CN115524275B - Fractured rock mass permeability tensor determination method considering rock mass seepage and fracture seepage - Google Patents
Fractured rock mass permeability tensor determination method considering rock mass seepage and fracture seepage Download PDFInfo
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- 239000011435 rock Substances 0.000 title claims abstract description 317
- 230000035699 permeability Effects 0.000 title claims abstract description 83
- 238000000034 method Methods 0.000 title claims abstract description 48
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- 239000011148 porous material Substances 0.000 claims abstract description 54
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
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Abstract
The application discloses a fracture rock mass seepage tensor determination method considering rock mass seepage and fracture seepage, which comprises the following steps: according to the fracture rock mass joint fracture geometric distribution characteristics obtained through on-site statistical analysis, constructing a fracture rock mass two-dimensional random fracture grid simplified model; generating fracture rock mass numerical calculation models with pores and fracture double medium seepage in different sizes; performing a fractured rock mass permeability numerical test to obtain an equivalent permeability coefficient, and determining the size of a fractured rock mass representative volume unit; generating fracture rock mass representative volume unit numerical calculation models with different rotation angles and pore and fracture dual medium seepage; and carrying out a seepage numerical test to obtain an equivalent seepage coefficient, and calculating the seepage tensor of the fractured rock mass. Compared with the prior art, the method and the device consider the influence of rock mass seepage and fracture seepage on the fracture seepage tensor, are more in line with the water permeability of the fractured rock mass, and have higher precision and accuracy of the determined fracture rock mass.
Description
Technical Field
The application relates to a method for determining a fracture rock mass permeability tensor, in particular to a fracture rock mass permeability tensor determination method taking rock mass seepage and fracture seepage into consideration simultaneously. The method can be applied to the field of hydraulic and hydroelectric engineering, and can be used for determining the seepage tensor of the fractured rock mass in seepage analysis of side slopes and underground engineering.
Background
The fractured rock mass is a common rock mass type in engineering construction, is formed by cutting a natural complete rock through a discontinuous structural surface (such as joint or fracture), and is a dual medium structure consisting of rock masses and fractures. Because of the randomness of the distribution of the fractures in the fractured rock mass, the permeability characteristics of the fractured rock mass exhibit significant anisotropic properties, and thus the anisotropic permeability characteristics of the fractured rock mass are typically described by a permeability tensor in engineering analysis.
Regarding determination of fracture permeability tensors, there are two methods currently in common use, field tests and numerical simulations. Because of the complex and costly field test procedures, numerical simulation methods are commonly employed in prior studies to determine the osmotic tensor of a fractured rock mass. Considering that the water permeability of the fractured rock mass is mainly dominant by the water permeability of the fracture, and the water permeability of the rock mass is weak, the existing fracture rock mass permeability tensor determination methods all assume that the rock mass is impermeable and the fracture is permeable, only the influence of the water permeability of the fracture is considered when the fracture rock mass permeability tensor is determined, and the contribution and the influence of the water permeability of the rock mass on the fracture rock mass permeability tensor are ignored. However, as the permeability of the rock mass increases with increasing osmotic pressure, its contribution and impact on the fracture mass osmotic tensor also increases, especially at high osmotic pressure, the water permeability of the rock mass will be significantly enhanced, with a more pronounced impact on the fracture mass osmotic tensor.
However, there is currently no method in the art to determine the fracture rock mass permeability tensor that can take into account both the effects of rock mass seepage and rock mass fracture seepage on the permeability tensor.
Disclosure of Invention
In view of the foregoing, it is an object of the present application to provide a fractured rock mass permeability tensor determination method taking into account rock mass permeability and fracture permeability. The method considers the contribution and influence of rock mass seepage and fracture seepage to the fracture permeability tensor, accords with the water permeability of the fractured rock mass better, and makes up the defects of the existing method.
In order to achieve the above purpose, the present application adopts the following technical scheme: a method of determining a fracture rock mass permeability tensor taking into account rock mass and fracture seepage, comprising the steps of:
s1, performing on-site statistics and analysis on geometric distribution characteristics of joint cracks according to on-site outcrop of a fractured rock mass to obtain the geometric distribution characteristics of the number, length, dip angle, trend and spacing of the joint cracks;
s2, constructing a two-dimensional random fracture grid simplified model of the fractured rock mass by adopting a computer random simulation method according to the geometric distribution characteristics of the joint fracture of the fractured rock mass;
s3, based on the two-dimensional random fracture network simplified model of the fractured rock mass constructed in the step S2, considering seepage of the rock mass and seepage of the fracture, and generating fracture rock mass numerical calculation models with pore and fracture dual medium seepage of different sizes;
s4, performing a horizontal and vertical permeation test on the numerical calculation models of the fractured rock mass with different sizes generated in the step S3 to obtain equivalent permeation coefficients of the fractured rock mass with different sizes, and determining the size of the representing volume unit of the fractured rock mass;
s5, based on the obtained discrete element block model of the fractured rock mass, generating a numerical calculation model of the fractured rock mass representative volume unit with pores and dual medium seepage of the fractured rock mass at different rotation angles;
s6, performing seepage tests in different rotation angle directions on the numerical calculation models of the fracture rock mass representative volume units with different rotation angles generated in the step S5 to obtain equivalent seepage coefficients of the fracture rock mass representative volume units with different rotation angles, and calculating the seepage tensor of the fracture rock mass.
