by access to a free (drained) boundary. The model provides a mechanistic explanation for the experimental observations and has applications in understanding the role of transient transport networks on the large-scale behavior of dehydrating and melting systems.     

A two-scale constitutive framework for modelling localised deformation in saturated dilative hardening material

Undrained deformation of dilative sand generates negative excess pore pressure. It enhances the strength, which is called dilative hardening. This increased suction is not permanent. The heterogeneity at the grain scale triggers localisations causing local volume changes. The negative hydraulic gradient drives fluid into dilating shear zones. It loosens the soil and diminishes the shear strength. It is essential to understand the mechanism behind this internal drainage and to capture it numerically. The purpose of this paper is to develop a macroscopic constitutive relationship for the undrained deformation of saturated dense sand in the presence of a locally fully or partially drained shear band. Separate constitutive relations are generated for the band and intact material. Both time and scale dependence during pore fluid diffusion in saturated sand are captured, eliminating the mesh dependency for finite element implementations. The model is applied to the Gauss points that satisfy the bifurcation criterion. The proposed method is calibrated to recreate the undrained macroscopic response bestowed by an extra-small mesh. The microscopic behaviours inside and outside shear band predicted by this model are qualitatively in good agreement with individual material point behaviours inside and outside the shear band in the extra-small mesh. Depending on the loading rate and the shear band thickness, the response inside the band can be fully or partially drained, which governs the ultimate global strength. The calibrated model is exploited to simulate an upscaled biaxial compression test with semipermeable boundaries.     

Metamorphic reaction rate controlled by fluid pressure not confining pressure: implications of dehydration experiments with gypsum

Pressure is a key control on the progress of metamorphic reactions. When fluids are present in rocks, the fluid pressure is commonly different to the load supported by the solid framework. Here, we show experimentally that, when the two pressures are varied independently, fluid pressure exerts the dominant control on reaction rate, even when the rock is compacting. We present 35 experiments on gypsum dehydration with independently controlled confining pressure, pore fluid pressure and temperature. Results show that a pore fluid pressure decrease at constant confining pressure has a strong effect on the average rate of the reaction. A decrease in confining pressure at constant pore fluid pressure has relatively little effect. Our results have implications for reaction kinetics: even though the product phase is supporting more and more load as reaction proceeds, that load does not appear to exert a chemical effect. On the large scale, our results imply that changes in fluid pressure will drive or stop the progress of metamorphic reactions. When estimating depth at which a metamorphic devolatilization reaction occurs, knowledge of the pore fluid pressure may be necessary rather than commonly used lithostatic pressure. This is relevant for basin diagenesis, mineralization in hydrothermal systems and chemical evolution after pore fluid pressure is perturbed by earthquakes.     

循环荷载下软黏土不排水强度弱化分析的动力有限元ABAQUS实现

在波浪循环荷载作用下饱和软黏土地基出现孔隙水压力升高,并导致不排水强度弱化,严重影响防波堤的承载性能。考虑静偏应力影响,基于最大孔隙水压力发展模型和正常固结软黏土不排水强度公式,推导出软黏土不排水强度随循环荷载作用次数和应力水平变化的动态折减规律。结合软黏土不排水强度动态折减规律和M-C屈服准则,在有限元软件ABAQUS上实现软黏土不排水强度循环弱化分析的数值开发和动力运算过程。运用该动力有限元方法对天津港防波堤地基软黏土的动、静三轴试验进行数值模拟运算。结果表明,最大孔隙水压力发展曲线以及循环荷载作用后不排水强度的数值预测结果与动三轴试验结果吻合良好。另外,动力有限元方法（DFEM）能够表示土体强度在循环荷载作用下的具体弱化过程。     

Two-phase Material Point Method applied to the study of cone penetration

This paper presents numerical simulations of Cone Penetration Test (CPT) in water-saturated soft soils taking into account pore pressure dissipation during installation. Besides modelling interaction between soil skeleton and pore fluid, the problem involves large soil deformations in the vicinity of the penetrometer, soil–structure interaction, and complex non-linear response of soil. This makes such simulations challenging. Depending on the soil’s permeability and compressibility, undrained, partially drained or drained conditions might occur. Partially drained conditions are commonly encountered in soils such as silts and sand–clay mixtures. However, this is often neglected in CPT interpretation, which may lead to inaccurate estimates of soil properties. This paper aims at improving the understanding of the penetration process in different drainage conditions through advanced numerical analyses. A two-phase Material Point Method is applied to simulate large soil deformations and generation and dissipation of excess pore pressures during penetration. The constitutive behaviour of soil is modelled with the Modified Cam Clay model. Numerical results are compared with experimental data showing good agreement.     

