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Regulation of the mechanical properties of the cell wall is a key parameter used by plants to control the growth behavior of individual cells and tissues. Modulation of the mechanical properties occurs through the control of the biochemical composition and the degree and nature of interlinking between cell wall polysaccharides. Preferentially oriented cellulose microfibrils restrict cellular expansive growth, but recent evidence suggests that this may not be the trigger for anisotropic growth. Instead, non-uniform softening through the modulation of pectin chemistry may be an initial step that precedes stress-induced stiffening of the wall through cellulose. Here we briefly review the major cell wall polysaccharides and their implication for plant cell wall mechanics that need to be considered in order to study the growth behavior of the primary plant cell wall.

The production of fractured unconventional reservoirs induces stress changes, which will affect the production performance of neighboring wells. To quantify such effects, the analytical solution is a convenient yet accurate tool. In this work, we have developed an analytical solution of the transient pressure and stress variation induced by the production of a point/line/plane source in a semi-infinite poroelastic reservoir with a traction-free surface boundary. We have benchmarked the derived solution with both analytical solution and numerical program. The solution demonstrates excellent accuracy. Moreover, the analytical approach reduces the computational time of numerical approaches from hours to seconds. We then apply the solution to study the surface subsidence control and stress interference between fractured horizontal wells. Results show that the derived solution is capable of quantifying complex hydraulic-mechanical processes during the recovery of shallow water as well as deep shale reservoirs. Upon investigation, we have found that infill wells can effectively reduce the surface subsidence induced by the production of shallow horizontal wells. Furthermore, shale reservoirs with lower permeability are more sensitive to pressure-stress changes. The range of stress reorientation can also be efficiently quantified by the developed approach. Also, normal stresses and shear stresses behave differently during fracture driven interactions. The above findings potentially benefit the decision-making in the asset development. The major novelty of our work lies in the extension of existing approaches that are limited to axisymmetric problems to line and plane sources problems, so that the solution can be used in unconventional reservoirs with fractures.

We propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium, known as Biot's consolidation problem. The steady-state version of the system is recast in terms of displacement, pressure, and volumetric stress, and both continuous and discrete formulations are analyzed as compact perturbations of invertible problems employing a Fredholm argument. In particular, the error estimates are derived independently of the Lamé constants. Numerical results indicate the satisfactory performance and competitive accuracy of the introduced methods.

Induced seismicity linked to geothermal resource exploitation, hydraulic fracturing, and wastewater disposal is evolving into a global issue because of the increasing energy demand. Moderate to large induced earthquakes, causing widespread hazards, are often related to fluid injection into deep permeable formations that are hydraulically connected to the underlying crystalline basement. Using injection data combined with a physics-based linear poroelastic model and rate-and state friction law, we compute the changes in crustal stress and seismicity rate in Oklahoma. This model can be used to assess earthquake potential on specific fault segments. The regional magnitude–time distribution of the observed magnitude (M) 3+ earthquakes during 2008–2017 is reproducible and is the same for the 2 optimal, conjugate fault orientations suggested for Oklahoma. At the regional scale, the timing of predicted seismicity rate, as opposed to its pattern and amplitude, is insensitive to hydrogeological and nucleation parameters in Oklahoma. Poroelastic stress changes alone have a small effect on the seismic hazard. However, their addition to pore-pressure changes can increase the seismicity rate by 6-fold and 2-fold for central and western Oklahoma, respectively. The injection-rate reduction in 2016 mitigates the exceedance probability of M5.0 by 22% in western Oklahoma, while that of central Oklahoma remains unchanged. A hypothetical injection shut-in in April 2017 causes the earthquake probability to approach its background level by ∼2025. We conclude that stress perturbation on prestressed faults due to pore-pressure diffusion, enhanced by poroelastic effects, is the primary driver of the induced earthquakes in Oklahoma.

In this paper, we study the equations of nonlinear poroelasticity derived from mixture theory. They describe the quasi-static mechanical behavior of a fluid saturated porous medium. The nonlinearity arises from the compressibility of the fluid and from the dependence of porosity and permeability on the divergence of the displacement. We point some limitations of the model. In our approach, we discretize the quasi-static formulation in time and first consider the corresponding incremental problem. For this, we prove existence of a solution using Brézis’ theory of pseudo-monotone operators. Generalizing Biot’s free energy to the nonlinear setting, we construct a Lyapunov functional, yielding global stability. This allows us to construct bounds that are uniform with respect to the time step. In the case when dissipative interface effects between the fluid and the solid are taken into account, we consider the continuous time case in the limit when the time step tends to zero. This yields existence of a weak free energy solution.

In this paper, we study two modes of locking phenomena in poroelasticity: Possion locking and pressure oscillations. We first study the regularity of the solution of the Biot model to gain some insight into the cause of Poisson locking and show that the displacement gets into a divergence-free state as the Lamé constant λ → ∞. We also examine the cause of pressure oscillations · from an algebraic point of view when a three-field mixed finite element method is used. Based on the results of our study on the causes of the two modes of locking, we propose a new family of mixed finite elements that are free of both pressure oscillations and Poisson locking. Some numerical results are presented to validate our theoretical studies.

