A cfd-dem coupling analysis method for sandstone cementation degradation

Abstract

The application provides a CFD-DEM coupling analysis method for sandstone cementation degradation, and aims at the problem that the existing CFD-DEM coupling simulation only considers the water drag force on particles, and ignores the influence of water on the cementation dissolution of particles, which causes the decrease of particle bonding strength and the increase of porosity between particles. The strength reduction effect of the cementation dissolution of particles on weakly cemented sandstone is considered, a cementation degradation and porosity change coupling model of weakly cemented sandstone under water immersion erosion is considered in the CFD-DEM fluid-solid coupling method, and the deficiency of the existing simulation method for sandstone water immersion erosion disaster is improved. The application finely reproduces the erosion of cementation under water immersion, which leads to the decrease of sandstone strength and the increase of porosity, and the CFD-DEM fluid-solid coupling analysis method is applied to the sand gushing disaster analysis of the weakly cemented rock mass such as sandstone in the water-rich area.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology, and in particular to a CFD-DEM coupled analysis method for sandstone cementation degradation. Background Technology

[0002] The Discrete Element Method (DEM) treats soil as an accumulation of discrete particles. Given a contact model between particles, it calculates the displacement and velocity of the particles according to Newton's second law, thus simulating the mesoscopic response of granular materials under different loading environments. Combining DEM with Computational Fluid Dynamics (CFD) to establish a fluid-structure interaction method to simulate the migration and motion of soil particles at the mesoscopic scale under liquid action is called the CFD-DEM coupled analysis method.

[0003] The key to analyzing the gradual increase in water content in weakly cemented rock masses such as sandstone and weathered rock caused by water-rock interactions lies in the dissolution of cementitious materials upon contact with water. Excavation disturbance alters the seepage path of weakly cemented sandstone, allowing groundwater to seep along fissures, eroding the intergranular cement, reducing rock mass strength, and increasing intergranular porosity. The rock mass exhibits a cycle of water absorption, cement weakening, porosity expansion, and intensified seepage, ultimately leading to a fluid-plastic morphology in the weakly cemented sandstone strata. However, existing CFD-DEM coupled simulation methods generally only consider the drag force of water on particles, neglecting the impact of water dissolution on cement, which reduces particle bonding strength and increases intergranular porosity. Therefore, the analysis of the catastrophic mechanism of weakly cemented sandstone is flawed. Furthermore, the porosity parameter setting ignores the local erosion differences in cement degradation caused by water content, such as the non-uniform distribution of cement degradation and porosity changes within different grid cells, resulting in inaccurate simulation analysis results. Therefore, it is necessary to establish a coupled model in the CFD-DEM fluid-structure interaction method that considers the cementation degradation and porosity changes of weak cemented sandstone under water erosion, so as to improve the shortcomings of existing methods for simulating the catastrophe of sandstone water erosion. Summary of the Invention

[0004] In view of the above problems, this application provides a CFD-DEM coupled analysis method for sandstone cementation degradation, which is used to perform CFD-DEM fluid-structure coupling calculations on the microscale strength degradation process under different water contents and the pore structure changes caused by the dissolution of weak cementing media composed of clay, so as to overcome the above problems or at least partially solve the above problems.

[0005] This application provides a CFD-DEM coupled analysis method for sandstone cementation degradation, the method comprising:

[0006] Collect target weakly cemented sandstone samples, construct discrete element rock sample models in DEM, and bond the individual particle models of the discrete element rock sample through parallel bond models.

[0007] Construct an erosion equation for water-rich, weakly cemented sandstone;

[0008] Establish the seepage control equation relating the water content of weak cemented sandstone to the seepage velocity of fluid units;

[0009] The erosion equation and seepage control equation of water-rich, weakly cemented sandstone were imported into the CFD-DEM coupled model.

[0010] In the CFD-DEM coupled model, fluid-structure interaction analysis is performed on the discrete element rock sample model until the set number of fluid-structure interaction calculations is reached or sand inrush occurs.

[0011] Furthermore, the construction of the erosion equation for water-rich, weakly cemented sandstone includes:

[0012] The bonding radius between two particles is determined by the bonding radius multiplier, and the polar moment of inertia of the parallel bond cross section is determined based on the bonding radius.

[0013] Based on the bonding radius multiplier, the equation for the change of macroscopic strength degradation degree of rocks under different water content conditions is determined;

[0014] Based on the equation for the change in the degree of macroscopic intensity degradation, the bonding radius multiplier under different water contents is determined;

[0015] Based on the bonding radius multiplier under different moisture contents, the parallel bond normal stress and shear stress of the parallel bond bonding model are determined.

[0016] The actual porosity of the weakly cemented sandstone particles within the fluid unit is determined based on the total volume of the adhesive contact between the particles in the weakly cemented sandstone fluid unit.

[0017] Furthermore, the equation for the change in the degree of macroscopic intensity degradation is as follows:

[0018]

[0019] in, Indicates the degree of macroscopic strength degradation of the rock; The initial macroscopic strength of weakly cemented sandstone in anhydrous conditions; Moisture content; This represents the maximum water content. The water content of the weakly cemented sandstone is Macroscopic intensity at that time; A and B are material parameters related to the interaction between water and rock.

[0020] Furthermore, the formulas for calculating the parallel bond normal stress and shear stress are as follows:

[0021] ,

[0022] ,

[0023] in, and These represent the parallel bond normal stress and shear stress after considering the moisture content, respectively; , , , These are the normal contact force, tangential contact force, torsional moment, and bending moment of the PBM contacting the parallel key. It is the smaller radius of the adjacent particles; Indicates water content as Bond radius multiplier at time; It is the torque contribution coefficient.

[0024] Furthermore, the determination of the bonding radius multiplier at different water contents based on the total volume of interparticle adhesive contact in weakly cemented sandstone fluid units and the macroscopic strength degradation degree variation equation includes:

[0025] Based on the equation for the change in macroscopic strength deterioration, the water content of the weakly cemented sandstone was determined to be: Macroeconomic intensity at time :

[0026]

[0027] Among them, C, D, and E are the relationship coefficients between the microscopic strength parameters and macroscopic strength parameters of weakly cemented sandstone;

[0028] Establish the water content of weakly cemented sandstone and moisture content Bond radius multiplier at time Relationship:

[0029]

[0030] in, The initial macroscopic strength of weakly cemented sandstone in anhydrous conditions.

