A method for predicting the transverse permeability coefficient of a geotextile waterproof layer for a mountain tunnel

Abstract

The application discloses a kind of mountain tunnel waterproof layer geotextile transverse permeability coefficient prediction method, comprising the following steps: using thickness coefficient to correct the solid volume fraction of geotextile, using fiber orientation coefficient to correct the initial resistance of fluid suffered by fiber and the initial length of fiber, to obtain the total resistance of fluid suffered by fiber, then calculate permeability coefficient based on Darcy's law and use thickness coefficient to correct transverse permeability coefficient resistance model;Using thickness coefficient to correct maximum pore diameter, cross-sectional area, and simultaneously establishing the empirical formula of fractal dimension according to existing data, and then establishing the fractal model of corrected transverse permeability coefficient;The product of the area density and thickness of geotextile is used as a boundary index, and the two models are combined into a comprehensive model.The model can consider the influence of random distribution of fibers and external load on the transverse permeation of geotextile, and is suitable for predicting the transverse permeability coefficient of geotextile with different thickness and area density, with high prediction accuracy and strong applicability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel waterproofing, and particularly relates to a method for predicting the transverse permeability coefficient of geotextile in a mountain tunnel waterproof layer. BACKGROUND

[0002] In mountain tunnel engineering, a composite lining form combining primary support and secondary lining is often used. A composite waterproof layer is used between the primary support and the secondary lining to achieve waterproofing and drainage of the tunnel lining. The waterproof board in the composite waterproof layer blocks the seepage water, preventing the seepage water from entering the secondary lining. The fibrous fabric geotextile in the composite waterproof layer guides the seepage water to the drainage system at the tunnel arch foot. With the progress of technology, composite geomembrane has become a feasible solution to replace the traditional composite waterproof layer. The fibrous fabric of the composite geomembrane is closely combined with the waterproof membrane layer, and the fibrous fabric also plays a role in transverse permeation. The waterproof membrane layer replaces the traditional and cumbersome waterproof board. Whether it is a traditional geotextile or a composite geomembrane, it belongs to geotextile. The transverse permeability performance of geotextile has a key influence on the waterproofing and drainage of the tunnel structure. The better the transverse permeability performance, the less likely the seepage water is to accumulate locally, and the smaller the waterproof pressure of the waterproof board.

[0003] Currently, there are reports on the calculation model of the transverse permeability coefficient of fibrous geotextile. The calculation model mainly includes a resistance model, a fractal model and a random network model. The resistance model combines the fluid resistance theory in porous media and the fibrous structure theory of geotextile to derive a formula for calculating the transverse permeability coefficient. The fractal model uses image processing technology to obtain relevant parameters and applies capillary fluid theory to establish a relevant formula. The random network model derives a formula for calculating the transverse permeability coefficient based on image processing technology and the probability distribution theory of pore distribution. However, the resistance model is only applicable to high-weight and large-thickness geotextile materials. The model has the problems of over-simplification of the arrangement and distribution of fibers in the geotextile, insufficient prediction accuracy due to the inability to consider the random angle distribution of fibers, and high calculation difficulty due to the lack of simplification of the arrangement and distribution of fibers. The fractal model and the random network model both need to obtain the fractal dimension and the maximum pore diameter based on image acquisition and processing technology. The two models have high requirements for instruments and equipment, a complicated parameter acquisition process, a long time consumption and insufficient prediction accuracy. In addition, the geotextile in the mountain tunnel is often under the pressure field applied by the secondary lining. The above three models cannot consider the influence of the applied load on the transverse permeability coefficient of the geotextile. The applicability of the three models to the new type of geotextile, i.e., the composite geomembrane, is also questionable. Therefore, it is necessary to propose a new type of transverse permeability coefficient prediction model and method that can consider the random distribution of fibers, the application of external load and is suitable for geotextiles with different thicknesses and areal densities. SUMMARY

[0004] To solve the above technical problems, the application provides a mountain tunnel waterproof layer geotextile transverse permeability coefficient prediction method, which can consider the influence of fiber random distribution and external load on the transverse permeability of geotextile, and is applicable to the transverse permeability coefficient prediction of geotextile with different thickness and surface density.

[0005] The application combines the transverse permeability coefficient resistance model and the fractal model, and takes the inherent parameter value of the geotextile as the demarcation point of the two models, so as to overcome the limitation that the prior art cannot be simultaneously applicable to geotextiles with large and small porosities / thicknesses. For the resistance model, it is assumed that the initial orientation of the fiber is divided into fiber inclination in the plane parallel to the fluid direction and overall inclination of the fiber with the plane relative to the plane of the geotextile, and the normal random distribution is considered for the inclination in the two directions, so as to convert the three-dimensional calculation into pseudo-three-dimensional calculation, and thus the correction considering the fiber random distribution is realized for the fluid resistance and the fiber length. For the fractal model, the calculation formula of the area fractal dimension, the bending fractal dimension and the maximum pore diameter is derived by taking the inherent parameter of the geotextile as a variable, so as to avoid the limitation that the prior fractal model needs to rely on high-precision instruments to measure the related parameters, and the calculation and prediction of the transverse permeability coefficient can be directly performed. Finally, the thickness coefficient is proposed to consider the influence of the external pressure load on the thickness change of the geotextile, and then the influence of the external pressure load on the solid volume fraction, the maximum pore diameter and the final transverse permeability coefficient is considered, so that the prediction model is applicable to the actual working condition that the geotextile in the tunnel composite waterproof layer is often in a pressure working state in engineering.

