Method for calculating rock permeability coefficient based on seepage-stress coupling high-pressure water pressure test

Abstract

The present application relates to the calculation method of rock mass permeability coefficient based on seepage-stress coupling high pressure water pressure test, the calculation method includes the following step content: (1) seepage continuity equation; (2) stress control equation; (3) flow calculation formula.The permeability coefficient result obtained by the present application is more accurate and reliable, a large amount of time and cost are saved, and another more actual calculation method for obtaining the permeability coefficient of high pressure water pressure test is provided.

Description

Technical Field

[0001] This invention belongs to the field of computational method technology, and in particular relates to a method for calculating the permeability coefficient of rock mass based on a seepage-stress coupled high-pressure water pressure test. Background Technology

[0002] In recent years, with the proposal of carbon neutrality goals and the rapid development of green energy, the scale of high-head, large-capacity hydropower station construction in the high mountain and canyon areas of western China has been continuously expanding. Long-distance, large-diameter, deep-buried, and high-head pressure tunnels have emerged one after another. These pressure tunnels often face problems such as internal water seepage and hydraulic fracturing under high water head conditions. The high seepage pressure on the surrounding rock of pressure tunnels poses a significant threat to the seepage stability of the project and also brings extremely high difficulty to seepage control. Therefore, conducting research on the seepage characteristics of tunnel surrounding rock under high seepage pressure is of great significance for guiding engineering construction.

[0003] To determine the permeability and stability of rock masses under high water head conditions, conventional pressure water tests are increasingly insufficient for assessing rock mass permeability and designing engineering seepage control systems under high permeability pressure. Therefore, many important projects have adopted high-pressure pressure water tests to study rock mass permeability, aiming to provide a basis for selecting seepage control measures. However, current analysis of rock mass permeability under high-pressure pressure water test conditions relies heavily on the complexity of groundwater movement. Conventional groundwater flow calculation models make many assumptions and impose strict requirements on the models. Currently, the recommended formulas in the industry specifications for borehole pressure water tests, based on the Darcy flow assumption, are still widely used.

[0004]

[0005] In the formula:

[0006] K: rock mass permeability coefficient (m / d); H: test head (m); l: test section length (m);

[0007] Q: Injection flow rate (m³) 3 / d); r0: Drilling radius (m);

[0008] This results in the rock permeability coefficient calculated by high-pressure water pressure tests on the same test section being significantly lower than that calculated by conventional water pressure tests. Although borehole high-pressure water pressure tests are an important means of studying the permeability characteristics of rock masses under high permeability conditions, current research on high-pressure water pressure tests and their analytical models is not yet in-depth, and a unified understanding of the relationship between the experimental PQ curve and the permeability characteristics of the rock mass has not yet been formed. Currently, the formulas recommended in the specifications are only applicable to the calculation of rock permeability coefficients under laminar and turbulent PQ flow rate curves with low permeability (<10 Lu). In addition, the specifications do not recommend formulas for calculating the permeability coefficient under dilatational PQ flow rate curves.

[0009] Furthermore, existing formulas and specifications do not consider the changes in the internal stress field of rock masses caused by high pore water pressure under high seepage pressure conditions, leading to compression deformation. This alters the joint and fracture characteristics within the rock mass, resulting in changes in the distribution of the seepage field and affecting the hydraulic properties of the rock mass, causing it to exhibit seepage characteristics different from those under normal pressure. Engineering practice also shows that during high-pressure water pressure tests, the seepage field and stress field are not independent; the seepage pressure in the seepage field significantly influences the stress distribution. As the test pressure increases, the pore water pressure within the rock mass also increases, and the complexity of fractures within the rock mass makes understanding the seepage patterns quite difficult. Therefore, the permeability of rock masses under high water pressure conditions will inevitably differ significantly from that under low water pressure conditions.

