Creep deformation of silicate materials in different chemical environments, is of paramount importance in practical engineering applications and geotectonic evolution. Over 100 circular cylinders of a polycrystalline quartz have been deformed at constant differential stresses σ of 100–1000 MPa, temperatures T of 600–900 °C, and a confining pressure of 1500 MPa using a soft solid medium apparatus. Oxygen, water, and hydrogen fugacities (fO2, fH2O, fH2) were controlled over wide ranges by a solid oxygen buffering technique. Under the experimental conditions, three different creep regimes were identified, based on mechanical data and microstructural observations: high temperature and low stress regime with a stress exponent n = 1, high temperature and high stress regime with n = 2.4, and low temperature regime with n = 3. The apparent activation energies for the n = 1 and n = 2.4 regimes were about the same (101 131 kJ/mol), but much smaller than that for the n = 3 regime (214 kJ/mol). Chemical environment had an effect on creep in all regimes. Creep rate had dependences upon (fH_2O)^0.41 , (fH_2O)^0.24 , and (fO_2)^-0.27(fH_2O)^1.83 in the n = 1, n = 2.4, and n = 3 regimes, respectively. Observations of strong grain flattening and widespread dislocation substructures led to the conclusion that deformation in all three regimes was dominated by dislocation creep processes. Specifically, it is suggested that the n = 1 behavior observed in all buffered environments may result from the operation of Harper-Dorn creep that has been demonstrated for many engineering materials. The identification of different creep regimes, especially Harper-Dorn creep, in quartz will have important implications for engineering and geotectonic applications of silicate materials.

The fundamental characteristic of a semi-permeable porous material is that the solvent is allowed to pass through it but the solute is not. Due to this characteristic, a solute concentration gradient can drive chemical osmosis flow in the solution-saturated semi-permeable porous material. Although analytical solutions have been derived for one-dimensional chemical osmosis induced flow and solute concentration variation problems, computational simulations of two-dimensional chemical osmosis induced flow and solute concentration variation problems remain lacking to date. To fill this gap, a new mathematical model is first established, in this paper, for describing two-dimensional chemical osmosis induced flow and solute concentration variation problems in solution-saturated semi-permeable porous materials. Then a computational simulation procedure, which contains the finite difference and finite element methods, is proposed to solve the partial differential equations involved in the established mathematical model. For the purpose of verifying the proposed computational simulation procedure, the analytical solution of a benchmark problem has been derived mathematically. The related computational simulation results have demonstrated that: (1) the proposed computational simulation procedure is correct and accurate for solving chemical osmosis induced flow and solute concentration variation problems; and (2) the applied boundary conditions have significant effects on the computational simulation results of two-dimensional chemical osmosis induced flow and solute concentration variation problems in the solution-saturated semi-permeable porous material.

This paper deals with three fundamental issues associated with theoretical analyses of reactive infiltration instability (RII) problems in fluid‐saturated porous media. The first fundamental issue is to determine the spatial shapes of chemical dissolution‐fronts in the limit case of the mineral dissolution ratio approaching zero in both conventional time (daily life time) and unconventional time (abstract time) domains. The chemical dissolution‐front is commonly represented by the spatial shape of the porosity profile. The second fundamental issue is to conduct theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through directly solving dimensional mathematical governing equations in the conventional time domain. The third fundamental issue is to carry out theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through solving dimensionless mathematical governing equations in the unconventional time domain. Through purely mathematical deductions, it has been proven that: (1) the spatially sharp shape of a chemical dissolution‐front, which is theoretically predicted either at a much smaller timescale than the dissolution timescale associated with the daily life time or at a much larger timescale than the dissolution timescale associated with the daily life time, can be observed in the daily life time domain; (2) the theoretical instability criterion of an RII problem can be established directly at three different length‐scales in the daily life time domain; and (3) although the spatial shape of a chemical dissolution‐front at the dissolution timescale associated with the daily life time cannot be observed in the daily life time domain, the theoretical instability criterion of an RII problem at the dissolution timescale associated with the daily life time can be established when a physically consistent mathematical transform is used in the theoretical analysis.