[0031] Further, determining the actual porosity of the weakly cemented sandstone particles within the fluid unit based on the total volume of the adhesive contact between the particles in the weakly cemented sandstone fluid unit includes:

[0032] The total volume of the adhesive contact between the fluid unit particles is obtained based on the spacing between the two particles and the cross-sectional area of ​​the parallel bond.

[0033] The true porosity of weakly cemented sandstone particles within a fluid unit is determined based on the total volume of the adhesive contact between particles in the fluid unit.

[0034] Furthermore, the formula for calculating the true porosity is as follows:

[0035]

[0036] in, This represents the true porosity of the fluid unit; Represents the pore volume of a fluid unit; Indicates the volume of a fluid unit; This represents the total volume of the fluid unit particles; This represents the volume of the bonding material between the particles in a fluid unit; Represents the empirical coefficient;

[0037]

[0038] in, This is the contact gap between two particles; It represents the total volume of the adhesive contact between fluid unit particles.

[0039] Furthermore, the seepage control equation is:

[0040]

[0041]

[0042] In the formula, t is the exposure time of the tunnel working face. The water content of the weakly cemented sandstone strata is [not specified]. The maximum water content is for weakly cemented sandstone strata; The initial water content of the weakly cemented sandstone strata is [value missing]. Parameters related to changes in water content caused by groundwater seepage through weakly cemented sandstone strata; For cumulative traffic; This represents the cumulative flow within the coupled computation time step; This refers to the single coupling time. The seepage velocity of the fluid unit; Let be the cross-sectional area of ​​the fluid element.

[0043] The specific beneficial effects are as follows:

[0044] This application presents a numerical model of weakly cemented sandstone based on the parallel bond model (PBM). It calculates the macroscopic strength degradation equation of the rock under different water contents, and the porosity of particles in the DEM after cement loss under water erosion. Simultaneously, it refines the relationship between water content and seepage velocity of the fluid element in the weakly cemented sandstone, and introduces the KC extended equation considering clay effects to calculate the permeability coefficient of the weakly cemented sandstone. Then, it performs CFD-DEM fluid-structure interaction calculations. This invention precisely reproduces the situation where cement is eroded under water immersion, leading to a decrease in sandstone strength and an increase in porosity. It provides guidance for expanding the application of CFD-DEM fluid-structure interaction analysis methods to the study of sand inrush disasters in water-rich areas involving weakly cemented rock masses such as sandstone. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 A schematic flowchart illustrating a CFD-DEM coupled analysis method for sandstone cementation degradation provided in this application embodiment;

[0047] Figure 2 (a)-(b) show the changes in particle cementation during debonding in the erosion process; where (a) shows the changes in weakly cemented sandstone; and (b) shows the bond contact in PBM.

[0048] Figure 3 (a)-(b) represent the changes in the parallel bond radius multiplier; where (a) represents the process of bond loss; and (b) represents the rate at which the parallel bond radius multiplier decreases with increasing water content.

[0049] Figure 4 This relates to the relationship between moisture content and the degree of macroscopic strength degradation, and the relationship between moisture content and uniaxial strength.

[0050] Figure 5 To simulate the geometry and boundary conditions of a uniaxial compression test.

[0051] Figure 6 The stress-strain curves are for different bonding contact radius multipliers.

[0052] Figure 7 This is the adhesive contact radius multiplier versus uniaxial compressive strength curve.

[0053] Figure 8 The workflow of CFD-DEM method for erosion model of water-rich, weakly cemented sandstone.

[0054] Figure 9 This is a schematic diagram illustrating the coupling information interaction with the erosion model of weakly cemented sandstone.

[0055] Figure 10 (a)-(d) show the particle motion at time steps of 50, 100, 150 and 200, respectively.

[0056] Figure 11 (a)-(d) represent the water content at time steps of 50, 100, 150, and 200, respectively.

[0057] Figure 12 (a)-(b) represent the changes in particle displacement and moisture content; where (a) is the curve of particle displacement in the monitoring area changing with time step; and (b) is the curve of moisture content in the monitoring area changing with time step.

[0058] Figure 13 (a)-(d) represent the resistance at time steps of 50, 100, 150, and 200, respectively.

[0059] Figure 14 (a)-(d) represent the bonding contact radii at time steps of 50, 100, 150, and 200, respectively; and the white transparent spheres in the figures represent the collapsed areas where the particle displacement is greater than 0.09 meters. The model only shows the bonding changes within the 3R height range of the tunnel.

[0060] Figure 15 This represents the porosity variation at different heights and during the evolution stages of sand inrush disasters in weakly cemented strata. Detailed Implementation

[0061] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0062] To account for the impact of water dissolution on cementitious materials leading to decreased particle bond strength and increased interparticle porosity, this invention provides a CFD-DEM coupled analysis method for sandstone particle cementation degradation under water erosion. (Refer to...) Figure 1 , Figure 1 This is a flowchart illustrating a CFD-DEM coupled analysis method for sandstone cementation degradation provided in an embodiment of this application. The method may include:

[0063] Step 1: Collect target weakly cemented sandstone samples and construct a discrete element rock sample model in the DEM. The discrete element rock sample model binds the particles together through a parallel bond model.

[0064] In DEM simulation, a rock sample is established in PFC for the target weakly cemented sandstone sample, and a discrete element rock sample model is obtained. This rock sample model includes several particles and bonding contact points.

[0065] Step 2: Construct the erosion equation for water-rich, weakly cemented sandstone.

[0066] Optionally, step 2 includes the following sub-steps:

[0067] Step 201: Determine the bonding radius between the two particles by using the bonding radius multiplier, and determine the polar moment of inertia of the parallel bond cross section based on the bonding radius;

[0068] The parallel bond model (PBM) is used to characterize the intrinsic properties of intergranular material within a finite region filled with sandwich or cementing material. It can be viewed as a set of springs uniformly distributed within the contact surface, each with constant normal and tangential stiffness. The relative motion of the particles at the contact point generates forces and torques within the bonding material, acting on the two bonding particles and relating to the maximum normal and tangential forces at the boundary of the bonding material assembly.

[0069] Because of its ability to transmit force and torque, bonding can be used to characterize the relatively dense cemented joints of sandstone; bonding that fractures after reaching the load limit can be used to characterize the load limit of sandstone cementation. When parallel bond contact is activated, two particles adhere together, and the contact gap between them... Less than or equal to 0, that is ≤0.