[0010] According to the survey, there are currently no good calculation models and methods for high-pressure water pressure tests that take into account hydraulic coupling, both domestically and internationally. To overcome the limitations of the formulas recommended in the specifications and to provide reference values ​​for the permeability coefficient considering hydraulic coupling, a calculation model for deep-hole high-pressure water pressure tests is established using COMSOL Multiphysics' analysis method based on the coupling of seepage field and stress field. This makes the numerical simulation results more consistent with actual engineering conditions. Summary of the Invention

[0011] The present invention aims to solve the above-mentioned problems and defects by providing a method for calculating the permeability coefficient of rock mass based on a seepage-stress coupled high-pressure water pressure test.

[0012] The present invention is implemented using the following technical solution.

[0013] The calculation method for rock mass permeability coefficient based on seepage-stress coupled high-pressure water test includes the following steps: (1) seepage continuity equation; (2) stress control equation.

[0014] The seepage continuity equation (1) described in this invention is:

[0015] Using a saturated continuous porous medium, the continuity equation for fluid flow through the micropores of the bulk medium is:

[0016]

[0017] Assuming fluid flow through the micropores of the rock mass conforms to Darcy's law:

[0018]

[0019] When considering the seepage-stress coupling effect in a medium, the influence of solid deformation on seepage is taken into account, that is, the influence of volumetric strain on the continuity governing equations of fluid flow in porous media:

[0020]

[0021] In the formula:

[0022] P: Fluid density, kg / m³ 3 ;

[0023] Q: Injection flow rate, L / min;

[0024] k: penetration rate, m 2 ;

[0025] μ: Dynamic viscosity of the fluid, N·s / m 2 ;

[0026] p: Pore water pressure at a distance of 0.1m from the pore wall, in Pa;

[0027] ε v : The volumetric strain of the medium;

[0028] α: Boit coefficient.

[0029] The stress control equation (2) described in this invention is:

[0030] When fluid flows through a rock mass, the water pressure changes, which in turn alters the effective stress.

[0031] When considering the effect of seepage on the internal stress of the rock mass, the rock blocks and structural surfaces (including cracks) are regarded as a continuous medium;

[0032] The stress balance equation of the rock mass is:

[0033] σ ij，j +F i =0 (4)

[0034] The stress-strain constitutive equation of the rock mass under pore water pressure is:

[0035] σ′ ij =2Gε ij +λδ ij δ kl ε kl -αPδ ij =D ijkl ε kl -αpδ ij (5)

[0036] In two dimensions, the expansion is simplified by utilizing the symmetry of the stress and strain tensors and the symmetry of the material, resulting in:

[0037]

[0038] In the formula:

[0039] σ′ ijEffective stress tensor, Pa;

[0040] F i Volume force, Pa;

[0041] D ijkl : Elastic tensor;

[0042] δ ij : is the Kronecher symbol, which is 0 when i ≠ j and 1 when i = j;

[0043] G: Shear modulus, Pa;

[0044] λ: Lamé coefficient;

[0045] In two dimensions, the relationship between displacement and strain is as follows:

[0046]

[0047] ε x2 =ε yz =ε zz =0

[0048] Because fluid pore pressure alters the effective stress in the rock mass, the inherent hydraulic parameter of the rock mass, the permeability coefficient, also changes. The Louis formula is introduced to characterize the variation of the permeability coefficient with pore pressure:

[0049] K1=K0e -α(γH-P) (8)

[0050] In the formula:

[0051] K0: Initial permeability, m 2 ;

[0052] γH-P: Effective normal stress in rock mass, Pa.

[0053] The calculation method described in this invention also includes (3) flow rate calculation formula: when the pore water pressure at a distance r from the borehole center is known, the permeability coefficient of the rock mass is calculated by using the relationship between the pore water pressure at a certain point when the pressurized water flow reaches a stable state and the water pressure in the pressurized water hole.