Further, the step S2 is a specific step of constructing a two-dimensional random fracture grid simplified model of the fractured rock according to the fracture geometrical distribution characteristics of the joint fracture of the fractured rock, and comprises the following steps:
s2.1, calculating the average length l of the joint fracture according to the joint fracture geometric characteristics counted on site:
wherein l is the average length of the crack, l i N is the number of cracks, which is the length of any crack;
s2.2, determining the dimension of a two-dimensional random network model of the fractured rock mass according to the average length of the fracture, namely:
wherein, I x And l y The horizontal length and the vertical length of the two-dimensional random network model are respectively;
s2.3, combining the pitch angle, the trend, the distance, the length and the number of joint cracks which are counted and analyzed on site, and adopting a computer random simulation method to generate an initial two-dimensional random crack network model of the fractured rock mass;
s2.4, simplifying the initial model to obtain a two-dimensional random fracture network simplified model of the fractured rock mass;
deleting any two cracks with the distance between the two cracks or the included angle smaller than a set threshold value to obtain a two-dimensional random crack network simplified model of the fractured rock mass, wherein the simplified formula is as follows:
wherein: del () is expressed as delete, min () is a function of minimum, d and α are the distance and angle between any two cracks, d threshold And alpha threshold The distance between the recommended cracks and the threshold value of the included angle are respectively 0.4m and 10 degrees.
Further, the step S3 considers the seepage of the rock mass and the seepage of the fracture, and the method for generating the fracture rock mass numerical calculation model with the pore and the fracture dual medium seepage of different sizes comprises the following steps:
s3.1, establishing a discrete element block model with the same size as the two-dimensional random fracture network simplified model of the fractured rock mass constructed in the step S2;
s3.2, carrying out grid segmentation on the discrete element block model to obtain a refined discrete element block model with pore seepage medium;
s3.3, cutting the thinned discrete element block model by utilizing the two-dimensional random fracture network simplified model constructed in the step S2 to generate a fracture rock mass discrete element block model with pores and fracture dual medium seepage;
s3.4, intercepting sub-models with different sizes from the center of a discrete element block model of the fractured rock mass with the dual-medium seepage of the pores and the fractures, and performing grid subdivision on the sub-models by considering the seepage of the rock mass and the seepage of the fractures to generate numerical calculation models of the fractured rock mass with the dual-medium seepage of the pores and the fractures with different sizes.
Further, in the step S4, the horizontal and vertical infiltration tests are performed on the generated numerical calculation models of the fractured rock mass with different sizes, so as to obtain the equivalent infiltration coefficients of the fractured rock mass with different sizes, and the method for determining the representative volume unit size of the fractured rock mass is as follows:
s4.1, applying a seepage test boundary condition, carrying out a horizontal and vertical seepage test on the numerical calculation models of the fractured rock mass with different sizes, monitoring the flow of the fractured rock mass with different sizes in the horizontal and vertical directions, simultaneously considering seepage of the rock mass and seepage of the fracture,
the seepage flow of water flow in the rock block pore is described by using a Darcy pore medium seepage flow model, and the calculation formula is as follows:
wherein:the flow rate of the unit section in the direction i, and k is the rock mass permeability coefficient; p is pore water pressure; ρ w Is the density of water; x is x j Coordinates in the j direction g j Is the gravity acceleration in the j direction; i, j represent X and Y directions, respectively, when 1 is taken, X direction, and when 2 is taken, Y direction;
the seepage flow of water flow in the cracks is described by adopting a smooth parallel plate seepage flow model, and the calculation formula is as follows:
wherein:for single wide flow in direction i ρ w Is the density of water, μ is the viscosity of water, φ is the head of the piezometric tube, φ=z+p/ρ w g, z is altitude, p is pore water pressure, g is gravitational acceleration, phi ,i A is the opening degree of the crack, which is the pressure water head gradient in the i-th direction;
because the seepage of the rock mass and the seepage of the cracks are considered at the same time, the seepage of the water flow passing through the fractured rock mass comprises the flow of the water flow passing through the rock mass and the flow passing through the cracks, and the calculation formula is as follows:
wherein: q (Q) i For the flow rate of the water flow in the direction of i of the fractured rock mass, Q i m The flow rate of the water flow in the direction of the rock mass i; q (Q) i f The flow rate of the water flow in the direction of the crack i; wherein Q is i m And Q i f Is determined by the following formula:
wherein A is the area of water flow passing through the rock mass, and B is the width of the crack;
s4.2, calculating equivalent permeability coefficients of the fractured rock masses with different sizes according to the obtained flow rates of the fractured rock masses with different sizes in the horizontal and vertical directions;
and S4.3, drawing a change curve of the equivalent permeability coefficient of the fractured rock mass along with the size of the fractured rock mass, and determining the size of the fractured rock mass representative volume unit according to the change trend.