Every nonlinear system grows by increments, and the final probability distributions for components of that system emerge from an amalgamation of these increments. The resulting probability distribution depends on the constraints imposed on each increment by the physical and chemical processes that produce the system. Hence there is the potential that the observed probability distribution can reveal information on these processes. Complex systems that grow by competition between the supply and consumption of energy and mass have growth laws that are cumulative probability distributions for their component parts that reflect such competition. We show that the type of probability distribution is characteristic of the endowment of orogenic gold deposits with the sequence: Weibull -> Frechet -> gamma -> log normal representative of increasing endowment. Further, the differential entropy of the probability distribution is indicative of the quality of the deposit, with low-quality deposits represented by high entropy and high-quality deposits represented by low or negative entropy. The type of probability distribution gives an indication of the processes that operated to produce the deposit. These conclusions hold for mineralisation as well as for the associated alteration assemblages. We suggest that the probability distribution for the mineralisation or the alteration assemblage gives a good indication of the endowment and quality of a deposit from a single drill hole.

Amphibolite facies marble surrounded by locally pure but mostly impure quartzite with -10-14% of dispersed white mica and crosscut by granite veins were jointly deformed within an extensional shear zone. Both marble and quartzite show three microstructural stages, M1m-M3m and M1q-M3qm, respectively, correlated with the onset of extension Stage 1 at -600 degrees C, and retrograde extension Stage 2 at -380 degrees C and Stage 3 at -300 degrees C. The coarse-grained microstructures M1m (1200 & mu;m) in marble and M1q (300 & mu;m) in pure quartzite showed the activity of basal (a) slip and prism (a) - rhomb (a) slip, respectively. The finer grained M2m (-50 & mu;m) microstructure in marble is associated with strain localization, subgrain rotation recrystallization and persistence of basal (a) slip. The M2q (175 & mu;m) microstructure in pure quartzite shows a crossed girdle c-axis pattern, while the M2qm (120 & mu;m) in impure quartzite shows locally c-axes parallel to the lineation, indicating the possible activity of prism [c] slip. Stage 3 in marble is characterised by minor recrystallization M3m that occurs mostly along microcracks formed subparallel to foliation. The impure quartzite M3qm microstructure shows further reduction in quartz grain size (80-90 & mu;m) related to pining of well-dispersed white mica. The microstructure M1m-M1q and M2m-M2q formed by dislocation creep, while the M2qm and M3qm suggest the Rachinger grain boundary sliding of quartz grains along micas. Piezometric calculations suggest differential stresses of 1-5 MPa and -20 MPa for the M1m and M2m microstructures and 7 MPa and 11 MPa for the M1q and M2q microstructures, respectively. Comparison of these data with experimental flow laws confirmed that during Stage 1 marble is weaker than quartzite. However, during Stages 2 and 3, mica in impure quartzite became more dispersed but also locally aggregated; thus, the bulk strength of quartzite became governed by mixture of quartz and weak mica behaviour. This change in microstructure and the resulting deformation mechanism facilitated fluid transport across quartzite, which resulted in embrittlement of dominantly coarse-grained and impermeable competent marble. This process is accompanied by the formation of stretching faults developed parallel to weak layers of altered granite dykes in the vicinity of the marble-quartzite contact. The rheology inversion thus results from a mixture of deformation mechanisms in the weak polyphase quartzite and fluid-induced drop of effective pressure of strong and brittle marble at late stages of the extensional deformation.

