Poroelastic Theory Research Articles

A poroelasticity theory for soil incorporating adsorption and capillarity

Adsorption and capillarity, in the order of high free energy to low, are the two soil–water interaction mechanisms controlling the hydro-mechanical behaviour of soils. Yet most of the poroelasticity theories of soil are based on capillarity only, leading to misrepresentations of hydro-mechanical behaviour in the low free energy regime beyond vaporisation. This inability is reasoned to be caused by two major limitations in the existing theories: missing interparticle attraction energy and incomplete definition of adsorption-induced pore-water pressure. A poroelasticity theory is formulated to incorporate the two soil–water interaction mechanisms, and the transition between them – that is, condensation/vaporisation, by expanding the classical three-phase mixture system to a four-phase mixture system with adsorptive water as an additional phase. An interparticle attractive stress is identified as one of the key sources for deformation and strength of soils induced by adsorption and is implemented in the poroelasticity theory. A recent breakthrough concept of soil sorptive potential is utilised to establish the physical link between adsorption-induced pore-water pressure and matric suction. The proposed poroelasticity theory can be reduced to several previous theories when interparticle attractive stress is ignored. The new theory is used to derive the effective stress equation for variably saturated soil by identifying energy-conjugated pairs. The derived effective stress equation leads to Zhang and Lu's unified effective stress equation, and can be reduced to Bishop's effective stress equation when only the capillary mechanism is considered and to Terzaghi's effective stress equation when a saturated condition is imposed. The derived effective stress equation is experimentally validated for a variety of soil in the full matric suction range, substantiating the validity and accuracy of the poroelasticity theory for soil under variably saturated conditions.

Theoretical investigation on characteristics of field reactions of saturated ground subjected to vibrations of inclined pile groups

Inclined pile groups have been adopted in engineering practice (e.g. offshore wind turbines) to withstand strong horizontal environmental loads that are repetitive in nature. Field reactions including the additional stresses and excess pore water pressures are responsible for the cyclic degradation of foundation soil, which may induce the accumulative deformation and fundamental frequency shifting of the marine structure. In this study, a theoretical model incorporating an inclined pile group and a saturated half-space was established, wherein the pile and saturated soil were described by the E–B beam and Biot poroelasticity theories, respectively. The pile and soil were coupled through the receptance matrix, which was established at the pile–soil interaction points in the transform domain. The dynamic impedances of the inclined pile group are first obtained, and then the field responses, including stresses and excess pore water pressure in the saturated ground, are evaluated for different types of loads applied to the pile cap. The frequency response function and spatial distributions of the field responses were obtained for varying rake angle of pile and permeability of soil. It was found that the horizontal force induces the largest responses in the ground when compared to the vertical force and the overturning moment applied to the inclined pile group. It is beneficial to employ an inclined pile group to withstand the horizontal force and overturning moment because the foundation stiffness increases, and the additional stresses in the ground decrease with increasing rake angle.

AVA inversion for novel fluid indicator considering consolidation parameter

Abstract Geofluid identification from seismic data are crucial for understanding reservoir characteristics. However, fluid indicators based on elastic parameter combinations show strong ambiguity in terms of geofluid identification. Although the effective pore-fluid bulk modulus proves to be the superior fluid indicator in geofluid discrimination, it is limited to empirical models such as the critical porosity model. The consolidation parameter model can evaluate the consolidation and compaction of sediments and is widely used due to its better applicability. Therefore, a novel fluid indicator considering consolidation parameter is proposed and a boundary-constrained inversion strategy for geofluid identification is developed. First, the novel fluid indicator is defined based on the poroelasticity theory. Then, the linearized AVA (amplitude variation with angle) approximation equation related to the new fluid indicator is derived to directly link seismic data and properties of pore-filling materials. The model analysis verifies the accuracy of the derived approximation equation at moderate incident angles, which can be used for parameter prediction by pre-stack seismic inversion. Furthermore, the contribution of each attribute of the novel equation to the reflectivity is analyzed to validate the feasibility of new fluid indicator inversion. Finally, a boundary-constrained AVA pre-stack inversion method is presented to enhance the robustness of the inversion results of the model parameter. The reliability of the improved method is proved by accurate inversion results of synthetic seismic records. After determining the consolidation parameter using well-log data combined with BGT (Biot–Gassmann Theory), the field data further demonstrated that the proposed approach is accurate and effective.