Further, the step S5 is based on the obtained discrete element block model of the fractured rock mass, and the method for generating the numerical calculation model of the fractured rock mass representative volume unit with pores and dual medium seepage of the fractured rock mass with different rotation angles comprises the following steps:
s5.1, based on the discrete element block model of the fractured rock mass obtained in the step S3.3, sub-models with different rotation angles and the same size as the representative volume unit of the fractured rock mass are intercepted from the center of the model;
s5.2, taking the seepage of the rock mass and the seepage of the cracks into consideration, meshing the sub-model, and generating a numerical calculation model of the crack rock mass representative volume unit with pore and crack dual medium seepage at different rotation angles.
Further, the step S6 performs a seepage test on the numerical calculation model of the representative volume unit of the fractured rock mass under different rotation angles to obtain equivalent seepage coefficients of the fractured rock mass under different rotation angles, and the method for calculating the seepage tensor of the fractured rock mass comprises the following steps:
s6.1, applying a seepage test boundary condition, carrying out seepage tests in different rotation angle directions on fracture rock mass representative volume units with different rotation angles, monitoring flow rates with different rotation angles, and simultaneously considering seepage of the rock mass and seepage of the fracture;
s6.2, obtaining equivalent permeability coefficients of the fractured rock mass representative volume units with different rotation angles according to the flow of the different rotation angles;
s6.3, performing infiltration ellipse fitting according to the obtained equivalent permeability coefficients of the fracture rock mass representative volume units with different rotation angles, and calculating the infiltration tensor of the fracture rock mass.
Compared with the prior art, when the method and the device for determining the permeability tensor of the fractured rock mass, the influence of the seepage flow of the fracture on the permeability tensor of the rock mass is considered, the influence and the contribution of the seepage flow of the rock mass on the permeability tensor of the rock mass are considered, the permeability characteristics of the fractured rock mass are more met, and the calculated permeability tensor of the fractured rock mass is more accurate. In particular, compared with the existing method, the method has higher precision and accuracy of the determined permeability tensor of the fractured rock mass for the fractured rock mass with stronger water permeability.
Drawings
FIG. 1 is a flow chart of a method of determining a fracture rock mass permeability tensor according to the present application;
FIG. 2 is a schematic diagram of a simplified model of a two-dimensional stochastic fracture network of a fractured rock mass generated by an embodiment of the present application;
FIG. 3 is a schematic diagram of a rasterized segmentation of a discrete primitive block model in accordance with an embodiment of the present application;
FIG. 4 is a schematic diagram of a discrete element block model of a fractured rock mass produced by an embodiment of the present application;
FIG. 5 is a schematic diagram of numerical calculation models of fractured rock mass with dual pore and fracture medium seepage of different sizes generated by an embodiment of the present application;
FIG. 6 is a schematic diagram of a pore bleed numerical model and a fracture bleed numerical model according to an embodiment of the present application;
FIG. 7A is a schematic illustration of the horizontal penetration test boundary conditions of an embodiment of the present application;
FIG. 7B is a schematic illustration of the vertical penetration test boundary conditions of an embodiment of the present application;
FIG. 8 is a graph showing the equivalent permeability coefficient of a fractured rock mass according to the embodiment of the present application according to the size of a sub-model;
FIG. 9 is a schematic diagram of a calculation model of dual medium seepage values of a fractured rock mass representative volume element pore and fracture at different rotation angles generated by an embodiment of the present application;
FIG. 10 is a schematic diagram of the boundary conditions of the permeation test at different rotation angles according to the embodiment of the present application;
fig. 11 is a schematic diagram of a permeation ellipse.
Detailed Description
The present application is further illustrated in the accompanying drawings and detailed description which are to be understood as being merely illustrative of the application and not limiting of its scope, and various modifications of the application, which are equivalent to those skilled in the art upon reading the application, will fall within the scope of the application as defined in the appended claims.
As shown in fig. 1, the method for determining the fracture rock mass seepage tensor by considering rock mass seepage and fracture seepage disclosed by the application comprises the following steps:
s1: and carrying out on-site statistics and analysis on the geometric distribution characteristics of the joint cracks according to the on-site outcrop of the fractured rock mass to obtain the geometric distribution characteristics of the joint cracks, such as the number, the length, the dip angle, the trend, the spacing and the like.