[0070] Therefore, the bonding radius between two particles can be determined by the bonding radius multiplier:

[0071] (1)

[0072] in, Indicates the bonding radius between two particles; Indicates the bonding radius multiplier ( (Default is 1). and These represent the radii of two adjacent particles, respectively. This indicates that the minimum value is taken among the radii of two adjacent particles; therefore, the bonding radius multiplier can be used to describe the bonding radius between two particles.

[0073] Furthermore, based on the bonding radius between the two particles We can obtain:

[0074] The cross-sectional area of ​​the parallel key ( The formula for calculating ) is:

[0075]

[0076] Moment of inertia of the cross section of the parallel key ( The formula for calculating ) is:

[0077] (3)

[0078] Polar moment of inertia of the cross section of the parallel key ( The formula for calculating ) is:

[0079] (4).

[0080] The initial parallel bond normal stress and shear stress of the parallel bond model can be expressed as:

[0081] ,

[0082] ,

[0083] in, For parallel bonding normal stress; For parallel bonding shear stress;

[0084] In the embodiments of this application, starting from the parallel bond contact state of the parallel bond model (PBM), a foundation is laid for subsequent updates of the parallel bond normal stress and shear stress considering changes in moisture content.

[0085] Step 202: Based on the bonding radius multiplier, determine the equation for the change in the macroscopic strength deterioration of rocks under different water content conditions.

[0086] Due to the altered seepage path caused by tunnel excavation, groundwater converges towards the tunnel face, leading to a continuous increase in the water content of the surrounding rock. This debinding process causes soluble cement in the weakly cemented sandstone to gradually dissolve into the water flow. As the water content continues to increase, the macroscopic strength degradation of the rock becomes increasingly significant. Macroscopic strength degradation refers to the gradual decrease in the overall mechanical properties (such as compressive strength, tensile strength, and shear strength) of the rock under external environmental or engineering disturbances.

[0087] The change in the interparticle bonding radius can be obtained through the bonding radius multiplier. The description, therefore, is based on the bond radius multiplier. The following equation can be established to reflect the change in the degree of macroscopic strength deterioration of rocks under different water content conditions:

[0088] (5)

[0089] in, Indicates the degree of macroscopic strength degradation of the rock; The initial macroscopic strength of weakly cemented sandstone in anhydrous conditions; Moisture content; This represents the maximum water content. The water content of the weakly cemented sandstone is Macroscopic strength at that time; A and B are material parameters related to the interaction between water and rock, such as uniaxial compressive strength, tensile strength, porosity, internal friction angle, etc.

[0090] When the water content When it is 0, That is At this point, the degree of macroscopic intensity deterioration The value is 0; when the moisture content reaches the maximum moisture content. At that time, the macroscopic intensity deteriorated. Reaching the maximum value;

[0091] The above analysis shows that the debonding effect caused by the gradual increase in water content will weaken the bond between sandstone particles, reduce their strength, and thus decrease the bond radius between particles. Decrease. According to equation (1), the bonding radius multiplier of fine-scale parallel bonding in the PBM model is... It can be used to characterize changes in interparticle bonding radius and peak strength of rocks. and The correlation is positive. It can be verified through uniaxial strength tests at different moisture contents, using a power function to reflect the macroscopic strength of weakly cemented sandstone and the bond radius multiplier. The relationship between them, such as Figure 3 As shown in (b), the decrease in macroscopic strength of weakly cemented sandstone due to increased water content can be addressed by reducing the water content to [a certain value]. Bond radius multiplier at time Implementation, i.e., in equation (5) It can be represented as:

[0092] (6)

[0093] Where C, D, and E are the relationship coefficients between the microscopic strength parameters and macroscopic strength parameters of weakly cemented sandstone.

[0094] Step 203: Based on the equation for the change in macroscopic strength degradation, determine the bonding radius multiplier under different water contents.

[0095] According to equation (6), when the weakly cemented sandstone is in its initial cemented state... =1, When all the cementing material in the weakly cemented sandstone disappears, The value is 0, and the weakly cemented sandstone transforms into a sandy state with very low residual uniaxial compressive strength. .

[0096] Secondly, by combining formulas (5) and (6), the water content of weakly cemented sandstone can be established. and moisture content Bond radius multiplier at time Relationship:

[0097] (7).

[0098] The bonding radius multiplier for different water contents can be obtained by equation (7).

[0099] Step 204: Determine the parallel bond normal stress and shear stress of the parallel bond bonding model based on the bonding radius multiplier under different water contents.

[0100] Simultaneously, considering the debonding effect caused by changes in moisture content, the initial parallel bond normal stress and shear stress of the parallel bond bonding model (PBM model) will also be updated with changes in moisture content. Therefore, based on a moisture content of... Bond radius multiplier at time The water content was obtained as The specific calculation formulas for the bonding normal stress and shear stress at the time of bonding are as follows:

[0101] , (8a)

[0102] , (8b)

[0103] (8c)

[0104] Parallel bond fracture condition:

[0105] (9a)

[0106] (9b)

[0107] In the formula, , , , These are the normal contact force, tangential contact force, torsional moment, and bending moment of the PBM contacting the parallel key. , , , These represent the normal contact force, tangential contact force, torsional moment, and bending moment of the PBM contacting the parallel key within the time step. It is the smaller radius of the adjacent particles; It is the normal stiffness; It is shear stiffness; It is the minute normal displacement between the contact surfaces under normal load; It is the relative slip increment of the contact surface under shear load; It is the relative torsional angle increment in the direction of the normal at the contact point; It is the relative bending angle increment perpendicular to the contact normal direction; and These represent the parallel bond normal stress and shear stress after considering the moisture content, respectively; and These represent the tensile strength and shear strength of the parallel key, respectively. and These represent the cohesive force and internal friction angle of the parallel bond, respectively. It is the torque contribution coefficient.

[0108] Step 205: Determine the actual porosity of the weakly cemented sandstone particles within the fluid unit based on the total volume of the adhesive contact between the particles in the weakly cemented sandstone fluid unit.

[0109] During the dissolution process of weakly cemented sandstone, the increased water content causes the cement in the sandstone to dissolve. Porosity increases with the dissolution of the cement, and this increase significantly affects the seepage velocity, intensifying the flow of granular cement and fine particles, and further exacerbating sand inrush. To quantitatively describe the porosity increase process under dissolution, in the embodiments of this application, the true porosity of the weakly cemented sandstone DEM particles within the fluid element can be calculated based on the cement contact volume in the intergranular PBM model.