A multisurface kinematic hardening model for the behavior of clays under combined static and undrained cyclic loading

In dynamic geotechnical problems, soils are often subjected to a combination of sustained static and fast cyclic loading. Under such loading conditions, saturated and normally consolidated clays generally experience a build-up of excess pore water pressure along with a degradation of stiffness and strength. If the strength of the soil falls below the static stress demand, a self-driven failure is triggered. In this paper, a constitutive model is presented for the analysis of such problems, based on a general multisurface plasticity framework. The hardening behavior, the initial arrangement of the surfaces, and the nonassociated volumetric flow rule are defined to capture important aspects of cyclic clay behavior. This includes nonlinear hysteretic stress-strain behavior, the effect of anisotropic consolidation, and the generation of excess pore water pressure during undrained cyclic loading along with a degradation of stiffness and strength. The model requires nine independent parameters, which can be derived from standard laboratory tests. A customized experimental program has been performed to validate the model performance. The model predictions show a good agreement with test results from monotonic and cyclic undrained triaxial tests, in particular with respect to the strain-softening response and the number of loading cycles to failure. A procedure for a general stress-space implicit numerical implementation for undrained, total stress-based finite element analyses is presented, including the derivation of the consistent tangent operator. Finally, a simulation of the seismic response of a submarine slope is shown to illustrate a possible application of the presented model.     

基于黏弹性理论的沉桩再固结问题分析

假设桩周土体为饱和黏弹性介质,采用Burgers流变模型进行描述,同时考虑竖向和径向固结,建立了固结控制方程。根据不排水和自由排水情况,将边界条件分为3类并分别得到超孔隙水压力消散的级数解答,该解答能够为孔压静力触探反求固结系数提供一定的理论依据。在此基础上编制了应用程序,对Burgers流变模型中主要参数进行了分析。结果表明,地基表面自由排水、桩端地基不排水条件下,在一定深度以内的桩周土体的固结速度随深度降低,但超过某一范围后固结速度趋于稳定;上、下边界均自由排水条件下,固结速度随深度增加呈现下降、稳定、升高;上、下边界均不排水条件时,孔压消散速度不随深度变化,可简化为本解答仅考虑径向固结的特例。同时土体的流变特性对超孔隙水压力消散的影响比较显著,流变参数G1/1的变化使超孔隙水压力趋于某不为0的定值,且该值随G1/1比值的增大而增加;其他参数不变时,土体剪切刚度比G1/G2的增大会引起孔压消散速度的下降。     

Stress dependent thermal pressurization of a fluid-saturated rock

Summary  Temperature increase in saturated porous materials under undrained conditions leads to thermal pressurization of the pore fluid due to the discrepancy between the thermal expansion coefficients of the pore fluid and of the solid matrix. This increase in the pore fluid pressure induces a reduction of the effective mean stress and can lead to shear failure or hydraulic fracturing. The equations governing the phenomenon of thermal pressurization are presented and this phenomenon is studied experimentally for a saturated granular rock in an undrained heating test under constant isotropic stress. Careful analysis of the effect of mechanical and thermal deformations of the drainage and pressure measurement system is performed and a correction of the measured pore pressure is introduced. The test results are modelled using a non-linear thermo-poro-elastic constitutive model of the granular rock with emphasis on the stress-dependent character of the rock compressibility. The effects of stress and temperature on thermal pressurization observed in the test are correctly reproduced by the model. Correspondence: Dr. S. Ghabezloo, CERMES, Ecole Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Cité Descartes, 77455 Champs-sur-Marne, Marne la Vallée cedex 2, France     

Comparative study of the compression and uplift of shallow foundations

This paper compares the compression and uplift capacity of a strip foundation from numerical coupled analyses using the Modified Cam Clay (MCC) soil model. The focus is on the failure mechanism and pore pressure development in the soil. Triaxial compression and tension tests were first modelled to develop a rigorous understanding of the pore pressure responses; then, the compression and uplift of a strip foundation were modelled. The results show that the balance of excess pore pressures due to the changes in mean total stress and deviatoric stress during the compression and uplift of a strip foundation are different, although the ultimate undrained capacities are identical. Furthermore, the resistance and excess pore pressure responses during uplift differ from those in compression under the K₀-consolidated condition because of the elastic unloading. Although the failure mechanisms have identical shape and size between undrained compression and uplift, the pore pressure distribution in the soil is different and affects the load–displacement behaviours under partially drained compression and uplift.     