S2: according to the geometric distribution characteristics of joint cracks of the fractured rock mass, a computer random simulation method is adopted to construct a two-dimensional random fracture grid simplified model of the fractured rock mass, and the specific steps are as follows:
s2.1: calculating the average length l of the joint fracture according to the joint fracture geometric characteristics counted on site:
wherein l is the average length of the crack, l i N is the number of cracks, which is the length of any crack;
s2.2: according to the average length of the fracture, determining the size of a two-dimensional random network model of the fractured rock mass, wherein the formula is as follows:
wherein, I x And l y The horizontal length and the vertical length of the two-dimensional random network model are respectively;
s2.3: combining geometrical characteristics such as pitch angle, trend, interval, length, quantity and the like of joint cracks subjected to field statistics and analysis, and adopting a computer random simulation method to generate an initial two-dimensional random crack network model of the fractured rock mass, wherein the initial two-dimensional random crack network model is shown in FIG. 2;
s2.4: and simplifying the initial model to obtain a two-dimensional random fracture network simplified model of the fractured rock mass.
Because the traditional fracture rock mass penetration tensor determination method assumes that the rock mass is watertight and only the fractures in the rock mass are pervious, mesh subdivision is not performed on the rock mass when a fracture rock mass numerical calculation model is established. However, in the method, not only the fracture seepage in the rock mass is considered, but also the seepage of the rock mass is considered when the seepage tensor of the fractured rock mass is determined, so that the method needs to mesh the rock mass for carrying out the seepage calculation of the rock mass. In order to avoid abnormal grids generated during the grid subdivision of the rock mass so as to influence the numerical calculation result, the application simplifies the generated initial two-dimensional random fracture network model of the fractured rock mass.
As shown in fig. 2, the method simplifies the initial two-dimensional random fracture network model of the fractured rock mass generated in the step S2.3 according to the distance and the included angle between the fractures, and when the distance between any two fractures or the included angle between any two fractures is smaller than a set threshold value, the fracture with smaller length is deleted, and after the simplification, the two-dimensional random fracture network simplified model of the fractured rock mass is obtained, wherein the simplified formula is as follows:
wherein: del () is expressed as delete, min () is a function of minimum, d and α are the distance and angle between any two cracks, d threshold And alpha threshold The distance between the recommended cracks and the threshold value of the included angle are respectively 0.4m and 10 degrees.
S3: based on the two-dimensional random fracture network simplified model of the fractured rock mass constructed in the step S2, considering seepage of the rock mass and seepage of the rock mass fracture, generating fracture rock mass numerical calculation models with pore and fracture dual medium seepage of different sizes, wherein the specific steps are as follows:
s3.1: and (3) establishing a discrete element block model with the same size as the two-dimensional random fracture network simplified model of the fractured rock mass constructed in the step (S2).
S3.2: and carrying out grid segmentation on the generated discrete element block model to obtain a refined discrete element block model with a pore seepage medium.
As shown in fig. 3, the discrete element block model established in the step S3.1 is subjected to equidistant grid division to obtain a refined discrete element block model with pore seepage medium.
S3.3: and (3) cutting the thinned discrete element block model with the pore seepage medium by using the two-dimensional random fracture network simplified model of the fractured rock mass generated in the step (S2) to generate the discrete element block model of the fractured rock mass with the pore and fracture dual medium seepage.
As shown in fig. 4, the refined discrete element block model with pore seepage medium generated in step S3.2 is cut by using the two-dimensional random fracture network simplified model of the fractured rock mass generated in step S2.4, so as to generate the discrete element block model of the fractured rock mass with pore and fracture dual medium seepage.
When the two-dimensional random fracture network simplified model is utilized to cut the thinned discrete element block model, if the fracture does not cut through a thinned small block, the fracture can be prolonged to the boundary of the small block, and the fracture is ensured to cut through the small block. From this, it is known that the length of the fracture will increase after the thinned block model is cut by using the two-dimensional random fracture network simplified model. Therefore, in order to ensure that the subdivided block model does not affect the calculation result, the pitch of the grids needs to be repeatedly adjusted and the step S3.3 is repeatedly executed until the lengths of the cracks in the discrete element block model of the fractured rock mass after the grids are thinned meet the following conditions:
wherein, I i ' is the length of any crack after grating, m is the number of cracks after grating;
l i for the length of any one slit, n is the number of slits.
S3.4: and (3) intercepting sub-models with different sizes from the center of the split rock mass discrete element block model with the pore and split dual medium seepage generated in the step (S3.3), and simultaneously carrying out grid subdivision on the sub-model rock mass by considering the seepage of the rock mass in the split rock mass and the split seepage of the rock mass to generate split rock mass numerical calculation models with different sizes and the pore and split dual medium seepage.
The existing method only considers the water permeability of the fracture and does not consider the water permeability of the rock when determining the fracture rock mass permeability tensor, namely, the rock mass is assumed to be impermeable, so that grid subdivision is not needed for the rock mass when establishing a fracture rock mass seepage numerical calculation model. In the application, when determining the seepage tensor of the fractured rock mass, not only the seepage of the rock mass fracture in the fractured rock mass, but also the seepage of the rock mass in the fractured rock mass are considered, so the application performs grid subdivision on the rock mass and establishes a void and fracture dual medium seepage numerical calculation model of the fractured rock mass. In the model, assuming that the seepage type of the water flow in the rock mass is pore seepage and the seepage type of the water flow in the fracture is fracture seepage, the application simultaneously considers the flow of the water flow in the rock mass and the flow of the water flow in the fracture.