[0110] Optionally, step 205 includes the following sub-steps:

[0111] Sub-step 2051: Based on the distance between the two particles and the cross-sectional area of ​​the parallel bond, obtain the total volume of the adhesive contact between the fluid unit particles;

[0112] The spacing between the two particles mentioned above refers to the contact gap between them when the parallel adhesive contact is activated and the two particles are bonded together. ;

[0113] The formula for calculating the total volume of the adhesive contact is:

[0114] (10a)

[0115] in, This is the contact gap between two particles; This represents the total volume of the adhesive contact between particles in a fluid unit;

[0116] As can be seen from the above formula, based on the spacing between particles and the radius of the bonding bond... It can be calculated .

[0117] Sub-step 2052: Determine the true porosity of all particles in the weakly cemented sandstone based on the total volume of the adhesive contact between fluid unit particles;

[0118] The formula for calculating the true porosity is as follows:

[0119] (10b)

[0120] in, This represents the true porosity of the fluid unit; Represents the pore volume of a fluid unit; Indicates the volume of a fluid unit; This represents the total volume of DEM particles; This represents the volume of the bonding material between the particles in a fluid unit; Represents the empirical coefficient;

[0121] like Figure 3 As shown, under the effect of debonding, the cementitious mud gradually dissolves with increasing moisture content, and the bonding radius multiplier decreases. As it decreases, the corresponding bonding radius... It also continuously decreases. This leads to the parallel bond adhesion contact volume within the fluid unit, i.e. The porosity between fluid unit particles increases as the number of particles decreases (Equation 10(a)).

[0122] Thus, based on equations (1), (4), (8a)-8 (8c), (9a)-9b, and (10a)-10b, the erosion equations for water-rich, weakly cemented sandstone are established.

[0123] Step 3: Establish the seepage control equation relating the water content of the weak cemented sandstone to the seepage velocity of the fluid unit.

[0124] After tunnel excavation, the moisture content of the tunnel face increases over time, exhibiting a clear power-law trend. The time to reach maximum moisture content varies depending on seepage through the weakly cemented sandstone strata. The greater the seepage, the shorter the time for the tunnel face to reach maximum moisture content.

[0125] In order to quantitatively analyze the water content and exposure time of the tunnel working face, in the embodiments of this application, it is assumed that there is a power function relationship between the seepage velocity of each fluid unit and the water content of the weakly cemented sandstone stratum. The seepage control equation of the relationship between the water content of the weakly cemented sandstone and the seepage velocity of the fluid unit can be established, as shown in equation (11):

[0126] (11a)

[0127] (11b)

[0128] In the formula, t is the exposure time of the tunnel working face. The water content of the weakly cemented sandstone strata is [not specified]. The maximum water content is for weakly cemented sandstone strata; The initial water content of the weakly cemented sandstone strata is [value missing]. Parameters related to changes in water content caused by groundwater seepage through weakly cemented sandstone strata; For cumulative traffic; This represents the cumulative flow within the coupled computation time step; This refers to the single coupling time. The seepage velocity of the fluid unit; Let be the cross-sectional area of ​​the fluid element.

[0129] Next, the permeability of weakly cemented sandstone can be calculated based on the Kozeny-Carman extended equation that takes into account the effect of clay.

[0130] In existing CFD-DEM coupled analysis systems, the Kozeny-Carman (KC) equation is typically used to establish the relationship between porosity and the average permeability of fluid elements, thereby characterizing the permeability changes caused by particle movement and realizing the influence of DEM particle movement on the seepage field distribution. However, since the KC equation cannot describe the permeability changes of clay and clay-bearing rocks, it cannot be used to describe weakly cemented sandstone containing clay minerals. Based on this, Ren et al. introduced the concept of effective porosity and derived an extended Kozeny-Carman equation considering the effect of clay based on Poiseuille's law and the KC equation. The expression is as follows:

[0131] (12a)

[0132] (12b)

[0133] in, The permeability of the fluid unit; Porosity of the fluid unit; This represents the actual porosity of the fluid unit; The pore structure influence coefficient; The density of the solid particles, denoted as , where is the specific surface area of ​​the solid particles; m is a constant given the soil or rock medium.

[0134] In the formula, It can refer to curvature and aperture distribution, used to characterize the effects of materials; It is related to the particle size; when m is 0~0.1, 1 and 1.5 respectively, it is applicable to the calculation of soil and rock masses with different clay contents. When m=0, the equation degenerates into the KC equation.

[0135] As shown above, based on the Kozeny-Carman (KC) equation considering the effect of clay, permeability evolution equations caused by particle loss under erosion can be established (Equations 12a-12b). Then, the sand inrush process of water-rich, weakly cemented sandstone strata at different water levels was simulated, and the seepage difference caused by the increase of coupling time was calculated based on the change in porosity between particles.

[0136] Step 4: Import the erosion equation and seepage control equation of water-rich, weakly cemented sandstone into the CFD-DEM coupled model.

[0137] Next, the erosion equation for water-rich, weakly cemented sandstone can be embedded into the PFC3D-PorePy fluid-structure interaction framework program using Python. The seepage control equation is calculated by the open-source software PorePy for porous media seepage simulation, and the PyGeoN database is used to convert the flow velocities of each fluid element from the surface to the center in the hybrid virtual finite method (VFM) in the PorePy solver; the DEM particle motion can be calculated by the commercial software PFC3D.

[0138] Step 5: In the CFD-DEM coupled model, perform fluid-structure interaction analysis on the discrete element rock sample model until the set number of fluid-structure interaction calculations is reached or sand inrush occurs.

[0139] Optionally, combined Figure 8 The fluid-structure interaction computation framework shown includes the following sub-steps in step 5:

[0140] Step 501: Generate fluid elements in the CFD model.

[0141] Step 502: In the DEM model, the discrete element rock sample model reads the nodes of each fluid element.

[0142] Step 503: In the DEM model, based on the PBM model of the fluid element spatial region, calculate the adhesive contact volume and actual porosity of each fluid element;

[0143] Specifically, the bonded contact volume and actual porosity can be calculated based on equations (10a) and (10b) in the imported water-rich, weakly cemented sandstone erosion equation.

[0144] Step 504: Based on the bonded contact volume and actual porosity, determine the flow rate and pressure of the fluid element in the CFD model according to the Darcy fluid model and the permeability of the fluid element;

[0145] The Darcy fluid model, which describes the motion of fluids through porous media, is an effective method for predicting fluid behavior by means of appropriate permeability. The governing equations for transient fluid flow through saturated porous media are based on the Darcy model and assume that the fluid phase is incompressible.