Reaction-induced fluid flow in synthetic quartz-bearing marbles

The reaction kinetics and fluid expulsion during the decarbonation reaction of calcite+quartz=wollastonite+CO₂ in water-absent conditions were experimentally investigated using a Paterson-type gas apparatus. Starting materials consisted of synthetic calcite/quartz rock powders with variable fractions of quartz (10, 20, and 30 wt%) and grain sizes of 10 µm (calcite) and 10 and 30 µm (quartz). Prior to reaction, samples were HIPed at 700 °C and 300 MPa confining pressure and varying pore pressures. Initial porosity was low at 2.7–6.3%, depending on pore pressure during HIP and the amount and grain size of quartz particles. Samples were annealed at reaction temperatures of 900 and 950 °C at 150 and 300 MPa confining pressures, well within the wollastonite stability field. Run durations were between 10 min and 20 h. SEM micrographs of quenched samples show growth of wollastonite rims on quartz grains and CO₂-filled pores between rims and calcite grains and along calcite grain boundaries. Measured widths of wollastonite rims vs. time indicate a parabolic growth law. The reaction is diffusion-controlled and reaction progress and CO₂ production are continuous. Porosity increases rapidly at initial stages of the reaction and attains about 10–12% after a few hours. Permeability at high reaction temperatures is below the detection limit of 10^–21 m² and not affected by increased porosity. This makes persistent pore connectivity improbable, in agreement with observed fluid inclusion trails in form of unconnected pores in SEM micrographs. Release of CO₂ from the sample was measured in a downstream reservoir. The most striking observation is that fluid release is not continuous but occurs episodic and in pulses. Ongoing continuous reaction produces increase in pore pressure, which is, once having attained a critical value (P_crit), spontaneously released. Connectivity of the pore space is short-lived and transient. The resulting cycle includes pore pressure build-up, formation of a local crack network, pore pressure release and crack closure. Using existing models for plastic stretching and decrepitation of pores along with critical stress intensity factors for the calcite matrix and measured pore widths, it results that P_crit is about 20 MPa. Patterns of fluid flow based on mineralogical and stable isotope evidence are commonly predicted using the simplifying assumption of a continuous and constant porosity and permeability during decarbonation of the rock. However, simple flow models, which assume constant pore pressure, constant fluid filled porosity, and constant permeability may not commonly apply. Properties are often transient and it is most likely that fluid flow in a specific reacting rock volume is a short-lived episodic process.Editorial responsibility: J. Hoefs     

Coupling of solid deformation and pore pressure for undrained deformation—a discrete element method approach

This paper presents a numerical scheme for fluid‐particle coupling that uses the discrete element method by taking into consideration solid deformation and pore pressure generation. A new water particle element is introduced to calculate pore water pressure due to porosity changes. The water particle element has the same size and shape as the solid element and experiences the same amount of deformation. On the basis of the effective stress principle at the element contact, the total force is equal to the sum of the force transmitted through the solid element contact and the water particle force due to pore water pressure. Analytical solutions of traditional soil mechanics problems, such as isotropic compression and consolidated triaxial undrained test, are used to quantitatively validate the proposed model. The numerical results show good agreement between the model and the analytical solutions. The model therefore provides an effective method to calculate pore pressure in a porous medium in discrete modeling.     

Eulerian finite element analysis of excess pore pressure generated by spudcan installation into soft clay

This paper reports an analytical exploration into excess pore pressures generated during offshore spudcan installations. The analysis was conducted using ABAQUS/Explicit for three effective-stress constitutive models coded using the user-defined material subroutine VUMAT. The results demonstrate the feasibility of conducting effective-stress finite element analysis of undrained spudcan penetration using Eulerian approach. They also show that the computed penetration resistance and pore pressure response depend significantly on the undrained shear strength computed by the different models.     