[0054] The flow rate calculation formula (3) of this invention is as follows: Assuming that the fractured rock mass is isotropic, the water flow in the fractured rock mass is approximately radial during the rock mass test. Under the condition that the test flow rate and pressure reach a relatively stable state during the water pressure test, the total flow rate on any cross-section of the water passage (a cylindrical surface with radius r) is equal. The flow rate calculation formula is as follows:

[0055]

[0056] According to Darcy's law, 2πrKi r L r=2πRKi R L R The length of the test section is L. R =L r ;then

[0057] The water head at a distance r from the borehole: pressure increment is:

[0058] dp = i r dr

[0059]

[0060]

[0061] The flow rate through the section at a distance R from the borehole is:

[0062] Q=2πRL0Ki R (11)

[0063] If the permeability coefficient is known, the formula for calculating Q is:

[0064]

[0065] In the formula:

[0066] P0: Test pressure (Pa);

[0067] P R : pore water pressure (Pa) at a distance R from the borehole center;

[0068] L0: Length of the test section (m);

[0069] R0: Drilling radius (m).

[0070] The beneficial effects of this invention are as follows: It allows for flexible selection of appropriate initial rock mass parameters based on actual hydrogeological conditions; it employs coupled analysis of seepage field and stress field to analyze the physical process of high-pressure water pressure tests; it incorporates the influence of pore medium deformation on the permeability coefficient into the model for calculation; and it provides a reference value for the permeability coefficient considering hydraulic coupling. Furthermore, it can simulate the head value at a point relative to the borehole wall, eliminating the need for long-term observation from observation wells to obtain background values. The collected water pressure test data requires no processing and can be directly used in the calculation. The obtained permeability coefficient results are more accurate and reliable, saving significant time and cost, and providing another more practical calculation method for determining the permeability coefficient in high-pressure water pressure tests.

[0071] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0072] Figure 1This is a schematic diagram of the water flow within the rock mass surrounding the test borehole of this invention;

[0073] Figure 2 This is a schematic diagram of the mesh partitioning of the computational model of the present invention;

[0074] Figure 3 This is a PQ curve fitting diagram of the present invention;

[0075] Figure 4 This is the kt curve diagram of the present invention. Detailed Implementation

[0076] (1) Seepage continuity equation

[0077] Using a saturated continuous porous medium, the continuity equation for fluid flow through the micropores of the bulk medium is:

[0078]

[0079] Assuming fluid flow through the micropores of the rock mass conforms to Darcy's law:

[0080]

[0081] When considering the seepage-stress coupling effect in a medium, the influence of solid deformation on seepage should be taken into account, that is, the influence of volumetric strain on the continuity governing equations of fluid flow in porous media:

[0082]

[0083] In the formula:

[0084] P: Fluid density (kg / m³) 3 );

[0085] Q: Injection flow rate (L / min);

[0086] k: penetration rate (m 2 );

[0087] μ: Dynamic viscosity of the fluid (N·s / m³) 2 );

[0088] p: Pore water pressure (Pa) at a distance of 0.1m from the borehole wall;

[0089] ε v : The volumetric strain of the medium;

[0090] α: Boit coefficient;

[0091] (2) Stress control equation

[0092] When fluid flows through a rock mass, the water pressure changes, which in turn alters the effective stress.

[0093] When considering the effect of seepage on the internal stress of the rock mass, the rock blocks and structural planes (including fractures) are treated as a continuous medium. The stress balance equation of the rock mass is:

[0094] σ ij，j +F i =0 (4)

[0095] The stress-strain constitutive equation of the rock mass under pore water pressure is:

[0096] σ′ ij =2Gε ij +λδ ij δ kl ε kl -αPδ ij =D ijkl ε kl -αpδ ij (5)

[0097] In two dimensions, the expansion is simplified by utilizing the symmetry of the stress and strain tensors and the symmetry of the material, resulting in:

[0098]

[0099] In the formula:

[0100] σ′ ij Effective stress tensor (Pa);

[0101] F i Volume force (Pa);

[0102] D ijkl : Elastic tensor;