Dynamic responses of an axisymmetric thermo-poroelastic half-space subjected to thermo-mechanical loads

The dynamic responses of a thermo-poroelastic half-space subjected to circular surface thermal or/and mechanical loads are studied semi-analytically. With the consideration of water seepage and inertia of both the soil particles and pore water, the governing equations of the thermo-poroelastic medium are established based on Biot’s dynamic poroelastic theory. The solutions of the governing equations are first derived in the transformed domain using Laplace-Hankel transform, following which the solutions in the time domain are obtained utilizing a numerical integration procedure. Finally, the dynamic responses of the thermo-poroelastic half-space under a rectangular thermal pulse load and/or a half-sinusoidal impact mechanical load are graphically presented. It is found that both the thermal loads and mechanical loads can induce time-dependent responses in the vertical displacements, vertical stresses, and pore water pressures within the saturated poroelastic medium. The resulting coupled dynamic responses of the thermo-poroelastic half-space due to the simultaneous application of the thermal and mechanical loads can be obtained as the superposition of the individual thermal and mechanical responses.

Spatiotemporal evolution of excess pore pressures in a silty seabed under progressive waves during residual liquefaction

Both transient and residual pore pressure responses are induced as ocean waves propagate over a silty seabed. In this study, the spatiotemporal evolution of excess pore pressure in a silty seabed under progressive waves was physically modelled in a large wave flume. Three typical stages were identified in the process of residual liquefaction via flume observations, including quasi-elastic, intensive build-up of residual pore pressure, and continuous liquefaction stages. During the initial quasi-elastic stage before the liquefaction of the silt bed, the transient pore pressure can be well predicted by the analytical solution based on poro-elastic theory. After that, the residual pore pressure builds up intensively to its maximum value, even in the case that the transient pore pressure is nearly negligible at deep soil layer. Once the residual liquefaction occurs, the poro-elastic theory becomes invalid for describing the pore pressure response. The residual liquefaction is not simultaneously induced within the entire bed, but gradually progresses downward from the shallow layer of the silt bed to deeper. The pore pressure amplitude is significantly amplified after the silt liquefies, while no amplitude-amplification was observed within the un-liquefied silt. An amplification ratio (ζ) is proposed to characterize the amplification effect and distinguish the onset of residual liquefaction. The value of ζ during the continuous liquefaction stage is found to be one order of magnitude larger than that in the quasi-elastic stage. Comparisons with the existing centrifuge tests further indicate that the critical cyclic stress ratio for the silt bed is much smaller than that for the sand bed, implying the silt bed is more prone to residual liquefaction.

Consolidation settlement of vertically loaded pile groups in multilayered poroelastic soils

Pile groups are commonly used as the foundations of many structures including those used in transportation infrastructures. Consolidation settlement of a pile foundation is an important design parameter. A theoretical model is developed in this study to estimate the consolidation settlement and axial load transfer of vertically loaded pile groups in multilayered poroelastic soils. The multilayered saturated soil is modeled according to Biot’s poroelasticity theory. In order to determine quasi-static response of pile groups, the interaction problem is first formulated in the Laplace transform domain. Vertical displacement compatibility is enforced at the pile-soil interface to simulate the pile group-soil interaction. Axial deformation of each pile is represented by an exponential series with undetermined coefficients, which are obtained from a variational approach. Vertical displacement influence functions due to a buried uniform vertical load applied to the layered soil are required in the formulation. The application of an exact stiffness matrix method yields the required influence functions. Time-domain solutions are obtained by employing a numerical Laplace inversion method. Numerical results for time-dependent vertical stiffness and consolidation settlement are presented for different pile group configurations, layer profiles, pile elastic moduli and pile lengths.