波浪作用下临海基坑超孔压响应试验研究

以港珠澳大桥拱北隧道明挖段基坑工程为背景,根据相似比尺理论,确定具体的试验模型,利用多功能波浪流水槽系统,研究了波浪作用下黏质粉土基坑周围的超孔压响应规律,研究发现,临海基坑周围的超孔压由振荡超孔压和累积超孔压两部分组成;振荡超孔压幅值沿着从坑外主动区到坑内被动区的渗流路径逐渐衰减,同时伴随着波动相位的滞后,且振荡超孔压幅值衰减值越大,相位滞后也就越明显;基坑主动区的超孔压以随着时间逐渐减小的速率累积,判断临海基坑周围某一位置处的超孔压累积情况,应该从该处的排水条件好坏及由波浪荷载产生的动应力大小两方面分析,排水条件越差或由波浪荷载产生的动应力越大,就越有利于该处超孔压的累积;基坑被动区的振荡超孔压及累积超孔压均相对较小。     

A cavity expansion–based solution for interpretation of CPTu data in soils under partially drained conditions

A cavity expansion–based solution is proposed in this paper for the interpretation of CPTu data under a partially drained condition. Variations of the normalized cone tip resistance, cone factor, and undrained-drained resistance ratio are examined with different initial specific volume and overconsolidation ratio, based on the exact solutions of both undrained and drained cavity expansion in CASM, which is a unified state parameter model for clay and sand. A drainage index is proposed to represent the partially drained condition, and the critical state after expansion and stress paths of cavity expansion are therefore predicted by estimating a virtual plastic region and assuming a drainage-index–based mapping technique. The stress paths and distributions of stresses and specific volume are investigated for different values of drainage index, which are also related to the penetration velocity with comparisons of experimental data and numerical results. The subsequent consolidation after penetration is thus predicted with the assumption of constant deviatoric stress during dissipation of the excess pore pressure. Both spherical and cylindrical consolidations are compared for dissipation around the cone tip and the probe shaft, respectively. The effects of overconsolidation ratio on the stress paths and the distributions of excess pore pressure and specific volume are then thoroughly investigated. The proposed solution and the findings would contribute to the interpretation of CPTu tests under a random drained condition, as well as the analysis of pile installation and the subsequent consolidation.     

开孔管桩复合地基排水固结解析解

现有复合地基的竖向增强体往往无法兼具排水能力与竖向刚度。基于该工程现状,提出一种桩身开孔、能够达到排水效果的新型预制管桩,并针对其开展地基固结分析。假设孔洞流体满足管流条件以及管桩内往孔压连续,并考虑褥垫层的协调作用,推导出排水桩等应变固结解析解。基于该解析解,首先对砂井、碎石桩、不排水桩以及排水桩在相同外径尺寸情况下的排水固结能力进行了对比,结果显示开孔排水桩具有最好的排水固结能力。接着分析了桩身模量、褥垫层模量以及井径比的影响。最后分析了桩身性质（桩身开孔和桩体弹性模量）的影响,计算结果表明,排水能力和模量是影响固结性能的两个主要因素,且排水能力最为重要。但在排水能力相同的情况下,桩身模量越大,则固结越快。     

孔壁地层超静孔隙水（气）压力的形成及其对瓦斯抽排井套管稳定性影响

瓦斯抽排井套管失稳的事故时有发生。为了探索套管失稳机理,应用土力学原理分析了钻井和固管过程中孔壁地层超静孔隙水（气）压力的形成机制;建立了孔壁地层超静孔隙水（气）压力对套管作用的力学模型,该模型包含超静孔隙水（气）压力、地层孔隙率、井液液柱压力、套管抗外挤强度、固管水泥圈使套管抗外挤强度提高的效应系数和固管水泥圈与孔壁岩层界面处的抗张强度等参数;分别就新地层、基岩和煤层的超孔隙水（气）压力对套管稳定性影响的特点进行了分析。结合实例介绍了煤层超瓦斯压力引起套管失稳的分析方法。提出了局部提高套管抗外挤强度、提高固管水泥圈强度、延迟井液排空时间、增设套管扶正器等提高套管稳定性的具体措施。     