[0006] To achieve the above object, the application adopts the following technical scheme:

[0007] A mountain tunnel waterproof layer geotextile transverse permeability coefficient prediction method, comprising the following steps:

[0008] S1, establishing a general expression of the thickness coefficient of the geotextile about the external load

[0009] The ratio of the thickness of the geotextile after the load to the initial thickness of the geotextile is defined as the thickness coefficient;

[0010] The actual thickness change of the geotextile under the action of different normal external loads is measured to obtain a series of thickness coefficient data corresponding to the load of the geotextile, and the thickness coefficient K is fitted by using the regression analysis method T The general expression about the external load;

[0011] S2, establishing a transverse permeability coefficient prediction model considering the action of the normal external load based on the resistance theory

[0012] The thickness coefficient K is adopted TAfter the solid volume fraction of the geotextile is corrected, the initial resistance of any fiber in the plane parallel to the water flow direction per unit length in the water flow direction is obtained according to the Russell micro-unit theory;

[0013] The initial resistance is corrected by using the fiber orientation coefficient to obtain the actual fluid resistance of any fiber in the plane per unit length in the water flow direction;

[0014] The initial length of the fiber is corrected by using the fiber orientation coefficient to obtain the calculated length of the fiber in the water flow direction;

[0015] After the total fluid resistance of the fiber in the geotextile is calculated according to the actual fluid resistance of the fiber and the calculated length of the fiber, the transverse permeability coefficient based on the resistance theory is obtained according to Darcy's law, and the thickness coefficient K T The transverse permeability coefficient is corrected to obtain a transverse permeability coefficient prediction model based on the resistance theory considering the effect of external load, denoted as K1 model;

[0016] The fiber orientation coefficient is determined according to the random inclined distribution characteristics of the fiber in the plane and the random inclined distribution characteristics of the plane relative to the plane of the geotextile;

[0017] S3, a transverse permeability coefficient prediction model considering the effect of external load is established based on fractal theory

[0018] According to the microscopic test data of the geotextile in the prior art, an empirical formula of the fractal dimension about the product of the surface density and the thickness of the geotextile is established;

[0019] The thickness coefficient K T The transverse permeability coefficient calculation model based on fractal theory when the fibers are uniformly distributed on the surface of the geotextile is corrected to obtain the maximum pore diameter of the geotextile and the cross-sectional area of the geotextile;

[0020] According to the fractal dimension, the maximum pore diameter and the cross-sectional area of the geotextile, a transverse permeability coefficient prediction model based on fractal theory considering the effect of external load is obtained, denoted as K2 model;

[0021] S4, a comprehensive prediction model of the corrected transverse permeability coefficient of the geotextile is established

[0022] The K1 model and the K2 model are combined to obtain a comprehensive prediction model of the corrected transverse permeability coefficient of the geotextile:

[0023]

[0024] In the formula, K is the transverse permeability coefficient; K1 is the transverse permeability coefficient based on the resistance theory; K2 is the transverse permeability coefficient based on the resistance theory; μ gis the surface density of geotextile; T g is the thickness of geotextile; [μ g T g ] is the limit value of the product of surface density and thickness of geotextile.

[0025] It should be noted that in S1, the thickness coefficient K T The general expression of external load is fitted by regression analysis according to formula (1.1):

[0026]

[0027] In the formula, K T is the thickness coefficient of geotextile; G is the normal external load; a, t, y are all fitting parameters, which are linearly related to the surface density of geotextile.

[0028] It should be noted that in S2, the thickness coefficient K T The solid volume fraction of geotextile is corrected according to formula (2.1):

[0029]

[0030] In the formula, Ф is the solid volume fraction of geotextile considering the effect of normal external load; μ g is the surface density of geotextile; ρ f is the fiber density; T g is the thickness of geotextile.