As shown in fig. 5, according to the application, for the split rock mass discrete element block model with the pore and crack dual medium seepage established in the step S3.3, submodels with different sizes are intercepted from the center of the model, and mesh subdivision is carried out on the submodels, so as to obtain the pore and crack dual medium seepage numerical calculation model of the split rock mass with different sizes.
When the calculation is performed by adopting a pore and crack dual medium seepage numerical calculation model, in order to consider the water flow exchange and the water flow continuity between rock mass seepage and rock mass crack seepage, the crack seepage calculation is performed firstly, then the calculation result of the crack seepage is used as the boundary condition of the pore seepage, and the pore seepage calculation is performed; the pore seepage numerical model, the fracture seepage numerical model and the pore and fracture dual medium seepage numerical calculation model which simultaneously consider rock mass seepage and rock mass fracture seepage are shown in fig. 6.
S4: performing a horizontal and vertical permeation test on the numerical calculation models of the fractured rock mass with different sizes generated in the step S3 to obtain equivalent permeation coefficients of the fractured rock mass with different sizes, and determining the size of the representative volume unit of the fractured rock mass, wherein the method comprises the following specific steps of:
s4.1: applying a seepage test boundary condition, carrying out a horizontal and vertical seepage test on the rock mass with different sizes of cracks, monitoring the horizontal and vertical flow of the rock mass with different sizes of cracks, and simultaneously considering seepage of the rock mass and seepage of the rock mass cracks;
when the seepage test is carried out, the seepage of water flow in the rock and the seepage of water flow in the cracks are considered, wherein the seepage of water flow in the pores of the rock is described by using a Darcy pore medium seepage model, and the calculation formula is as follows:
wherein:the flow rate of the unit section in the direction i, and k is the rock mass permeability coefficient; p is pore water pressure; ρ w Is the density of water; x is x j Coordinates in the j direction g j Is the gravity acceleration in the j direction; i, j represent the X and Y directions, respectively, when it takes 1, the X direction, and when it takes 2, the Y direction.
The seepage flow of water flow in the cracks is described by adopting a smooth parallel plate seepage flow model, and the calculation formula is as follows:
wherein:for single wide flow in direction i ρ w Is the density of water, μ is the viscosity of water, φ is the head of the piezometric tube, φ=z+p/ρ w g, z is altitude, p is pore water pressure, g is gravitational acceleration, phi ,i The pressure head gradient in the i-th direction is shown, and a is the opening of the crack.
Because the seepage of the rock mass and the seepage of the cracks are considered at the same time, the seepage of the water flow passing through the fractured rock mass comprises the flow of the water flow passing through the rock mass and the flow passing through the cracks, and the calculation formula is as follows:
Q i ＝Q i m +Q i f (7)
wherein: q (Q) i For the flow rate of the water flow in the direction of i of the fractured rock mass, Q i m The flow rate of the water flow in the direction of the rock mass i; q (Q) i f The flow rate of the water flow in the direction of the crack i; wherein Q is i m And Q i f Is determined by the following formula:
wherein A is the area of water flow passing through the rock mass, and B is the width of the crack.
According to the application, seepage boundary conditions are applied to numerical calculation models of fracture rock masses with different sizes, so that seepage tests in horizontal and vertical directions are respectively carried out, and flow rates in the horizontal and vertical directions of the models are monitored in the tests; as shown in fig. 7A, for the horizontal permeation test, a constant water head boundary is applied on the left and right sides of the horizontal, the water head on the left side is h1, the water head on the right side is h2, the water head boundary with linear change on the upper and lower sides is provided, and the flow rates of the left and right sides of the monitoring model in the test are respectively Q xL And Q xR The flow rates of the upper and lower streams are respectively Q yT And Q yB The method comprises the steps of carrying out a first treatment on the surface of the As shown in fig. 7B, for the vertical direction permeation test, constant water head boundaries are applied to the upper and lower ends, the upper water head is h2, the lower water head is h1, the left and right sides are water head boundaries which change linearly, and the flow rates of the upper and lower ends of the monitoring model are respectively Q in the test yT And Q yB The flow rates of the left and right flows are respectively Q xL And Q xR 。
S4.2: and calculating the equivalent permeability coefficients of the samples with different sizes according to the obtained flow rates of the fractured rock masses with different sizes in the horizontal and vertical directions.