高速滑坡形成机制： 土粒子破碎导致超孔隙水压力的产生

通过排水剪切试验，揭示出易于产生粒子破碎的土体易于产生体积变化，土体初始结构和粒子破碎难易度对体积变化各阶段的影响。在与之相对应的不排水试验中，产生粒子破碎的土体最终产生了较高的超孔隙水压力，而且孔隙水压力产生的各阶段与排水试验中的体积变化阶段具有良好的对应关系。揭示了不同诱因产生的高速滑坡的共同特征，即在长距离运动中，由于粒子破碎的影响，滑动面土体在不排水条件下，抗剪强度因超孔隙水压力上升而下降，最终导致高速滑坡。同时，由于粒子破碎将导致土体自身渗透系数降低，土粒子破碎因而具有促进超孔隙水压力产生和减缓超孔隙水压力消散的双重效果。     

循环荷载作用下竖向排水板加固软黏土的孔隙水压力累积特性研究

采用大型动三轴试验仪进行重塑高岭土试样的循环三轴试验,试样直径为300 mm,高度为600 mm。圆柱体试样中心放置了一块竖向排水板,在循环加载试验进行时和结束后都可进行径向排水。试验结果验证了径向排水可以有效地消散循环荷载引起的孔隙水压力。通过结合径向固结理论与不排水循环加载土体模型,提出了一个循环荷载作用下径向固结模型,用来描述在允许径向排水的情况下软黏土在循环荷载作用下的孔压累积特性。模型中考虑了应力历史和孔隙水压力消散对孔隙水压力生成的影响,并用大型循环三轴试验结果进行验证。研究发现,当施加较大循环荷载时,径向排水减缓了孔隙水压力累积到临界值的速率,因而土体在破坏前可以经历更多次的循环荷载;当施加中等循环荷载时,径向排水可有效阻止孔隙水压力增长至临界值。除此之外,还研究了加载间歇期对孔压累积特性的影响,结果显示3组循环加载结束后,累积孔隙水压力开始减小,表明之后更多的循环加载并不会引起孔隙水压力的累积增长。     

Modelling the pre-failure instabilities of sand

A simple incremental model describing the pre-failure behaviour of granular soils is presented. The model describes both the dry/fully drained and undrained response. It takes into account an initial anisotropy of soil and an initial state defined as either contractive or dilative. A physically sound definition of loading/unloading is assumed, which differs from elasto-plastic approaches. The model is based on extensive empirical data and gives predictions conformable with experimental results. It also describes pre-failure instabilities of granular soils, both dry/fully drained and undrained. The Hill’s criterion was used to examine stability. It was shown that this condition can be formulated either in terms of the effective stresses or by the total stresses. In the extreme cases of either dry/fully drained or undrained conditions, these alternative formulations are equivalent. This is not so in the case of partial drainage of pore water and associated volumetric deformations as well as pore pressure changes. The model describes the pre-failure instabilities well, and additionally allows for analytical derivation of the instability line. It was shown that the second order work, appearing in the Hill’s condition, is equivalent to the entropy source.     

冲击作用下饱和土性状的试验研究

在三轴条件下,对饱和土（砂土和黏土）进行排水与不排水条件下的冲击试验及冲击后再固结试验,对比研究了不同渗透性土在不同排水条件下的冲击动力响应和冲击后再固结性状。结果表明：饱和黏土不排水冲击时的孔隙水压力随冲击击数增加而升高并逐渐稳定,排水冲击时的孔隙水压力则是先达到峰值然后有所下降;砂土不排水冲击时的冲击能量对孔隙水压力影响最明显;饱和砂土不排水冲击时的轴向应变与冲击击数呈近似线性关系,饱和黏土冲击及饱和砂土排水冲击则呈近二次曲线关系;饱和砂土不排水冲击后再固结阶段的孔隙水压力立即消散为0,同时体变迅速增大到一定值;饱和黏土在冲击后再固结阶段的孔隙水压力在一定时间内逐渐消散完毕,同时体变逐渐增大;饱和黏土排水冲击时,冲击阶段产生的体变占冲击引起总体变的39%～49%,冲击后再固结阶段产生的体变占51%～61%;砂土和黏土的总体变均表现为排水冲击明显大于不排水冲击,改善冲击时的排水条件有利于提高加固效果。