[0146] Based on the Darcy fluid model, the formulas for calculating the velocity and pressure of the fluid element are as follows:

[0147] (15)

[0148] (16)

[0149] in, This represents the average porosity of the fluid unit in which the particle resides. For fluid dynamic viscosity; The pressure gradient of the fluid element; For fluid velocity; Porosity is The permeability of the fluid unit;

[0150] The permeability of the fluid unit in Equation (15) can be calculated based on Equation (12a) according to the bonded contact volume and the actual porosity.

[0151] Step 505: Obtain the flow rate and pressure of each fluid element in the DEM, and update the particle position according to Newton's equations and the particle position update equation.

[0152] Since the motion of the particles is controlled by Newton's second law, the particle velocity can be calculated according to Newton's second law:

[0153] (13)

[0154] (14)

[0155] In the formula, Indicates the velocity of particle movement; Indicates the time required for numerical computation; It is the sum of the additional forces (external forces and contact forces) acting on a particle; This represents the total fluid-particle interaction force exerted by the fluid on the particles; Indicates particle mass; Represents gravitational acceleration; Indicates the angular velocity of the particle; This represents the contact torque experienced by the particle; This represents the moment of inertia of a particle.

[0156] The total fluid-particle interaction force It consists of three parts: fluid drag force, force caused by fluid pressure gradient, and buoyancy of the fluid on the particles, as follows:

[0157] (17)

[0158] in, For fluid drag force; r is the fluid density; r is the particle radius;

[0159] Fluid drag force Defined as the resistance exerted by the fluid on a particle, it always acts on the particle's center of mass. The particle does not exert a rotational torque, and it is calculated using the following formula:

[0160] (18)

[0161] In the formula: For the drag force of a single particle, This is an empirical factor for correcting the local average porosity. This correction term will be applicable to both high and low porosity systems as well as a wide range of Reynolds numbers.

[0162] (19)

[0163] In the formula: The drag coefficient, This represents the particle velocity.

[0164] drag coefficient It can be calculated as:

[0165] (20)

[0166] In the formula: is the particle Reynolds number.

[0167] Additionally, adjust empirical factors. Defined as:

[0168] (twenty one)

[0169] Reynolds number Calculated as:

[0170] (twenty two)

[0171] In the formula, is the fluid dynamic viscosity coefficient.

[0172] Step 506: Determine whether the preset coupling cycle has been reached or sand inrush has occurred. If yes, complete the coupling analysis; otherwise, calculate the water content and water content of each fluid element in the DEM model. The bonding radius multiplier of the parallel bond model, as well as the parallel bond normal stress and shear stress, are determined, and the process returns to step 503.

[0173] Specifically, the bonding radius multiplier under different water contents is obtained according to equations (1), (4), and (7) in the imported water-rich weakly cemented sandstone erosion equation. Then, the parallel bond normal stress and shear stress can be obtained according to equations (8a)-(8a) and (9a)-(9b). The water content is calculated according to the imported seepage control equations (equations 11a-11b). Finally, the calculated water content, bonding radius multiplier, parallel bond normal stress, and shear stress are returned to step 503 to calculate the bond contact volume and actual porosity.

[0174] Real-world engineering cases

[0175] This invention proposes a CFD-DEM coupled analysis method for sandstone cementation degradation under water erosion. Since the pore space between particles increases due to the decrease in the volume content of soluble cement, macroscopically this manifests as a decrease in strength and an increase in porosity. Therefore, this CFD-DEM coupled analysis method can be used to analyze sand inrush hazards in water-rich areas. Using the steps of the CFD-DEM coupled analysis method for sandstone cementation degradation in the embodiments of this application, CFD-DEM coupled analysis is performed on the weakly cemented sandstone of the Xiangshan Tunnel. Specific implementation steps include:

[0176] Step 101: Immerse the weakly cemented sandstone grain PBM bond model in water for erosion.

[0177] In the embodiments of this application, the PBM method is used to study the mechanical properties of weakly cemented sandstone during erosion. During the erosion of weakly cemented sandstone, the particles themselves are not eroded, but due to the increase in water content, the debinding effect of erosion causes the soluble cement in the weakly cemented sandstone to disappear and be discharged from the internal pores with the water flow. This leads to a decrease in the bonding force between mineral particles due to the bonding radius. The decrease in strength weakens the overall strength, while the decrease in the volume content of soluble cementitious material increases the pore space between mineral particles, resulting in a decrease in strength and an increase in porosity macroscopically. Figure 2 As shown.

[0178] Step 102: Calculate the degree of macroscopic strength degradation of the weakly cemented sandstone in Xiangshan Tunnel under different moisture contents.

[0179] Since existing studies have conducted uniaxial strength tests on the weakly cemented sandstone of the Xiangshan Tunnel under different moisture contents, the results of the uniaxial strength tests are shown in Table 1. Among them, the uniaxial strength degradation in Table 1... It can be calculated according to the above formula (5). This represents the degree of macroscopic strength degradation of rocks under different water contents.

[0180]

[0181] The test results in Table 1 show that as the water content of weakly cemented sandstone increases, its strength deteriorates more significantly, with prominent mudification, and its mechanical properties gradually approach those of normal cemented clay or loose sand. Based on the test results in Table 1, the degree of macroscopic strength deterioration can be determined. Uniaxial strength Based on this, the moisture content and the degree of macroscopic strength deterioration can be obtained. And the functional relationship between moisture content and uniaxial strength, such as Figure 4 As shown.

[0182] Step 103: Calibrate the microscopic parameters and erosion coefficient of the weakly cemented sandstone in Xiangshan Tunnel.

[0183] In the embodiments of this application, a trial-and-error method can be used to determine the relationship between microscopic and macroscopic parameters. Based on the experimental results of weakly cemented sandstone with 0% water content in Table 1, it can be seen that when the water content is 0%, the PBM bonding contact radius multiplier is 1.0. The microscopic parameters of the rock sample in the DEM simulation are determined by calibration using a uniaxial compression test (UCT). A rock sample with dimensions of 1.0m × 0.5m is constructed in the PFC, as follows... Figure 5 As shown, the rock sample consisted of 16,853 particles and 66,654 bonding contact points, with the particle size uniformly distributed between 0.025 and 0.026 μm.