This paper proposes a computational simulation procedure for simulating chemical dissolution-front instability problems, in which radially divergent flow is involved in fluid-saturated porous media. In the proposed computational simulation procedure, a combination of the finite element and finite difference methods is used to simulate a chemical dissolution-front instability problem involving radially divergent flow, while a new algorithm is used to apply a small perturbation to the problem. Particular attention is paid on simulating low-order modes of an unstable circular chemical dissolution-front propagating in a fluid-saturated porous medium, in which dissolvable materials only occupy a small part, so that the final porosity is remarkably smaller than unity when dissolvable materials are completely dissolved in the chemical dissolution system. To verify the proposed computational simulation procedure, analytical solutions for a benchmark chemical dissolution-front instability problem involving radially divergent flow are derived in a purely mathematical manner. The related computational simulation results have demonstrated that: (1) the proposed computational simulation procedure is correct and useful for simulating chemical dissolution-front instability problems, which are associated with both stable and unstable chemical dissolution systems involving radially divergent flow in fluid-saturated porous media; (2) the simulated shapes of the second-order, third-order and fifth-order modes associated with an unstable chemical dissolution-fronts are respectively an ellipse, a star of three angles and a star of five angles in the unstable chemical dissolution system involving radially divergent flow in the fluid-saturated porous medium; (3) although the heterogeneity of a porous medium can affect the propagation speed of a chemical dissolution-front, it does not affect the low-order mode shape in the unstable chemical dissolution system involving radially divergent flow in the fluid-saturated heterogeneous porous medium.

This paper investigates the near-field performance of chemical dissolution-front instability (CDFI) around a circular acid-injection-well in fluid-saturated porous media (FSPM) through using purely mathematical deductions. After the mathematical governing equations of the CDFI problem involving radially divergent flow are briefly described, both analytical base solutions and perturbation solutions for the considered problem are mathematically derived These analytical solutions lead to the theoretical expression of the perturbation induced dimensionless growth-rate and the following two new findings. The first new finding is that the critical Peclet number of a chemical dissolution system (CDS) associated with radially divergent flow in FSPM is not only a function of the permeability ratio between the undissolved and dissolved regions as well as the dimensionless wavenumber, but also a function of the circular chemical dissolution-front location relative to the circular acid-injection-well in FSPM. The second new finding is that as the direct result of considering a nonzero radius of the circular acid-injection-well, there exits a critical closeness number, which may be used to assess where the circular chemical dissolution-front starts becoming unstable in the CDS associated with radially divergent flow. Based on these two new findings, a theoretical criterion of two parts has been established. The first part of the established theoretical criterion answers the scientific question when a circular chemical dissolution-front can become unstable, while the second part of the established theoretical criterion answers the scientific question where a circular chemical dissolution-front can become unstable. Through applying the established theoretical criterion, a long-term existing mystery why the wormhole pattern of fractal nature and the compact pattern of fingering nature are formed at different locations away from the circular acid-injection-well circumference in fluid-saturated carbonate rocks has been successfully revealed.

PurposeThe objective of this paper is to establish a solution strategy for obtaining dual solutions, namely trivial (conventional) and nontrivial (unconventional) solutions, of coupled pore-fluid flow and chemical dissolution problems in heterogeneous porous media.Design/methodology/approachThrough applying a perturbation to the pore-fluid velocity, original governing partial differential equations of a coupled pore-fluid flow and chemical dissolution problem in heterogeneous porous media are transformed into perturbed ones, which are then solved by using the semi-analytical finite element method. Through switching off and on the applied perturbation terms in the resulting perturbed governing partial differential equations, both the trivial and nontrivial solutions can be obtained for the original governing partial differential equations of the coupled pore-fluid flow and chemical dissolution problem in fluid-saturated heterogeneous porous media.FindingsWhen a coupled pore-fluid flow and chemical dissolution system is in a stable state, the trivial and nontrivial solutions of the system are identical. However, if a coupled pore-fluid flow and chemical dissolution system is in an unstable state, then the trivial and nontrivial solutions of the system are totally different. This recognition can be equally used to judge whether a coupled pore-fluid flow and chemical dissolution system involving heterogeneous porous media is in a stable state or in an unstable state. The proposed solution strategy can produce dual solutions for simulating coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media.Originality/valueA solution strategy is proposed to obtain the nontrivial solution, which is often overlooked in the computational simulation of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. The proposed solution strategy provides a useful way for understanding the underlying dynamic mechanisms of the chemical damage effect associated with the stability of structures that are built on soil foundations.