Numerical investigation of solute transport into deformable marine sediments driven by ocean waves

Most existing studies do not consider the effect that the deformability of submarine sediments may have on solute transport under the action of ocean waves. In this study a two-dimensional numerical model based on Biot’s poro-elastic consolidation theory and an advection–dispersion equation is established to investigate the transport of non-reactive solute into a deformable porous seabed under the influence of ocean waves. The numerical model is then validated against experimental and analytical results in order to demonstrate its accuracy and robustness. The simulation results indicate that ignoring the deformability of seabed soil and associated seepage force due to ocean waves may lead to a significant underestimation of the rate of solute transport in shallow layers of marine sediment, particularly fine sand or silt. The effects of parameters such as the shear modulus, non-dimensional mechanical dispersion coefficient (related to particle size and permeability), dimensionless sediment thickness, wave steepness and the relative water depth have on solute transport into deformable sediments were investigated. The results indicate that the ratio of the longitudinal coefficient of mechanical dispersion between deformable and non-deformable sediments that can represent the enhancement of solute migration due to soil deformation may reach up to 85. This becomes more pronounced as the shear modulus and permeability of sediments decrease and the depth of water increases when the sediment thickness is less than 0.8 times the wavelength. The rate of solute transport in deformable sediments reaches its maximum when the sediment thickness is about 0.2 times the wavelength. In fact, as the relative water depth increases from 0.1 to 0.3, the enhancement of solute migration due to wave-induced soil deformation increases by about 60%-80%. In comparison to linear waves, shallow water waves, e.g., the first-order cnoidal waves, can increase the transport of solute more due to its strong non-linear behaviour, particularly in deformable seabed.

A Review of Techniques for Measuring the Biot Coefficient and Other Effective Stress Parameters for Fluid-Saturated Rocks

Abstract Predicting the behavior of a saturated rock with variations in pore fluid pressure during geo-energy production and storage, deep geological disposal of nuclear wastes, etc. with skeletal mechanical behavior in the linear elastic range is carried out using the isothermal theory of poroelasticity that incorporates Biot's effective stress principle. For conditions that are not within linear elasticity, other effective stress coefficients are used. Several experimental methods for determining Biot's and other effective stress coefficients have been documented in the literature. The objective of this study is to review the fundamentals of these techniques, their advantages and disadvantages, and to include several case studies. Current techniques for Biot's coefficient are based on different premises: jacketed and unjacketed bulk moduli or compressibility values; volume changes of the bulk and pore fluid from a drained triaxial test on a saturated sample; isotropic-isochoric compression tests on a saturated sample; matching volumetric strains for dry and saturated samples; estimation of the Biot coefficient from other poroelastic parameters; and approximation of the jacketed bulk modulus from ultrasonic wave velocities and/or unjacketed bulk modulus from the mineralogical compositions. Other effective stress coefficients are based on matching failure envelopes for dry and saturated samples and variations of rock properties (such as volumetric strain, permeability, and ultrasonic wave velocities) with respect to confining stress and pore pressure. This article discusses variations in Biot's and other effective stress coefficients produced using the different techniques and how factors such as pore geometry, test conditions, stress path, and test temperature affect the coefficients.

Magnitudes and orientations of present-day in-situ stresses in the Kurdistan region of Iraq: Insights into combined strike-slip and reverse faulting stress regimes

The study area is in the Kurdistan Region of Iraq, including the northwestern extension of the Zagros suture zone, where present-day stress data derived from actual measurements is rare. The magnitudes and orientations of principal in-situ stresses were determined using well logging data. The deepest drilled formation in this study was the Albian upper Qamchuqa Formation in northeastern Iraq, which is a carbonate hydrocarbon reservoir. In the present study, several wireline logs including borehole image logs, conventional wireline logs, and six-arm caliper logs for two vertical wells provided detailed borehole breakout and drilling-induced tensile fracture (DITF) data between depths of 1600 and 2240 m. Two oil wells (wells A and B) were evaluated, and in well A, several breakouts occurred in eight distinct zones. Below the depth of 1600 m, 26 pairs of breakouts with considerable length were observed. The standard deviation of breakout azimuths was 11°, and the mean azimuth of the breakouts was N162°E. Using breakout and DITF data, the orientations of the maximum and minimum horizontal stresses (SH and Sh) were determined, and the results were validated by six-arm caliper measurements and lithological evaluation from wireline log data. The mean azimuth of maximum horizontal in-situ stress was N72°E, which showed relative consistency with the NE–SW to E–W direction of tectonic movement and previous studies in the nearby Zagros suture zone. Ultimately, the magnitudes of the three principal in-situ stresses were determined by two methods: poroelastic strain theory and breakout analysis. The stress regime below the depth of 1600 m was a reverse faulting stress regime, and above this depth, it likely changed to a strike-slip faulting stress regime. The determined stress regime was consistent with the nature and dynamics of the tectonic plate movement of the Arabian and Eurasian (Iranian) plates. Consequently, results suggest that the pattern of present-day tectonic stress is controlled mainly by the collision between the Arabian and Eurasian plates.

