Hydromechanical modeling of a geological formation under shearing by the nonuniform crust movement during 10000 years was carried out to investigate the solid stress and pore pressure coupling processes of the formation from the intact to the fractured or faulted. Two threedimensional numerical models were built and velocities in opposite directions were applied on the boundaries to produce the shearing due to the nonuniform crust movement. The results show that the stress and pore pressure became more and more concentrated in and around the middle of the formation as time progresses. In Model I with no fault, stress and pore pressure are concentrated in the middle of the model during shearing; however, in Model II with a fault zone of weakened mechanical properties, they are more complex and concentrated along the sides of the fault zone and the magnitudes decreased. The distribution of stress determines pore pressure which in turn controls fluid flow. Fluid flow occurs in the middle in Model I but along the sides of the fault zone in Model II. The results of this study improve our understanding of the rockfluid interaction processes affected by crustal movement and may guide practical investigations in geological formations.
It is commonly recognized that fluid flow in bedrock regions is mainly controlled by faults and fractures [
The speed of the earth crust movement in a formation is generally nonuniform. Based on the GPS data, for example, Niu et al. [
The coupling processes of bedrock deformations and pore pressure changes can be described by the theory of poroelasticity [
In this study, we carried out hydromechanical simulations to investigate the coupling processes of solid stress and fluid pressure in a shallow geological formation under a continuous loading caused by the nonuniform crustal movement during 10000 years. Two threedimensional solidfluid coupling models were built: Model I without a fault zone and Model II with a fault zone. Based on the simulation results, we analyzed the evolution of the solid stress and fluid pressure in the formation during this time period. The results of this study help to improve our understanding of these complex processes. In the following, we will first describe the methodology, then present the results and discussion, and finally draw some conclusions.
As mentioned before, the speed of the earth crust movement is uneven and this nonuniform movement may create fractures and/or faults. Groundwater flow in bedrocks is usually controlled by faults and fractures. The coupling processes of the solid stress and pore pressure of bedrocks from the intact to the fractured or faulted under the nonuniform crust movement are very important in controlling the groundwater flow pattern. Therefore, two solidfluid coupling numerical models were built. One model is for a homogenous formation without a fault zone (Model I, Figure
The two conceptual models: (a) is Model I and (b) is Model II. Two opposite velocity fields were applied to the two boundary faces (the shaded areas) to simulate the shear stress generated from nonuniform crust movement. The unit of the displacement,
The solid phase is governed by the elasticity equations including the kinetic equation, the geometric equation, and the constitutive equation. The liquid phase is governed by a constitutive equation based on Darcy’s law. The coupled behavior of solid and fluid is governed by the equilibrium equation between the volumetric strains, pore pressure, and saturation.
Based on the elastic theory and movement equation, the solid stress is governed by the kinetic equation:
Velocities cause changes in strains, and thus the relationship between the velocity and strain can be described with the geometric (compatibility) equation:
Based on the linear poroelasticity theory, the strainstress relation for small deformation of the porous geological media is commonly described by the following constitutive equation:
The fluid flow in the bedrock is described by Darcy’s law:
Fluid mass can be expressed with continuity equation as follows:
The change in the fluid content is related to the change in pore pressure (
The initial and mechanical boundary conditions for deformation of the two model are the same and are set as follows:
The initial and boundary conditions for fluid flow of two models are different. For Model I,
For Model I, the initial hydraulic head is equal to the static pressure (see (
The densities of the formation and groundwater are taken to be 2500 kg/m^{3} and 1000 kg/m^{3}, respectively. Relative large porosity values of the bedrock are adopted in order to generate optimistic scenarios for the pore pressure redistribution induced by the continuous plate movement. The other material mechanical and physical parameters used in the computation of Models I and II are listed in Table
Parameters for Models I and II.
Bulk modulus  Cohesion  Shear modulus  Tension  Friction  Dilation  Hydraulic conductivity  Porosity  

(Pa)  (Pa)  (Pa)  (Pa)  (°)  (°)  (m/yr)  
Bedrock 




30  0 

0.5 
Fault 




15  0  1  0.6 
The two numerical models were constructed with FLAC3D which is a threedimensional finite difference numerical software for solving problems in engineering mechanics, that is, static and dynamic mechanics and hydraulic effects, including their coupling process [
As mentioned above, two models were built with dimension of 1000 m × 500 m × 300 m, and we generated a threedimensional mesh of 50 × 10 × 10 with a total of 6171 nodes for Model I and a mesh of 50 × 10 × 10 (40 × 10 × 10 in the bedrock and 10 × 10 × 10 in the fault zone) with a total of 6171 nodes for Model II. The dynamic damping type is Rayleigh with two relevant parameters
The coupled equation (
The changes of the maximum principal stress (
Contour map of the maximum principle stress (
At
The changes of the horizontal distribution of
Similar to Figure
Contour map of the maximum principle stress (
Corresponding to
Contour map of the pore pressure (
Corresponding to
Two typical cross sections of
The flow direction in two cross sections (
Corresponding to
Contour map of the pore pressure (
Corresponding to
The same cross sections were selected to display the flow direction in Model II (Figure
The flow direction in two cross sections (
It is worth noting that the distribution of
The distribution of
The changes of the pore pressure with time at seven observation points in the models are depicted in order to better understand the coupling process of rock deformation and fluid flow. Figure
Locations of the seven observation points.
Observation points  0 








500  0  250  500  500  500  500 

250  250  250  0  250  250  250 

150  150  150  150  150  0  300 
Locations of the seven observation points.
Figure
Changes of the pore pressure (
In this study we carried out hydromechanical modeling of a geological formation: Model I without a fault zone and Model II with a fault zone, to investigate the coupling processes of the solid strain and pore pressure of the formation under shearing by the nonuniform crust movement during 10000 years. The changes of the maximum principal stress (
The initial stress field controlled by gravity is positive (tensile) at the top of the formation and changes to negative (compressive) at the bottom. As time progresses,
The distribution of
The changes of
The distribution of
The pore pressure in the middle of the formation increases with time to reach their respective peak values and then decreases at late time during shearing. At the rest of the formation, the pore pressure stays relatively constant. The effect of the existing fault zone on the pressure is to reduce the magnitude (including the peak) of
The authors declare that they have no conflicts of interest.
This study was partially supported by the research grants from the National Nature Science Foundation of China (NSFC41272260; NSFC41330314; NSFC41302180), the Department of Science and Technology of Jiangsu Province (BE2015708), and the research fund provided by the Southern University of Science and Technology, China.