Through using rigorously mathematical deductions, this article derives analytical solutions for chemical dissolution‐front instability (CDFI) problems, in which radially divergent flow is involved within fluid‐saturated porous media. Since the acid injection‐well to be considered is a circle of nonzero radius in the horizontal plane, a polar coordinate system is used to describe the coupled mathematical governing equations of the CDFI problem. To facilitate deriving analytical solutions, an appropriate mathematical transform is used to convert the coupled mathematical governing equations from a dimensional form into a dimensionless one. This enables the generalized linear stability approach to be utilized for deriving both analytical base and perturbation solutions for the CDFI problem involving radially divergent flow within a fluid‐saturated porous medium. Consequently, a theoretical criterion, which is usable for assessing the CDFI in the chemical dissolution system (CDS), is further established from the corresponding analytical perturbation solutions. The related theoretical results have demonstrated that: (1) the proposed theoretical criterion is useful and applicable for assessing the CDFI associated with radially divergent flow within fluid‐saturated porous media; (2) the permeability ratio between the downstream and upstream regions can affect significantly the critical Peclet number of a CDS associated with radially divergent flow; (3) the initial porosity can have remarkable effects on the critical Peclet number of a CDS associated with radially divergent flow; and (4) the difference between the final and initial porosities can also affect significantly the critical Peclet number of a CDS associated with radially divergent flow in the fluid‐saturated porous medium.

This paper proposes a mechanism called the mode-switching model that is presented as an alternative to the fault-valve model. This mechanism is relevant to open-flow, low-porosity, fluid-saturated systems deforming by pressure solution creep. As opposed to most constitutive models discussed in the geological literature, the yield envelope is capped at high normal stresses, as demonstrated by experimental studies. A low-permeability rock has relatively high pore fluid pressure for a given input fluid flux. This increases the dissolution rate for quartz that in turn leads to a higher-permeability rock, low fluid pressure for the same flux and decreased quartz solubility and deposition, returning to a low permeability. This cycle continues indefinitely so long as the rock mass is stressed, a fluid flux is applied, and pressure solution operates. The high fluid pressure drives the Mohr stress circle to the tensile end of the yield envelope resulting in crack-seal and extensional veins. The low fluid pressure drives the Mohr stress circle to the cap end of the yield envelope resulting in laminated veins in rocks undergoing mineral reactions with large net volume losses coupled with solute transfer. Failure at the cap end of the yield envelope results in displacement discontinuities inclined at high angles to & sigma;(1). Previously, these orientations have been taken to represent reactivated normal faults, an integral component of the fault-valve process. In the model presented, the yield surface prohibits the system ever reaching super-lithostatic pressures. The process of effective stress-driven switching between tensile and cap ends of the yield envelope arises from competition between dissolution and deposition, and is independent of any seismic events, fault reactivation or the episodic breaching of an impermeable seal. It provides a unifying, self-consistent concept for the interpretation of joints, faults and veins in hydrothermal systems.

The production of breccias and cataclasites is commonly proposed to result in power-law or log-normal probability distributions for fragment (grain) size. We show that in both natural and experimental examples, the common best fit probability distributions for the complete distributions are members of the Generalised Gamma (GG), Extreme Value (GEV) and Pareto (GP) families; power-law and log-normal distributions are commonly, but not always, poor fits to the data. An hierarchical sequence, GG → GEV → GP, emerges as the sample mean of the fragment size decreases. The physical foundations (self-similar fragmentation, collisional fragmentation, shattering) for these distributions are discussed. Particularly important is the shattering continuous phase transition that results in the simultaneous development of both coarse fragments and ultra-fine particles (dust). This phase transition leads to Generalised Pareto fragment size distributions for the coarse fragments. Also included is a discussion of the relations between fragment size distribution, processes and deformation history in the context of monomineralic rocks. The overall reported size distributions are compatible with theoretical developments but the topic would benefit from observations and experiments conducted with the theories in mind.