A reservoir induced earthquake swarm in the Central Highlands of Sri Lanka

An anomalous seismic sequence of five small (MW < 3) felt earthquakes occurred between 29 August 2020 and 05 December 2020 around the Victoria Reservoir in the central highlands of Sri Lanka that clearly exceeded the established national background seismic rate. Using seismic waveform template-matching and a newly developed single-station earthquake location method based on travel-time back-projection, we detected an additional co-located 23 microseismic events, of which 18 occurred within the same period as the felt events. This hitherto undetected seismic swarm defines a seismogenic zone beneath the western flank of the reservoir between 1.5 and 3 km depths. The reservoir-induced peak stresses, resolved on E-W striking faults, predicted from the poroelastic theory that include both drained and undrained crustal responses are ~ 15 kPa in an area overlapping the seismogenic zone, which, together with the physical and spatio-temporal characteristics of the seismic swarm, establish a causal link between reservoir-induced stresses and the earthquake swarm with implications to seismic hazard. This is the first record of induced seismicity in Sri Lanka. The newly developed efficient computational workflows with minimal operational costs described in our study provide a blueprint for monitoring reservoir-induced seismicity in developing countries with severe resource limitations.

Generalized finite difference method based meshless analysis for coupled two-phase porous flow and geomechanics

This paper applies GFDM to analyze coupled two-phase flow and geomechanics for the first time, to our knowledge, is also the first meshless solver for two-phase fluid-solid coupling problems in porous media. Firstly, the implicit GFDM-based discrete schemes of the hyperbolic two-phase flow equation and elliptic stress equilibrium equation coupled by Biot's poroelastic theory are derived. Then the nonlinear solver based on Newton's method is used to solve the fluid pressure, water saturation, and displacement at each node simultaneously. Two technical details are found critical to the implementation of this method. The one is using different radii of the node influence domain to discretize the flow equation and the stress equilibrium equation respectively, and the other one is the selection criterion of the two radii of the node influence domain, which improves the implementation flexibility of the multi-physics coupling calculation, reduces the dissipation error of the calculation results of the convection-dominated water saturation distribution, and ensure a low computational cost. Several numerical test cases are implemented to analyze the computational efficiency and accuracy, and illustrate that GFDM can achieve good computational performance in case of regular domains, irregular domains, and different point clouds.Overall, this work may provide an important reference for building a GFDM-based general-purpose numerical simulator for multi-physics flow problems in porous media.

Arnold Verruijt (1940-2022).

Arnold Verruijt (1940-2022).

Earthquake-induced persistent and instantaneous groundwater variations caused by volumetric strain of soil in Taiwan from 1999 to 2020

Estimating the magnitude of earthquake-induced groundwater level (GWL) based on poroelastic theory is a challenge for researchers. To address this challenge, the present study explores this topic in the context of volumetric strain induced by ground shaking. Specifically, GWL records on the Chi-Chi earthquake in Taiwan, along with other selected events from 2004 to 2020, are analyzed to identify the persistent and instantaneous changes of GWL under distinct geological conditions. The magnitude of the persistent GWL change is highly correlated with peak ground acceleration, and thickness and density of sandy layers. This finding is explained by the magnitude of volumetric strains caused by soil particle rearrangement associated with ground motion intensities and site-specific conditions. Meanwhile, the instantaneous GWL change caused by seismic wave propagation exhibits a highly negative correlation with the vertical ground motion velocity time history because the compression wave induces instantaneous contraction or dilation of the soil. Moreover, the peak instantaneous GWL change correlates well with the peak ground velocity (PGV) in the vertical direction because the compressional (volumetric) strain is theoretically proportional to the PGV of vertical motion.