[0103] δ ij : This is the Kronecher symbol (0 when i ≠ j, 1 when i = j)

[0104] G: Shear modulus (Pa);

[0105] λ: Lamé coefficient;

[0106] In two dimensions, the relationship between displacement and strain is as follows:

[0107]

[0108] ε xz =ε yz =ε zz =0

[0109] Because fluid pore pressure alters the effective stress in the rock mass, the inherent hydraulic parameter of the rock mass, the permeability coefficient, also changes. The Louis formula is introduced to characterize the variation of the permeability coefficient with pore pressure:

[0110] K1=K0e -α(γH-P) (8)

[0111] In the formula:

[0112] K0: Initial permeability (m 2 );

[0113] γH-P: Effective normal stress of the rock mass (Pa);

[0114] (3) Flow calculation formula

[0115] When the pore water pressure at a distance r from the borehole center is known, the permeability coefficient of the rock mass can be calculated by using the relationship between the pore water pressure at a certain point when the pressurized water flow reaches a steady state and the water pressure inside the pressurized borehole.

[0116] Assuming the fractured rock mass is isotropic, the water flow within the fractured rock mass during the rock mass test is approximately radial, such as... Figure 1 As shown. During the water pressure test, when the flow rate and pressure reach a relatively stable state, the total flow rate is equal on any cross-section (a cylindrical surface with radius r). The flow rate calculation formula is:

[0117]

[0118] According to Darcy's law, 2πrKi r L r =2πRKi R L R The length of the test section is L. R =L r ;then

[0119] The increase in water head (pressure) at a distance r from the borehole is:

[0120] dp = i r dr

[0121]

[0122]

[0123] The flow rate through the section at a distance R from the borehole is:

[0124] Q=2πRL0Ki R (11)

[0125] If the permeability coefficient is known, the formula for calculating Q is:

[0126]

[0127] In the formula:

[0128] P0: Test pressure (Pa);

[0129] P R : pore water pressure (Pa) at a distance R from the borehole center;

[0130] L0: Length of the test section (m);

[0131] R0: Drilling radius (m);

[0132] (4) Practical Application

[0133] The calculation model is an axisymmetric rectangle with length x width = 25m x 10m (e.g.) Figure 2 The mesh contains 1159 domain elements and 89 boundary elements, and the number of degrees of freedom to be solved is 2247.

[0134] Boundary conditions for seepage field: The borehole wall is designed as a 5m long permeable layer with a conductivity of R. b =1e-4(1 / s), the injection stage pressure is selected as follows: 0~30min: 1.5MPa; 30~60min: 2MPa; 60~90min: 2.5MPa; 90~120min: 3MPa; the upper and lower parts are no flow boundary, and the right side is the constant head boundary;

[0135] Stress field boundary conditions: The initial ground stress of the horizontal boundary is 4.4 MPa, and horizontal displacement constraints are applied; the stress of the vertical boundary is 2.2 MPa, and vertical displacement constraints are applied.

[0136] Select zk412-7, which exhibits a clear linear relationship: initial permeability is taken as 1.9e-15m. 2 α is taken as 2e-8 (1 / Pa); zk412-13: initial permeability is taken as 8.2e-15m 2 α is set to 3.8e-7(1 / Pa), and the global parameter settings are shown in Table 1;

[0137] Table 1 Global Parameter Settings

[0138]

[0139] The pressure head at a distance of 0.1m from the orifice wall was determined by hydraulic coupling numerical simulation. The PQ curve was obtained by calculating the flow rate and then fitted and compared with the measured PQ curve.

[0140] It can be seen that the PQ curve fitting effect of the high-pressure water test using hydraulic coupling analysis is good, with a maximum error of 5.7%. The average value of the obtained permeability numerical solution is ZK412-7: 1.79e-15m. 2 The calculated value 2e-15m is consistent with the formula in the specification. 2Approximate; ZK412-13: 3.75e-15m 2 The calculated value is 4.8e-15m, which is consistent with the formula in the specification. 2 The results are similar, indicating that the hydraulic coupling analysis is reliable and can provide a more realistic reference for determining the permeability coefficient in anti-seepage design.