An unexpected Mw7.45 earthquake struck the Noto Peninsula on 1 January 2024, preceded by several long‐living earthquake swarms, providing a valuable opportunity to study seismic and aseismic slips, as well as their interactions. We derived coseismic and 19‐day postseismic slip distributions by inverting co‐ and post‐seismic displacements from Global Navigation Satellite System (GNSS) data. The inverted coseismic slip distribution shows two slip patches, with a maximum slip of ∼4 m. The early postseismic afterslip is 0.1–0.25 m within coseismic slip asperity and 0.1–0.6 m northward of the rupture area. The afterslip within the rupture area is accompanied by numerous aftershocks and coincides with a ∼6 MPa stress drop, suggesting that aftershocks are likely driven by the afterslip. The pattern of poroelastic rebound implies a potential effect of fluid flow on aftershock triggering. This study sheds lights on the intricate interplay between seismic and aseismic processes following large earthquakes. Plain Language Summary A Mw7.45 earthquake hit the northeastern tip of the Noto Peninsula on 1 January 2024. This region has hosted several long earthquake swarms. This unusual earthquake provides a good opportunity to explore the fault behaviors following a major earthquake. The coseismic and early postseismic deformation have been well recorded at the GNSS stations with unprecedentedly high spatial and temporal resolutions. We inverted the coseismic and early postseismic slip distributions from the GNSS data. The coseismic slip distributes mostly in two patches and reaches up to approximately 4 m. The 19‐day postseismic slip distributes mainly in the coseismic slip region as well as to the north of it. The postseismic slip in the rupture area overlapped with the aftershocks. The result suggests that these aftershocks were likely triggered by the afterslip. Additionally, the pattern of poroelastic rebound implies that fluid flow may play a role in triggering these aftershocks. This study helps advance our understanding of earthquake‐triggering mechanisms and fault behaviors following large earthquakes. Key Points We inverted coseismic and early afterslip distributions of Noto Peninsula earthquake using co‐ and post‐seismic displacements from Global Navigation Satellite System The early afterslip occurred within and to the north of the two main coseismic slip patches The occurrence of aftershocks may result from the early afterslip and possible fluid flow

Complex coupled thermo-hydromechanical (THM) loading paths are expected to occur in clay rocks which serve as host formations for geological radioactive waste repositories. Exothermic waste packages heat the rock, causing thermal strains and temperature induced pore pressure build-up. The drifts are designed in such a way as to limit these effects. One has to anticipate failure and fracturing of the material, should pore pressures exceed the tensile resistance of the rock. To characterise the behaviour of the Callovo-Oxfordian claystone (COx) under effective tension and to quantify the tensile failure criterion, a laboratory program is carried out in this work. THM loading paths which correspond to the expected in situ conditions are recreated in the laboratory. To this end, a special triaxial system was developed, which allows the independent control of radial and axial stresses, as well as of pore pressure and temperature of rock specimens. More importantly, the device allows one to maintain axial effective tension on a specimen. Saturated cylindrical claystone specimens were tested in undrained conditions under constrained lateral deformation and under nearly constant axial stress. The specimens were heated until the induced pore pressures created effective tensile stresses and ultimately fractured the material. The failure happened at average axial effective tensile stresses around 3.0 MPa. Fracturing under different lateral total stresses allows one to describe the failure with a Hoek–Brown or Fairhurst’s generalized Griffith criterion. Measured axial extension strains are analysed based on a transversely isotropic thermo-poroelastic constitutive model, which is able to satisfactorily reproduce the observed behaviour.HighlightsThermal pressurization of clay rock in deep radioactive waste repositories can reduce the effective stresses, which can lead to damage or failure.Our novel laboratory triaxial device is able mimic in situ conditions: Constant vertical total stress, zero lateral deformation and thermal pressurization.Pore pressure increase, vertical extension strains and thermal pressurization failure were recorded in a series of tests on Callovo-Oxfordian claystone specimens.The effective tensile strength was reached at values around 3 MPa in tension and temperatures between 53 and 64 °C, creating sub-horizontal fractures.The experimental responses can be well reproduced using a thermo-poroelasticity model.Hoek–Brown and Fairhurst generalized Griffith criteria appear suitable to account for the rock's tensile resistance.

In this paper, we introduce and solve a novel model that integrates confined flow within a dual porosity poroelastic medium with free flow in conduits. The model is structured around three distinct but interconnected regions: the matrix, micro-fractures, and conduits. Fluid flow within the dual porosity poroelastic medium is described by a dual-porosity poroelastic model, while fluid flow within the conduits is modeled by the Stokes equations. The integration of these two flow dynamics is achieved through a set of interface conditions, including a novel no-exchange condition. Theoretical achievements include the establishment of the existence and uniqueness of the solution for the weak formulation, alongside stability and error estimates for the semi-discrete continuous-in-time discontinuous Galerkin method. Furthermore, the convergence of the full discretisation using the backward Euler time stepping is thoroughly analysed. Two-dimensional numerical experiments are conducted and highlight the optimal convergence rate of the numerical solution, affirming the relevance and applicability of the model to real-world scenarios.

In situ rock is often saturated with fluid, the presence of which affects both elastic parameters and inelastic deformation processes. Techniques were developed for testing fluid-saturated porous rock under the limiting conditions of drained (long-term), undrained (short-term) and unjacketed (solid matrix) response in hydrostatic, axisymmetric and plane-strain compression. Drained and undrained poroelastic parameters, including bulk modulus, Biot and Skempton coefficients, of Berea sandstone were found to be stress dependent up to 35 MPa mean stress, and approximately constant at higher levels of loading. The unjacketed bulk modulus was measured to be constant for pressure up to 60 MPa, and it appears to be larger than the unjacketed pore bulk modulus. An elasto-plastic constitutive model calibrated with parameters from drained tests provided a first-order approximation of undrained inelastic deformation: dilatant hardening was observed due to pore pressure decrease during inelastic deformation of rock specimens with constant fluid content. This article is part of the themed issue ‘Energy and the subsurface’.