For a horizontal direction penetration test, the equivalent penetration coefficient calculation formula of the fractured rock mass with different sizes is as follows:
wherein k is xx And k xy Equivalent permeability coefficients in horizontal and vertical directions of the fracture rock mass numerical calculation model in horizontal direction permeability test are respectively l x And l y Respectively calculating the horizontal length and the vertical length of the model for the numerical value of the fractured rock mass, and Q xx And Q xy The horizontal flow and the vertical flow of the numerical calculation model of the fractured rock mass during the horizontal permeability test are respectively calculated by, for exampleThe following formula is calculated:
in which Q xL And Q xR Respectively the flow rate of the left side and the right side of the numerical calculation model of the fractured rock mass during the horizontal permeability test, Q yT And Q yB And respectively calculating the flow of the upper side and the lower side of the model for the numerical value of the fractured rock mass with different sizes in the horizontal direction penetration test.
For a vertical direction penetration test, the equivalent penetration coefficient calculation formula of the fractured rock mass with different sizes is as follows:
wherein k is yy And k yx Equivalent permeability coefficients in the vertical direction and the horizontal direction of the fracture rock mass numerical calculation model in the vertical direction permeability test are respectively Q yy And Q yx And respectively calculating the flow in the vertical direction and the horizontal direction of the fracture rock mass numerical calculation model in the vertical direction penetration test, wherein the flow is calculated by the following formula:
further, k is calculated from the formula (8) and the formula (10) xy And k yx The two may not be equal, so the fracture mass permeability tensor is assumed to be a symmetrical second order tensor,
wherein k' xy And k' yx Elements of the fracture rock mass permeation tensor diagonal, respectively;
s4.3: and drawing a change curve of equivalent permeability coefficients of the fractured rock bodies with different sizes along with the sizes of the fractured rock bodies, and determining the sizes of the representing volume units of the fractured rock bodies according to the change trend.
As shown in FIG. 8, the equivalent permeability coefficient k of different sizes of fractured rock mass is plotted xx ，k' xy ，k yy As the change curve of the size of the fractured rock mass, the equivalent permeability coefficient k of the fractured rock mass can be seen according to the change trend xx ，k' xy ，k yy When the size of the fractured rock mass gradually tends to a stable value along with the increase of the size of the fractured rock mass, the size of the fractured rock mass is the representative volume unit size l REV 。
S5: based on the obtained discrete element block model of the fractured rock mass, and considering seepage of the rock mass and seepage of the fracture, generating a pore and fracture dual medium seepage numerical calculation model of the fractured rock mass representative volume unit with different rotation angles. The method comprises the following specific steps:
s5.1: based on the fracture rock mass discrete element block model obtained in the step S3.3, sub-models representing the sizes of the units with different rotation angles are intercepted from the center of the model;
as shown in fig. 9, based on the fractured rock mass discrete element block model obtained in step S3.3, sub-models representing the sizes of the volume units with different rotation angles are respectively cut from the center of the model, and sub-models representing the sizes of the volume units with different rotation angles are obtained.
S5.2: taking the seepage of the rock mass and the seepage of the cracks into consideration, carrying out grid subdivision on the sub-model, and generating a pore and crack dual medium seepage numerical calculation model of the crack rock mass representative volume unit with different rotation angles;
and (3) meshing the submodels representing the sizes of the volume units with different rotation angles obtained in the step (S5.1) to generate a pore and crack dual medium seepage numerical calculation model of the fracture rock mass representing the volume unit sample with different rotation angles.
S6: and carrying out seepage tests under different rotation angles on the fractured rock mass representing volume units with different rotation angles to obtain equivalent seepage coefficients of the fractured rock mass representing volume units with different rotation angles, and calculating the seepage tensor of the fractured rock mass.
The method comprises the following specific steps:
s6.1: and applying a seepage test boundary condition, performing a seepage test on the fracture rock mass representative volume units with different rotation angles, monitoring the flow of the different rotation angles, and simultaneously considering the seepage of the rock mass and the seepage of the fracture.
The application develops seepage tests on the representative volume units of the fractured rock mass with different rotation angles, and monitors the flow Q of the fractured rock mass with different rotation angles alpha in the tests α As shown in fig. 10, for the penetration test of different rotation angles, the water heads on both sides in the α direction are h1 and h2, respectively, and the boundaries on both sides perpendicular to the α direction are watertight boundaries.
S6.2: obtaining equivalent permeability coefficients of the fractured rock mass representative volume units with different rotation angles according to the flow of different rotation angles;
for penetration tests at different rotation angles, the fractured rock mass represents the equivalent permeability coefficient k of the volume element α The calculation formula is as follows:
wherein k is α Equivalent permeability coefficient, l, of a sample representing volume elements for fractured rock masses of different rotation angles alpha REV Representing the size length of the volume unit for the fractured rock mass, h 1 And h 2 A head applied to the bottom and upper part respectively;
Q α for the flow rate in the penetration test of different rotation angles alpha, the flow rate is calculated by the following formula:
in which Q α1 And Q α2 Respectively the flow rates at two sides of the alpha direction of the sample during the penetration test at different rotation angles;
s6.3: and performing infiltration ellipse fitting according to the obtained equivalent infiltration coefficients of the fracture rock mass representative volume units with different rotation angles, and calculating the infiltration tensor of the fracture rock mass.