Dynamic response of sheet‒pile groin under tidal bore considering pile‒pile mutual interaction and hydrodynamic pressure

Sheet‒pile groin appearing as two rows of piles, with both pile heads connected by a concrete sheet, are widely applied to resist the tidal bores, although its dynamic soil‒structure mechanism is still under research. This paper utilizes the Euler beam and one‒dimensional rod to simulate the pile and sheet constituting the framework of the sheet‒pile groin, respectively, and Biot's poroelastic theory is introduced to simulate the layered saturated soil in which the sheet‒pile groin is embedded. To account for the pile‒pile mutual interactions, interaction factors considering the secondary wave effect are adopted. Radiation wave theory is adopted to simulate the hydrodynamic pressure. The theoretical solutions to the dynamic response of the sheet‒pile groin in the frequency and time domains are derived by applying the matrix calculations and the Fourier transform. The correctness and accuracy of the present solution have been verified through FEM results. An extensive parametric analysis is then conducted to investigate the influence of various factors on the dynamic horizontal complex impedance of the sheet‒pile groin.

Numerical simulation of rock erosion performance of a high-speed water jet using an immersed-body method

Water jet drilling (WJD) is an effective technique for drilling micro-holes in the subsurface for reservoir stimulation . This study aims to investigate numerically the failure mechanism of rock during WJD and to assess the WJD performance before drilling. A 3D fluid-solid coupling model is developed for simulating WJD by coupling a mechanical solver based on the combined finite-discrete element method (FDEM) with a fluid solver using an immersed-body method. The new numerical model is capable of simulating crack initiation and propagation and fragment removal under the impact load of a high-speed water jet. The poroelastic effect is implemented via Biot's theory of poroelasticity . The numerical results show that: (1) rock failure is only observed in the Gildehaus sandstone with the lowest strengths among the three types of rock tested, (2) most of the cracks are tensile failures and pure shear cracks are rare, mixed mode cracks account for 15%∼40% of the total crack number depending on the mechanical boundary conditions , (3) increased water back pressure significantly suppresses jet erosion. The poroelastic effect on the rock failure is insignificant in the mesoscale simulations and will be further investigated using a microscale model in future.

A finite difference approach to study the impact of boundary conditions on the acoustical behavior of particle stacks

The responses of particle stacks to incident sound waves show interesting features that are very different from those of a homogeneous continuum. Further studies of the acoustical performance of particle stacks can help both to discover potential noise control applications of these types of materials, and to help provide better insight into the internal status of the particle stacks. In the current study, a finite difference (FD) model for a particle stack was built based on the Biot poro-elastic theory. The intention in developing this model is to describe the acoustical behavior of particle stacks with consideration of not only the finite stiffness of the particles, but also the influence of gravity and friction between the particles and the inner wall of their enclosure: i.e., the cylindrical sample holder of a standing wave tube, in this work. The derivation of governing equations and boundary conditions is introduced, together with acoustic measurement results of particles stacks consisting of micron-scale glass bubbles, including absorption coefficients and surface impedances that are compared with the theoretical predictions. The possible application scenarios of such materials, and potential developments that will further improve the FD model will also be discussed.

Poro-Mechanical Coupling for Flow Diagnostics

Accounting for poro-mechanical effects in full-field reservoir simulation studies and uncertainty quantification workflows using complex reservoir models is challenging, mainly because of the high computational cost. We hence introduce an alternative approach that couples hydrodynamics through existing flow diagnostics simulations with poro-mechanics to screen the impact of coupled poro-mechanical processes on reservoir performance without significantly increasing computational overheads. In flow diagnostics, time-of-flight distributions and influence regions can be used to characterise the flow field in the reservoir, which depends on the distribution of petrophysical properties that are altered due to production-induced changes in pore pressure and effective stress. These extended flow diagnostics calculations hence enable us to quickly screen how the dynamics in the reservoirs (e.g. reservoir connectivity, displacement efficiency, and well allocation factors) are affected by the complex interactions between poro-mechanics and hydrodynamics. Our poro-mechanically informed flow diagnostics account for steady-state and single-phase flow conditions based on the poro-elastic theory and assume that the reservoir does not contain fractures. Fluid flow and rock deformation calculations are coupled sequentially. The equations are discretised using a finite-volume method with two-point flux-approximation and the virtual element method, respectively. The solution of the coupled system considers stress-dependent permeabilities. Due to the steady-state nature of the calculations and the effective proposed coupling strategy, these calculations remain computationally efficient while providing first-order approximations of the interplay between poro-mechanics and hydrodynamics, as we demonstrate through a series of case studies. The extended flow diagnostic approach hence provides an efficient complement to traditional reservoir simulation and uncertainty quantification workflows and enable us to assess a broader range of reservoir uncertainties.