[0184] Based on the microscopic parameters at 0% moisture content (as shown in Table 2), uniaxial compression tests were conducted by varying the value of the parallel bond contact radius multiplier. Stress-strain curves corresponding to different radius multipliers were obtained using the controlled variable method, as shown below. Figure 6 As shown, the bonded contact radius decreases continuously with the decrease of the radius multiplier, which can effectively describe the strength degradation effect during the dissolution process of weakly cemented sandstone. Figure 7 As shown, based on the uniaxial compression test results at this time, the radius multiplier and the uniaxial compressive strength of the rock (i.e., the water content of the weakly cemented sandstone) were determined according to equation (6). Macroeconomic intensity at time The relationship between )

[0185]

[0186] Numerical simulation experiments show that when the radius multiplier equals 0.069, the uniaxial compressive strength of the rock is zero, indicating that the cementation content can no longer support the uprightness of the sample, and the sample is in a sand-like state. Based on the uniaxial strength and macroscopic deterioration test results of weakly cemented sandstone under different water contents (i.e., the uniaxial strength test results of weakly cemented sandstone in Xiangshan Tunnel under different water contents), the model micro-parameters of the initial cementation state are shown in Table 2. Table 2 shows the model micro-parameters when the water content is 0, which remain unchanged in the simulation. According to equation (7), the relationship between water content and the bonding radius multiplier is:

[0187]

[0188]

[0189] according to Figure 7 Without considering the volume of interparticle contact, substituting the data from Table 2 into formula (10a) yields a porosity of 0.34 for the rock sample. Corresponding parameters are then set in the DEM model to ensure the particle arrangement conforms to the actual situation. According to formula 10(b), all contact points are traversed and their volumes are accumulated, where the length of a single contact is determined by… Calculation, such as Figure 4 As shown.

[0190] To simulate a primary weakly cemented sandstone with a porosity of 0.26 in the bonding material between sandstone grains, the empirical coefficients in Formula 10(a) were determined. It is 0.33.

[0191] Based on field exploration data, the permeability of the weakly cemented sandstone strata in Xiangshan Tunnel and the self-stabilization time of the tunnel working face are shown in Table 3. As can be seen from Table 3, before the sand inrush, the seepage velocity of the weakly cemented sandstone is very low, but as the tunnel working face is exposed, the water content increases continuously, and after about 4-5 hours, the tunnel working face begins to become unstable. According to the power function variation law of the water content of the tunnel working face with time, it is shown in Equation (11). Combining Table 3, the maximum water content and the initial water content of the weakly cemented strata are 20% and 7%, respectively. Considering the calculation efficiency, the maximum seepage velocity of the tunnel working face is set to 5. 23×10-5 m / s is selected as the average seepage velocity of the fluid unit, and the average self-stabilization time step is 100 steps. Therefore, the water content in Equation (11) can be determined. The coefficient of variation is 3.12.

[0192]

[0193] Based on the permeability coefficient (2.1×10⁻⁶ m / s) and initial porosity (0.26) of the weakly cemented sandstone, the pore structure influence coefficient in equation (9a) can be calculated. In the DEM model, the particle size is 0.024 m–0.026 m, and the particle density is 1860 kg / m³. Therefore, the specific surface area of ​​the particles is... The value is 0.129 m² / kg. The pore structure influence coefficient ( The calculated result is 537 m². The pore structure remains unchanged, ignoring changes caused by particle erosion and loss.

[0194] Step 104: Determine the fluid unit seepage velocity and water content of the weakly cemented sandstone in Xiangshan Tunnel.

[0195] The above-mentioned equations for controlling the erosion of water-rich, weakly cemented sandstone are embedded into the PFC3D-PorePy fluid-structure interaction framework program using Python, as shown below. Figure 8 As shown.

[0196] Due to the multiplier of the bonding radius between particles in different fluid units The contact volume varies with flow velocity and time step. To achieve this, it is first necessary to group different particles according to the spatial region of the fluid unit and determine the flow velocity, adhesion radius multiplier, adhesion contact volume between particles, and particle volume within different fluid units. We utilize the node information of the fluid unit to create the "Rblock" class in the PFC software using Python and FISH, then convert it to a "Geometry" class attribute, and use the ray casting method to determine the points in the polygon area function. Grouping all particles according to the spatial distribution of the fluid unit significantly reduces the calculation time for grouping and permutation of particle contact based on the spatial region of the fluid unit.

[0197] Then, based on formula (10), the flow field is calculated for the actual porosity within each fluid unit. Next, the force-displacement calculation and fluid-structure interaction calculation between particles are performed. According to the erosion law of water-bearing weakly cemented sandstone, the PBM cemented contact radius multiplier and contact volume reduction are calculated. In the next fluid-structure interaction cycle, the PBM calculation parameters are updated, and the particles are regrouped according to their positions after migration. Then, the seepage field update and fluid-structure interaction calculation are started until the set number of fluid-structure interaction calculations is reached.

[0198] Step 105: Establish a CFD-DEM coupled model of the weakly cemented sandstone of Xiangshan Tunnel.

[0199] (a) DEM model setup

[0200] The Xiangshan Tunnel section from DK43+925 to DK44+515 is composed of weakly cemented sandstone, with a burial depth of 120 m to 150 m. Section DK44+134 to 208 is selected, with a burial depth of 135 m. The tunnel cross-section has a diameter of 15.0 m and a height of 12.25 m. Considering computational efficiency, the model is scaled down by a factor of 25. Particles are generated through free fall, with gravity... By applying servo loads, the formation pressure (1.395e6 Pa) at a formation height of 75 meters was simulated. Because the model is symmetrical to the tunnel, only half of the DEM model was constructed, with dimensions of 1.6 m × 0.8 m × 2.4 m, as shown below. Figure 9 As shown. 157,161 non-overlapping particles in the DEM model were used to form the weakly cemented sandstone strata. The particle micro-parameters and values ​​of the PBM model are shown in Table 2. The initial water content was 7%, so the bonding contact radius multiplier was set to 0.96 according to formula (7). In addition, particles located in the 0.5-meter-long excavated tunnel were removed, and the tunnel lining was set as a rigid wall.

[0201] Each coupling calculation step in the PFC software requires a total of 2e4 cycles. The drag of a particle is updated every 20 cycles for different particles. On a workstation (Intel i9-9900K and 32GB RAM), one coupling calculation step takes an average of 20 minutes.

[0202] (b) CFD model setup

[0203] Compared to the DEM domain, the additional region in the CFD domain is a groundwater region. According to the similarity theorem, the gravity of water is set to 25g. The top of the CFD domain and the tunnel face are considered as pressure-out zones, and the other boundaries of the CFD domain are a wall. There is no water inside the excavated tunnel; therefore, only one side of the tunnel face experiences a water pressure of 0 Pa. Figure 9 As shown, four water level conditions caused by precipitation were simulated in the CFD domain: 3.4m, 2.4m, 1.4m, and 0.4m, where 3.4m is the initial groundwater depth and 0.4m is the depth at the bottom of the tunnel. When the water level is 0.4m, the water content of the surrounding rock of Xiangshan Tunnel is set to 9%, and the influence of the seepage field is not considered.