As shown in FIG. 11, the equivalent permeability coefficient k of the fractured rock mass according to the obtained different rotation angles alpha α ToDrawing a polar coordinate scatter diagram with a polar axis alpha as a polar angle, then carrying out ellipse fitting on the scatter diagram to obtain a semi-minor axis and a semi-major axis of a penetration ellipse, and further obtaining the maximum equivalent penetration coefficient k of the fractured rock mass 1 And a minimum equivalent permeability coefficient k 2 ；
Still further, the permeability tensor of the fractured rock mass may be calculated as follows:
in the formula, k xx ，k″ yy ，k″ xy ，k″ yx Seepage coefficients in xx, yy, xy and yx directions respectively; θ is the angle between the positive x-axis and the major axis of the permeation ellipse; k (k) 1 The maximum equivalent permeability coefficient of the fractured rock mass; k (k) 2 Is the minimum equivalent permeability coefficient of the fractured rock mass.
Further, the permeability tensor K of the fractured rock mass is:
to check whether the determined permeability tensor K can characterize the seepage anisotropy of the fractured rock mass, the equivalent permeability coefficient K of the fractured rock mass samples with different rotation angles is calculated α Permeability coefficient k 'at different rotation angle from the fitted permeate ellipse' α Is determined by the mean square error (RMS) of the equation:
wherein N is the number of different rotation angles, k' α To fit toPermeation coefficients of permeation ellipses at different rotation angles; when RMS<And at 0.2, the penetration ellipse fitting degree is high, and the obtained penetration tensor can represent the penetration anisotropy of the fractured rock mass.
Compared with the prior art, the method for determining the seepage tensor of the fractured rock mass not only considers the influence of seepage of the fracture on the seepage tensor of the rock mass, but also considers the influence and contribution of seepage of the rock mass on the seepage tensor of the rock mass, so that the accuracy and the precision of the seepage tensor of the fractured rock mass determined by the method are higher.
Finally, it should be noted that: the embodiments described above are only for illustrating the technical solution of the present application, and are not limiting; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the application.
Claims (4)
1. A fracture rock mass permeability tensor determination method taking rock mass seepage and fracture seepage into consideration is characterized in that: it comprises the following steps:
s1, performing on-site statistics and analysis on geometric distribution characteristics of joint cracks according to on-site outcrop of a fractured rock mass to obtain the geometric distribution characteristics of the number, length, dip angle, trend and spacing of the joint cracks;
s2, constructing a two-dimensional random fracture network simplified model of the fractured rock mass by adopting a computer random simulation method according to the geometric distribution characteristics of the joint fracture of the fractured rock mass;
s2.1, calculating the average length l of the joint fracture according to the joint fracture geometric characteristics counted on site:
wherein l is the average length of the crack, l i Is the length of any crack, n isThe number of fissures;
s2.2, determining the dimension of a two-dimensional random network model of the fractured rock mass according to the average length of the fracture, namely:
wherein, I x And l y The horizontal length and the vertical length of the two-dimensional random network model are respectively;
s2.3, combining the pitch angle, the trend, the distance, the length and the number of joint cracks which are counted and analyzed on site, and adopting a computer random simulation method to generate an initial two-dimensional random crack network model of the fractured rock mass;
s2.4, simplifying the initial model to obtain a two-dimensional random fracture network simplified model of the fractured rock mass;
deleting any two cracks with the distance between the two cracks or the included angle smaller than a set threshold value to obtain a two-dimensional random crack network simplified model of the fractured rock mass, wherein the simplified formula is as follows:
wherein: del () is expressed as delete, min () is a function of minimum, d and α are the distance and angle between any two cracks, d threshold And alpha threshold The distance between the recommended cracks and the threshold value of the included angle are respectively 0.4m and 10 degrees;
s3, based on the two-dimensional random fracture network simplified model of the fractured rock mass constructed in the step S2, considering seepage of the rock mass and seepage of the fracture, and generating fracture rock mass numerical calculation models with pore and fracture dual medium seepage of different sizes;
s3.1, establishing a discrete element block model with the same size as the two-dimensional random fracture network simplified model of the fractured rock mass constructed in the step S2;
s3.2, carrying out grid segmentation on the discrete element block model to obtain a refined discrete element block model with pore seepage medium;
s3.3, cutting the thinned discrete element block model by utilizing the two-dimensional random fracture network simplified model constructed in the step S2 to generate a fracture rock mass discrete element block model with pores and fracture dual medium seepage;
s3.4, intercepting sub-models with different sizes from the center of a discrete element block model of the fractured rock mass with the dual-medium seepage of the pores and the fractures, and performing grid subdivision on the sub-models to generate numerical calculation models of the fractured rock mass with the dual-medium seepage of the pores and the fractures with different sizes by considering the seepage of the rock mass and the seepage of the fractures;
s4, performing a horizontal and vertical permeation test on the numerical calculation models of the fractured rock mass with different sizes generated in the step S3 to obtain equivalent permeation coefficients of the fractured rock mass with different sizes, and determining the size of the representing volume unit of the fractured rock mass;
s5, based on the obtained discrete element block model of the fractured rock mass, generating a numerical calculation model of the fractured rock mass representative volume unit with pores and dual medium seepage of the fractured rock mass at different rotation angles;
s6, performing seepage tests in different rotation angle directions on the numerical calculation models of the fracture rock mass representative volume units with different rotation angles generated in the step S5 to obtain equivalent seepage coefficients of the fracture rock mass representative volume units with different rotation angles, and calculating the seepage tensor of the fracture rock mass.