Despite many studies of orogenic gold systems, the underlying processes involved in their formation and in defining their location and endowment remain enigmatic. This arises because such processes are multiscale and nonlinear so that patterns of alteration and mineralisation are apparently irregular and unpredictable. The goal of a nonlinear dynamical analysis is to extract the dynamics of the underlying nonlinear and multiscale physical and chemical processes that produced these data. We review nonlinear analysis methodology and explore hyperspectral and gold assay data for a drill-hole in an orogenic gold system. The analysis is non-parametric and purely data driven. We use recurrence, cross-and joint-recurrence plots to extract quantitative measures of the system and construct the attractor for the mineral distributions. The resulting dynamical model is tested using nonlinear prediction algorithms. Cross recurrence analysis shows strong spatial correlations of gold with carbonates and weaker correlations with phengitic micas and chlorite. Joint recurrence analysis reveals that all components of the system belong to the same dynamical attractor and hence are parts of the same physical-chemical system. This means that data from one part of the system can be used to predict other parts of the system. The probability distributions for mineral abundance are members of the Generalised Extreme Value family, reflecting the details of the ways in which the systems grow. We speculate on the coupled processes responsible for the mineralising system, propose that autocatalytic reactions associated with quartz and carbonate deposition contribute to pH variations responsible for gold deposition and present a new view of mineralising systems where the probability distributions reflect the endowment of the system. This approach permits a good prediction of the grade distribution into substantial volumes of rock within the mineralized system, outside the zone where the data were obtained. We suggest that such an approach has potential to become an important component of the definition of ore reserves, as the current methods, based on Gaussian or log-normal probability distributions, commonly produce poor outcomes as ore deposits are developed.

Measuring the predictability and complexity of 2D data (image) series using entropy is an essential tool for evaluation of systems’ irregularity and complexity in remote sensing and geophysical mapping. However, the existing methods have some drawbacks related to their strong dependence on method parameters and image rotation. To overcome these difficulties, this study proposes a new method for estimating two-dimensional neural network entropy (NNetEn2D) for evaluating the regularity or predictability of images using the LogNNet neural network model. The method is based on an algorithm for converting a 2D kernel into a 1D data series followed by NNetEn2D calculation. An artificial test image was created for the study. We demonstrate the advantage of using circular instead of square kernels through comparison of the invariance of the NNetEn2D distribution after image rotation. Highest robustness was observed for circular kernels with a radius of R = 5 and R = 6 pixels, with a NNetEn2D calculation error of no more than 10%, comparable to the distortion of the initial 2D data. The NNetEn2D entropy calculation method has two main geometric parameters (kernel radius and its displacement step), as well as two neural network hyperparameters (number of training epochs and one of six reservoir filling techniques). We evaluated our method on both remote sensing and geophysical mapping images. Remote sensing imagery (Sentinel-2) shows that brightness of the image does not affect results, which helps keep a rather consistent appearance of entropy maps over time without saturation effects being observed. Surfaces with little texture, such as water bodies, have low NNetEn2D values, while urban areas have consistently high values. Application to geophysical mapping of rocks to the northwest of southwest Australia is characterized by low to medium entropy and highlights aspects of the geology. These results indicate the success of NNetEn2D in providing meaningful entropy information for 2D in remote sensing and geophysical applications.