[0204] (c) Coupling parameters

[0205] The CFD-DEM interactive calculation parameters are shown in Table 4. Under 200 coupled calculation steps, the coupling process simulated sand inrush in weakly cemented sandstone. In each fluid-structure interaction calculation step, particles and particles with bonded contact were grouped according to the fluid element distribution, such as... Figure 9 As shown. For Figure 9In the DEM model, different colors represent different particle groups. Then, the flow rate is calculated based on the flow velocity, fluid cross-sectional area, and fluid volume in each fluid unit (Equation 11(b)). Then, the water content is calculated based on the cumulative flow rate in each fluid unit (Equation 11(a)), the parallel bonding radius multiplier between particles in different fluid units is updated (Equation (7)), and the parallel bonding normal stress and shear stress of the PBM model are updated when the water content changes (Equation (8)). At the same time, the porosity change and the corresponding permeability caused by the dissolution of intergranular cement are calculated and updated (Equation (12)). After obtaining the permeability, it is used in the subsequent CFD model fluid simulation in step 106. In the simulation, the CFD-DEM fluid-solid coupling continues to operate interactively until sand inrush occurs.

[0206]

[0207] Each coupling calculation step in the PFC software requires a total of 2e4 cycles. The resistance of different particles is updated every 20 cycles. On a workstation (Intel i9-9900K and 32GB memory), one coupling calculation step takes an average of 20 minutes.

[0208] Step 106: Based on the CFD-DEM coupled model established in Step 105, simulate the sand inrush process of water-rich, weakly cemented sandstone strata at different water levels.

[0209] (a) erosion and damage to the strata

[0210] After the tunnel face was exposed, the seepage path converged towards the tunnel face, and no damage occurred before 40 time steps. As the seepage time increased, the tunnel face was damaged. At 50 time steps, particles detached from the tunnel face, followed by sand inrush, and the strata above the tunnel face continued to collapse. Figure 10 The data shows particle migration within the strata at different time steps after the tunnel working face was exposed. Figure 10 The portion within the dashed box on the right side of each figure (a) to (d) is an XOZ profile of the strata at the tunnel working face. In large-porosity and uncemented strata, the fracture angle of the slurry-water inrush disaster zone is smaller, and the failure morphology is more often elliptical. The sand inrush and successive collapse processes in weakly cemented strata are mainly due to the decrease in the strength of cementing particles caused by seepage erosion, rather than by seepage force. Figure 11 The moisture content at different time steps is shown.

[0211] To further analyze the sand inrush process, particle displacement and water content in the monitored strata area were selected for analysis, such as... Figure 12 As shown. The monitoring points are arranged as follows. Figure 10As shown in (d), where R is the tunnel radius. Four particles are selected, and their displacement over time is tracked at the monitoring point locations before sand inflow begins. When particles enter the tunnel, they are removed and no longer tracked in the next coupling cycle. The water content in the fluid element closest to the four monitoring points is selected. From... Figure 12 (a) It can be seen that the occurrence of sand inrush disaster exhibits a significant lag. Before t1 (50 time steps), the tunnel face remains basically stable with minimal particle displacement. However, after t1, the tunnel face undergoes significant deformation, and at t2 (60 time steps), the surrounding rock at the tunnel arch, with a height equal to one radius, also experiences substantial deformation. At time step 110, monitoring points 0R and 1R are selected, and particles are flushed into the tunnel. However, the surrounding rock at the tunnel arch, with a height equal to two radius, remains stable before time t3 (120 time steps). Figure 12 As shown in (b), as the tunnel face is exposed, water flows towards the tunnel face, and the water content of the surrounding rock increases rapidly. Comparing the time when particles at different heights begin to migrate, the water content of the surrounding rock generally increases to 16%-18%.

[0212] (b) Flow field

[0213] The resistance vectors of the strata surrounding the tunnel at different time steps are shown below. Figure 13 Resistance values ​​less than 1.0N are filtered out and not displayed. Initial resistance is relatively small, with only resistance greater than 1.0N distributed on the tunnel surface. As particles disappear, more space is provided for fluid flow, increasing the difference between particle velocity and seepage velocity, thus increasing resistance. The area of ​​increased resistance expands as the subsidence zone within the strata expands, and the directional vector converges towards the tunnel surface, forming a funnel shape. From Figure 13 (d) It can be seen that the maximum resistance does not occur at the tunnel surface, but the maximum difference between particle velocity and seepage velocity occurs in the collapse zone inside the stratum.

[0214] (c) Microscopic mechanical behavior

[0215] The macroscopic behavior of particles is reflected in profound changes in their microscopic behavior. Figure 14 The distribution of the bond contact radius at different time steps is shown, with a minimum bond contact radius of 9.6e-4 m, representing a deterioration of the bond contact radius coefficient to a minimum of 0.069. At the onset of seepage, the water converges towards the tunnel face, reducing the bond contact radius around the tunnel face, simulating the loss of cementing media in weakly cemented sandstone. As seepage time increases, the shrinking bond contact surface continuously expands towards the upper part of the tunnel face, consistent with the development pattern of ground subsidence zones. However, the range of the bond contact radius with a minimum value of 9.6e-4 m is larger than the range of formation particle subsidence, indicating a decrease in interparticle cementation, leading to particle stripping and inflow into the tunnel.

[0216] Porosity serves as a crucial bridge connecting soil deformation and groundwater flow. By updating porosity changes in real time, the CFD-DEM fluid-solid coupling model can reflect the complex interactions during sediment inrush and reveal the coupling mechanism between soil deformation, particle transport, and groundwater flow. Figure 15 The changes in porosity of the monitored strata over time are shown. Based on the changes in porosity, and combined with the above analysis of the flow field and solid field at both macroscopic and microscopic scales during the sand inrush process, the sand inrush process in the water-bearing, weakly cemented sandstone strata at the tunnel face can be divided into four stages.