2. The method for determining the permeability tensor of the fractured rock mass considering the rock mass seepage and the fracture seepage according to claim 1, wherein the step S4 is characterized in that the generated numerical calculation models of the fractured rock mass with different sizes are subjected to the horizontal and vertical permeability tests to obtain the equivalent permeability coefficients of the fractured rock mass with different sizes, and the method for determining the representative volume unit size of the fractured rock mass is as follows:
s4.1, applying a seepage test boundary condition, carrying out a horizontal and vertical seepage test on the numerical calculation models of the fractured rock mass with different sizes, monitoring the flow of the fractured rock mass with different sizes in the horizontal and vertical directions, simultaneously considering seepage of the rock mass and seepage of the fracture,
the seepage flow of water flow in the rock block pore is described by using a Darcy pore medium seepage flow model, and the calculation formula is as follows:
wherein:the flow rate of the unit section in the direction i, and k is the rock mass permeability coefficient; p is pore water pressure; ρ w Is the density of water; x is x j Coordinates in the j direction g j Is the gravity acceleration in the j direction; i, j represent X and Y directions, respectively, when 1 is taken, X direction, and when 2 is taken, Y direction;
the seepage flow of water flow in the cracks is described by adopting a smooth parallel plate seepage flow model, and the calculation formula is as follows:
wherein:for single wide flow in direction i ρ w Is the density of water, μ is the viscosity of water, φ is the head of the piezometric tube, φ=z+p/ρ w g, z is altitude, p is pore water pressure, g is gravitational acceleration, phi ,i A is the opening degree of the crack, which is the pressure water head gradient in the i-th direction;
because the seepage of the rock mass and the seepage of the cracks are considered at the same time, the seepage of the water flow passing through the fractured rock mass comprises the flow of the water flow passing through the rock mass and the flow passing through the cracks, and the calculation formula is as follows:
Q i ＝Q i m +Q i f (7)
wherein: q (Q) i For the flow rate of the water flow in the direction of i of the fractured rock mass, Q i m The flow rate of the water flow in the direction of the rock mass i; q (Q) i f The flow rate of the water flow in the direction of the crack i; wherein Q is i m And Q i f Is determined by the following formula:
wherein A is the area of water flow passing through the rock mass, and B is the width of the crack;
s4.2, calculating equivalent permeability coefficients of the fractured rock masses with different sizes according to the obtained flow rates of the fractured rock masses with different sizes in the horizontal and vertical directions;
and S4.3, drawing a change curve of the equivalent permeability coefficient of the fractured rock mass along with the size of the fractured rock mass, and determining the size of the fractured rock mass representative volume unit according to the change trend.
3. The method for determining the permeability tensor of the fractured rock mass considering the rock mass seepage and the fracture seepage according to claim 1, wherein the step S5 is based on the obtained discrete element block model of the fractured rock mass, and the method for generating the numerical calculation model of the representative volume unit of the fractured rock mass with the pore and the fracture dual medium seepage at different rotation angles is as follows:
s5.1, based on the discrete element block model of the fractured rock mass obtained in the step S3.3, sub-models with different rotation angles and the same size as the representative volume unit of the fractured rock mass are intercepted from the center of the model;
s5.2, taking the seepage of the rock mass and the seepage of the cracks into consideration, meshing the sub-model, and generating a numerical calculation model of the crack rock mass representative volume unit with pore and crack dual medium seepage at different rotation angles.
4. The method for determining the permeability tensor of the fractured rock mass considering the rock mass seepage and the fracture seepage according to claim 1, wherein the step S6 is to perform the seepage test on the numerical calculation model of the representative volume unit of the fractured rock mass under different rotation angles to obtain the equivalent permeability coefficients of the fractured rock mass under different rotation angles, and the method for calculating the permeability tensor of the fractured rock mass is as follows:
s6.1, applying a seepage test boundary condition, carrying out seepage tests in different rotation angle directions on fracture rock mass representative volume units with different rotation angles, monitoring flow rates with different rotation angles, and simultaneously considering seepage of the rock mass and seepage of the fracture;
s6.2, obtaining equivalent permeability coefficients of the fractured rock mass representative volume units with different rotation angles according to the flow of the different rotation angles;
s6.3, performing infiltration ellipse fitting according to the obtained equivalent permeability coefficients of the fracture rock mass representative volume units with different rotation angles, and calculating the infiltration tensor of the fracture rock mass.
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