Lateral Dynamic Response of Offshore Pipe Piles Considering Effect of Superstructure

The dynamic characteristics of pipe piles are of considerable importance for the dynamic foundation design of offshore wind turbines. In this study, we develop an analytical model for the lateral vibration of offshore pipe piles with consideration of the inertia effect and axial loading from the superstructure. A coupled dynamic saturated soil–pile interaction model is established based on Biot’s poroelastic theory and Euler–Bernoulli theory. The potential function, operator decomposition method, variable separation method and matrix transfer method are introduced herein to obtain the lateral force of the inner and outer soil acting on the pile shaft. Then, the analytical solution of the pile dynamic impedance in the frequency domain is derived by employing the soil–pile continuous deformation conditions and the boundary conditions of the pile. The rationality and accuracy of the presented solution have were by comparing its results with those predicted by existing solutions. The influence of superstructure, pile geometry and soil plug height on the lateral dynamic impedance and natural frequency of pipe piles was thoroughly investigated based on the theoretical model. The main findings can be summarized as: (1) The dynamic stiffness of piles will be remarkably underestimated if the inertia effect of the superstructure is not accounted for. (2) The vertical load of the superstructure is main factor affecting the natural frequency, whereas the inertia effect of the superstructure will enlarge the resonance amplitude. (3) The overall lateral dynamic impedance and first-order natural frequency of the pile increase significantly with the soil plug height.

Influence of defects on the lateral dynamic characteristics of offshore piles considering hydrodynamic pressure

This paper develops an analytical framework to reflect the associative effect of dynamic soil-pile interaction (DSPI) and dynamic water-pile interaction (DWPI) on the lateral dynamic characteristics of offshore concrete piles. The pile is assumed to be an Euler-Bernoul20beam and the soil is described by the Biot's poroelastic theory. The hydrodynamic pressure applying on the pile shaft is calculated based on the radiation wave theory with the consideration of water compressibility. The influence of defects along with the hydrodynamic pressure on the lateral dynamic impedance and natural frequency of offshore piles is thoroughly investigated with the proposed solution. The results show that the hydrodynamic pressure cannot be ignored when analyzing the lateral dynamic characteristics, especially for those offshore piles with deep water depth subjected to high frequency vibration. The damage caused by necking defects is much larger than that of bulging defects, and even a small necking defect can lead to a significant decrease of dynamic stiffness and natural frequency of piles. The lateral dynamic characteristics of piles are more sensitive to the variation of defect radius rather than the defect length.

A 3D finite element model updating of spinal lumber segment applying experimental modal data and particle swarm optimization algorithm

The dynamic loadings can be more harmful than static ones for the human lumbar spine health. Consequently, the prediction of the spine behavior under dynamic and vibration loads is vital and can be achieved by creating a precise finite element model in which the dynamic mechanical properties of the components need to be estimated. For this purpose, noninvasive experimental modal analysis can be applied to evaluate the dynamic mechanical properties of the spine in the numerical simulation by supplying the structural dynamic characteristics (natural frequencies, mode shapes, and damping ratio) of the system. Since the most adequate model for the human lumbar segment is a sheep model, in this paper, a 3D finite element model of a fresh spinal lumber segment of a sheep is generated based on the poroelasticity theory via Abaqus and is updated utilizing particle swarm optimization (PSO) algorithm and experimental modal analysis. In this regard, the frequency response function (FRF) of the specimen is obtained by performing the experimental modal test and the modal parameters are derived by using the rational fraction polynomial method. Afterward, the sensitivity analysis is carried out to determine the appropriate design variables. Finally, the PSO algorithm using experimental data is employed to update the design variables, including the elastic material properties and the structural damping factors of the specimen components, and the stiffness and damping coefficient of the suspension system. According to the results, the error percentage between the numerical FRF and the experimental one decreases remarkably after model updating indicating the high efficiency of the methods used.