[0217] Phase 1 (0-50): Debonding and Erosion Phase

[0218] After the tunnel face was exposed, the seepage paths converged towards the tunnel face. The water content of the weakly cemented sandstone surrounding the tunnel face increased rapidly. Figure 12 (b) Under debinding, the micro-cementing medium in the weakly cemented sandstone gradually dissolves into the water and is washed away by the water flow. Figure 14 (a) Due to the loss of the cementing medium, the pore space gradually and slowly increases ( Figure 15 As the pore water pressure gradually decreases, the seepage velocity gradually increases.

[0219] Phase 2 (51-100): Erosion and Debonding Stage

[0220] As the water content of the formation increases, when the weak cementation erosion reaches a certain critical value, sandstone particles are gradually stripped away under the influence of formation pressure, resulting in erosion. Figure 10 (b) and ( Figure 12 (a) The contact state between the particles and the framework structure was adjusted. Due to the loss of sandstone particles, the pore space increased significantly. Figure 15 Simultaneously, a sharp increase in seepage velocity was observed, reaching two orders of magnitude. This increase in seepage velocity induces a scouring effect. Under the combined effects of debonding and scouring, the particle loss rate further increases, and the porosity increase rate further improves.

[0221] Stage 3 (101-150): Collapse of the upper strata

[0222] The weakly cemented sandstone surrounding the tunnel face has reached its maximum deterioration due to debonding erosion, which extends upwards into the strata. Figure 12 (b) Under the combined effects of debonding and scouring, the sand inrush at the tunnel face further evolved ( Figure 14 (c)). As the seepage time increases, the sand inrush advances into the strata above the tunnel face. Figure 10 (c) caused the upper strata to collapse towards the tunnel face, filling the pore space of the tunnel face. Figure 15 ).

[0223] Phase 4 (151-200): Continuous Large Deformation

[0224] The chain-like collapse within the strata continued to develop towards the upper strata above the tunnel face. Figure 10 (d) The chimney-shaped collapse zone extends upwards. The strata surrounding the tunnel face are in a loose state and surge into the tunnel, causing continuous large deformations as they enter. Figure 14 ).

[0225] The CFD-DEM coupled analysis method for sandstone cementation degradation provided in this application has been described in detail above. Specific examples have been used to illustrate the principle and implementation of this application. The description of the above embodiments is only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A CFD-DEM coupled analysis method for sandstone cementation degradation, characterized in that, The method includes: Collect target weakly cemented sandstone samples, construct discrete element rock sample models in DEM, and bond the individual particle models of the discrete element rock sample through parallel bond models. Construct an erosion equation for water-rich, weakly cemented sandstone; Establish the seepage control equation relating the water content of weak cemented sandstone to the seepage velocity of fluid units; The erosion equation and seepage control equation of water-rich, weakly cemented sandstone were imported into the CFD-DEM coupled model. In the CFD-DEM coupled model, fluid-structure interaction analysis is performed on the discrete element rock sample model until the set number of fluid-structure interaction calculations is reached or sand inrush occurs. The construction of the erosion equation for water-rich, weakly cemented sandstone includes: The bonding radius between two particles is determined by the bonding radius multiplier, and the polar moment of inertia of the parallel bond cross section is determined based on the bonding radius. Based on the bonding radius multiplier, the equation for the change of macroscopic strength degradation degree of rocks under different water content conditions is determined; Based on the equation for the change in the degree of macroscopic intensity degradation, the bonding radius multiplier under different water contents is determined; Based on the bonding radius multiplier under different moisture contents, the parallel bond normal stress and shear stress of the parallel bond bonding model are determined. The actual porosity of the weakly cemented sandstone particles within the fluid unit is determined based on the total volume of the adhesive contact between the particles in the weakly cemented sandstone fluid unit. The determination of the actual porosity of the weakly cemented sandstone particles within a fluid unit based on the total volume of the adhesive contact between particles in the weakly cemented sandstone fluid unit includes: The total volume of the adhesive contact between the fluid unit particles is obtained based on the spacing between the two particles and the cross-sectional area of ​​the parallel bond. The true porosity of weakly cemented sandstone particles within a fluid unit is determined based on the total volume of the adhesive contact between particles in the fluid unit. The seepage control equation is: ； ； In the formula, t is the exposure time of the tunnel working face. The water content of the weakly cemented sandstone strata is [not specified]. The maximum water content is for weakly cemented sandstone strata; The initial water content of the weakly cemented sandstone strata is [value missing]. Parameters related to changes in water content caused by groundwater seepage through weakly cemented sandstone strata; For cumulative traffic; This represents the cumulative flow within the coupled computation time step; This refers to the single coupling time. The seepage velocity of the fluid unit; Let be the cross-sectional area of ​​the fluid element.

2. The method according to claim 1, characterized in that, The equation for the change in the degree of macroscopic intensity degradation is as follows: ； in, Indicates the degree of macroscopic strength degradation of the rock; The initial macroscopic strength of weakly cemented sandstone in anhydrous conditions; Moisture content; This represents the maximum water content. The water content of the weakly cemented sandstone is Macroscopic intensity at that time; A and B are material parameters related to the interaction between water and rock.

3. The method according to claim 1, characterized in that, The formulas for calculating the parallel bond normal stress and shear stress are as follows: , ； , ； in, and These represent the parallel bond normal stress and shear stress after considering the moisture content, respectively; , , , These are the normal contact force, tangential contact force, torsional moment, and bending moment of the PBM contacting the parallel key. It is the smaller radius of the adjacent particles; Indicates water content as Bond radius multiplier at time; It is the torque contribution coefficient.

4. The method according to claim 1, characterized in that, The determination of the bonding radius multiplier at different water contents, based on the total volume of interparticle adhesion contact in weakly cemented sandstone fluid units and the equation governing the change in macroscopic strength degradation, includes: Based on the equation for the change in macroscopic strength deterioration, the water content of the weakly cemented sandstone was determined to be: Macroeconomic intensity at time : ； Among them, C, D, and E are the relationship coefficients between the microscopic strength parameters and macroscopic strength parameters of weakly cemented sandstone; Establish the water content of weakly cemented sandstone and moisture content Bond radius multiplier at time Relationship: ; in, The initial macroscopic strength of weakly cemented sandstone in anhydrous conditions.

5. The method according to claim 4, characterized in that, The formula for calculating the true porosity is as follows: ； in, This represents the true porosity of the fluid unit; Represents the pore volume of a fluid unit; Indicates the volume of a fluid unit; This represents the total volume of the fluid unit particles; This represents the volume of the bonding material between the particles in a fluid unit; Represents the empirical coefficient; ； in, This is the contact gap between two particles; It represents the total volume of the adhesive contact between fluid unit particles.

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