This paper deals with how to implement perturbations in the computational simulations of chemical dissolution‐front instability (CDFI) problems in fluid‐saturated porous media. On the basis of theoretical analysis, it is found that the application of a perturbation to the chemical dissolution front is equivalent to the application of an alternative perturbation to the dimensionless pore‐fluid normal velocity (relative to the planar chemical dissolution front) in the chemical dissolution zone, where the chemical dissolution front is located. This avoids the difficulty to find the spatial coordinates of the chemical dissolution front locations in the computational simulations of CDFI problems. Based on this new finding, a novel algorithm for implementing perturbations in the computational simulations of CDFI problems is proposed. The key point of the proposed algorithm is that the perturbed pore‐fluid normal velocity (relative to the planar chemical dissolution front) is used to directly replace the original pore‐fluid normal velocity (relative to the planar chemical dissolution front) in the related mathematical governing equations (MGEs), so that the proposed algorithm works for the porosity‐velocity‐concentration scheme when it is used to solve CDFI problems in fluid‐saturated porous media. In addition, the related theoretical analysis in this study has answered the previous unanswered question why the application of a perturbation to porosity works in the porosity‐pressure‐concentration scheme but does not work in the porosity‐velocity‐concentration scheme for solving the same CDFI problems in fluid‐saturated porous media. Through solving two illustrative examples with two different distributions of initial porosity, in which one is homogeneous and another is heterogeneous in the chemical dissolution system, the validity and usefulness of the proposed algorithm for implementing perturbations in the computational simulations of CDFI problems have been demonstrated.

We describe the localized folding of thick layers embedded in a viscoelastic framework. Higher-order partial differential equations such as the Swift-Hohenberg equation are standard for modelling the folding process. Using a high-order shear theory, we modify the Swift-Hohenberg equation to describe the buckling of thick layers and consider the folded layer's viscoelastic behavior. The use of thick layers enables us to consider shear strains parallel to the layers during folding. Our model naturally captures the softening-stiffening behavior by including a non-linear viscoelastic description using a Winkler-type foundation. Next, we study the linear stability behavior of the system and derive the dispersion relations. Finally, we simulate this new model using a robust custom-built isogeometric analysis solver, which allows us to describe thick folded layers with localized folding. The numerical results show that the folding of an elastic layer produces periodic patterns while a viscoelastic layer deflects locally. When the horizontal forces are unequal, the periodic folds initiate in the direction of the smaller force and the localized deformations occur parallel to the larger force. Later, the nonlocal deformation occurs in the direction of a smaller force. Domes and basins or more linear ridges and valleys are formed according to the relative magnitudes of the applied forces. Domes and basins are the results of equal horizontal applied forces, and non-equal forces result in ridges and valleys.

The concept of fractal spatial distributions of mineralisation has been widely proposed since Mandelbrot (1965) who emphasised the stable Pareto-Lévy distribution as the relevant distribution. The concept of a fractal is used as a basis for estimating endowment and for erecting exploration models based on self-organised criticality. This paper explores the proposition that the growth kinetics for a mineralising system are reflected in the probability distributions that describe the spatial patterns of mineralisation. We revisit the data sets and ask the question: What are the best fit probability distributions for the spatial distribution of mineralisation? The answer is: members of the Extreme Value Distribution family (Gumbel-, Fréchet- and Weibull-distributions) and not the Pareto distribution. Thus, the spatial distribution of mineralisation is not a fractal although the tails of the distributions can be or resemble power-laws. The standard box counting procedure for a spatial point distribution establishes a nearest neighbour distribution and hence, by definition, the resulting distribution is Weibull and not Pareto. The mass distributions are Fréchet and not Pareto. The extreme end members are Gumbel. We discuss the implications of these distributions for models that generate mineralisation sites within a system and for the underlying thermodynamics.