[0141] The above descriptions are merely some specific embodiments of the present invention. Commonly known details or common knowledge in the solutions are not described in detail here (including but not limited to abbreviations and acronyms). It should be noted that the above embodiments do not limit the present invention in any way. For those skilled in the art, any technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for calculating the permeability coefficient of rock mass based on seepage-stress coupled high-pressure water pressure test, characterized in that, The calculation method includes the following steps: (1) seepage continuity equation; (2) stress control equation; The seepage continuity equation (1) is as follows: Using a saturated continuous porous medium, the continuity equation for fluid flow through the micropores of the bulk medium is: Assuming fluid flow through the micropores of the rock mass conforms to Darcy's law: When considering the seepage-stress coupling effect in a medium, the influence of solid deformation on seepage is taken into account, that is, the influence of volumetric strain on the continuity governing equations of fluid flow in porous media: In the formula: P: Fluid density, kg / m³ 3 ; Q: Injection flow rate, L / min; k: penetration rate, m 2 ; 𝜇: Dynamic viscosity of the fluid, N∙s / m 2 ; p: Pore water pressure at a distance of 0.1m from the pore wall, in Pa; 𝜀 𝑣 : The volumetric strain of the medium; 𝛼: Boit coefficient; The stress control equation (2) is as follows: When fluid flows through a rock mass, the water pressure changes, which in turn alters the effective stress. When considering the effect of seepage on the internal stress of the rock mass, the rock blocks and structural surfaces are treated as a continuous medium. The stress balance equation of the rock mass is: The stress-strain constitutive equation of the rock mass under pore water pressure is: In two dimensions, the expansion is simplified by utilizing the symmetry of the stress and strain tensors and the symmetry of the material, resulting in: In the formula: Effective stress tensor, Pa; F i Volume force, Pa; D ijkl : Elastic tensor; δ ij : is the Kronecher symbol, which is 0 when i ≠ j and 1 when i = j; G: Shear modulus, Pa; λ: Lamé coefficient; In two dimensions, the relationship between displacement and strain is as follows: Because fluid pore pressure alters the effective stress in the rock mass, the inherent hydraulic parameter of the rock mass, the permeability coefficient, also changes. The Louis formula is introduced to characterize the variation of the permeability coefficient with pore pressure: In the formula: 𝐾0: Initial penetration rate, m 2 ; 𝛾H − 𝑃: Effective normal stress of rock mass, Pa.

2. The method for calculating the permeability coefficient of rock mass based on seepage-stress coupled high-pressure water pressure test according to claim 1, characterized in that, The calculation method also includes (3) flow rate calculation formula: when the pore water pressure at a distance r from the borehole center is known, the permeability coefficient of the rock mass is calculated by using the relationship between the pore water pressure at a certain point when the pressurized water flow reaches a steady state and the water pressure in the pressurized water hole.

3. The method for calculating the permeability coefficient of rock mass based on seepage-stress coupled high-pressure water pressure test according to claim 2, characterized in that, The flow rate calculation formula (3) is as follows: Assuming that the fractured rock mass is isotropic, the water flow in the fractured rock mass is approximately radial during the rock mass test. Under the condition that the test flow rate and pressure reach a relatively stable state during the water pressure test, the total flow rate on any cross-section is equal. The flow rate calculation formula is: According to Darcy's Law, The length of the test section is L. R =L r ;then ; The water head at a distance r from the borehole: pressure increment is: The flow rate through the section at a distance R from the borehole is: If the permeability coefficient is known, the formula for calculating Q is: In the formula: 𝑃0: Test pressure, Pa; 𝑃 𝑅 : pore water pressure at a distance R from the borehole center, in Pa; F0: Length of the test segment, in meters; 𝑅0: Drilling radius, in meters.

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