The porosity structures of a permeable rock can have remarkable effects on pore-fluid flow within the rock. According to the modern mineralization theory, the mineralization pattern in a hydrothermal ore-forming system is strongly dependent on the pore-fluid flow velocity, so that different porosity structures of a permeable rock can affect significantly hydrothermal mineralization patterns within the permeable layers consisting of fluid-saturated porous rocks. This paper presents a semi-analytical approach, in which pore-fluid velocity is directly used as fundamental primary variables in the governing equations of the problem and the property matrices of finite elements are analytically evaluated in a purely mathematical manner, to ensure the high accuracy of the obtained pore-fluid velocity, which is involved in controlling mineralization patterns in hydrothermal ore-forming systems. After the proposed semi-analytical approach is verified through comparing the numerical solution with the analytical solution for a benchmark problem, it has been used to investigate how different porosity structures can affect the hydrothermal mineralization patterns within permeable horizontal layers consisting of fluid-saturated porous rocks through using a generic model, which can be viewed as the representation of a generalized and simplified geological model. Main outcomes of this study have demonstrated that: (1) the proposed semi-analytical approach can produce highly-accurate numerical solutions for solving coupled pore-fluid flow and heat transfer problems in fluid-saturated porous rocks with different porosity structures; (2) the different porosity structure within a permeable horizontal layer consisting of fluid-saturated porous rocks can have a significant effect on the hydrothermal mineralization pattern of the permeable horizontal layer; (3) layered pore-fluid vertical velocity focusing may take place within a permeable horizontal layer involving a heterogeneous porosity structure.

AbstractWe consider the implications of adding a cap to the yield surface for elastic–plastic and elastic–visco-plastic solids with coupling between deformation, fluid flow and mineral reactions. For a suitable combination of (low) permeability and strain rate, opening-mode veins can form in compression. Such behaviour is enhanced by dissolution and by simultaneous mineral reactions with negative ΔV. These are the opening-mode equivalents of compaction bands in rocks with high permeability. Stylolite parallel veins are considered as forming in this way; such veins are commonly the laminated or ribbon-quartz veins associated with intense gold mineralization. Axial plane veins and melt segregations are in this class also. The addition of a yield surface cap limits the permissible stress states portrayed by a failure-mode diagram and has implications for breccia formation. Failure discontinuities that form at the cap require adecreasein fluid pressure to form as opposed to extension joints and veins that require anincreasein fluid pressure; discontinuities that form at the cap are in orientations that are commonly interpreted as reactivated early discontinuities. The switching between high fluid pressure and low fluid pressure, which we callmode-switching, arises from competition between mineral dissolution and deposition. This is an alternative to the fault-valve mechanism and does not require fault reactivation or failure at a ‘seal’ linked to seismicity or fault reactivation. The capped yield surface concept provides a unifying self-consistent approach for vein/breccia formation and for the kinematics of brittle and visco-plastic rocks.

This article presents an accurate porosity‐velocity‐concentration approach, in which porosity, pore‐fluid velocity and the concentration of dissolvable substances in the pore fluid are selected as four primary unknown variables for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with arbitrarily initial porosity distributions. The first advantage of using the proposed approach is that since pore‐fluid velocity, instead of pore‐fluid pressure, is selected as the primary unknown variable to describe the pore‐fluid flow process, the pore‐fluid velocity obtained from the proposed approach is more accurate than that obtained from the numerical simulation, in which pore‐fluid pressure is selected as the primary unknown variable to describe the pore‐fluid flow. The second advantage of using the proposed approach is that because the property matrices of a four‐node rectangular element are precisely calculated in a purely mathematical way, the overall accuracy of numerical solutions can be ensured. After the proposed approach is verified by a benchmark problem, it has been applied for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with three different kinds of initial porosity distributions. It has been demonstrated that: (1) the proposed approach can produce highly‐accurate numerical solutions for solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with arbitrarily initial porosity distributions; (2) the initial porosity distribution in a porous medium can have remarkable effects on the reactive mass transport process in the porous medium; (3) the porosity and dimensionless concentration fronts propagate from the entrance to the exit of the problem domain, which is identical to the pore‐fluid flow direction.