[0031] It should be noted that in S2, the initial fluid resistance per unit length of any fiber in any plane parallel to the flow direction in the flow direction is determined according to formula (2.2):

[0032]

[0033] In the formula, f'(α i ) is the initial fluid resistance per unit length of any fiber in any plane parallel to the flow direction in the flow direction; μ is the viscosity coefficient of fluid, v is the average flow velocity of water flow on the surface of geotextile; T is a function related to the solid volume fraction Ф; α i is the orientation angle of the i-th fiber in the plane, which is the angle between the i-th fiber and the flow direction, α i ∈ [0°, 180°];

[0034] Among them,

[0035] It should be noted that in S2, the actual fluid resistance per unit length of any fiber in any plane parallel to the flow direction in the flow direction is determined according to formula (2.3):

[0036]

[0037] where f(α i ) is the actual fluid resistance per unit length of any fiber in any plane parallel to the fluid direction in the flow direction; P(α i ) is the fiber orientation factor (indicating the random tilt distribution characteristics of the fiber in the plane);

[0038] where P(α i ) is determined according to the random tilt distribution characteristics of the fiber in the plane by the following formula:

[0039]

[0040] where h is the mathematical expectation of the normal distribution function, σ is the variance of the normal distribution function, and C is a constant, and the recommended value is 1.03.

[0041] It should be noted that in S2, the calculated length of any fiber in any plane parallel to the flow in the flow direction is as formula (2.4):

[0042] l ij = l0·sinθ j ·P(θ j )(2.4)

[0043] where l ij is the calculated length of any fiber in any plane parallel to the flow in the fluid direction; l0 is the initial length of any fiber; and P(θ j ) is the fiber orientation factor (indicating the random tilt distribution characteristics of the plane in which the fiber is located relative to the plane of the fabric).

[0044] where P(θ j ) is determined according to the random tilt distribution characteristics of the plane relative to the plane of the fabric by the following formula:

[0045]

[0046] where θ j is the angle of any plane parallel to the flow relative to the plane of the fabric, and θ j ∈ [0°, 180°].

[0047] It should be noted that in S2, the total fluid resistance of the fiber in the geotechnical fabric is determined by formula (2.5):

[0048]

[0049] wherein, l is the total length of the geotextile fiber; P(α), P(θ) are the fiber orientation coefficients, α is the orientation angle of the fiber in the plane of the fiber group, α ∈ [0°, 180°]; θ is the plane inclination angle of the jth fiber group, θ ∈ [0°, 180°];

[0050] wherein, l is determined according to formula (2.6):

[0051]

[0052] wherein, d f is the fiber diameter; V g is the volume of the geotextile.

[0053] It should be noted that in S2, the transverse permeability coefficient prediction model considering the action of the normal external load is obtained according to formula (2.8a) based on the resistance theory:

[0054]

[0055] wherein, K1 is the transverse permeability coefficient based on the resistance theory; ρ is the fluid density, g is the gravitational acceleration, μ g is the geotextile surface density, ρ f is the fiber density, T g is the geotextile thickness, and μ is the viscosity coefficient of the fluid; K T is the thickness coefficient of the geotextile, T is a function of the solid volume fraction Ф; d f is the fiber diameter.

[0056] It should be noted that in S3, the transverse permeability coefficient prediction model considering the action of the external load is obtained according to formula (3.1) based on the fractal theory:

[0057]

[0058] wherein: K2 is the transverse permeability coefficient based on the fractal theory; L0 is the characteristic length of the capillary, which is taken as the length of the geotextile in the direction of the water flow; D t is the bending fractal dimension, D f is the area fractal dimension; A G is the cross-sectional area of the geotextile considering the action of the external pressure load; λ max-G is the maximum pore diameter of the geotextile considering the action of the external pressure load;

[0059] wherein, λ max-G and A G are calculated according to formula (3.2), (3.3), respectively:

[0060]

[0061] wherein, l is the total length of the geotextile fiber; P(α), P(θ) are the fiber orientation coefficients, α is the orientation angle of the fiber in the plane of the fiber group, α ∈ [0°, 180°]; θ is the plane inclination angle of the jth fiber group, θ ∈ [0°, 180°];

[0050] wherein, l is determined according to formula (2.6):

[0051]

[0052] wherein, d f is the fiber diameter; V g is the volume of the geotextile.

[0053] It should be noted that in S2, the transverse permeability coefficient prediction model considering the action of the normal external load is obtained according to formula (2.8a) based on the resistance theory:

[0054]

[0055] wherein, K1 is the transverse permeability coefficient based on the resistance theory; ρ is the fluid density, g is the gravitational acceleration, μ g is the geotextile surface density, ρ f is the fiber density, T g is the geotextile thickness, and μ is the viscosity coefficient of the fluid; K T is the thickness coefficient of the geotextile, T is a function of the solid volume fraction Ф; d f is the fiber diameter.

[0056] It should be noted that in S3, the transverse permeability coefficient prediction model considering the action of the external load is obtained according to formula (3.1) based on the fractal theory:

[0057]

[0058] wherein: K2 is the transverse permeability coefficient based on the fractal theory; L0 is the characteristic length of the capillary, which is taken as the length of the geotextile in the direction of the water flow; D t is the bending fractal dimension, D f is the area fractal dimension; A G is the cross-sectional area of the geotextile considering the action of the external pressure load; λ max-G is the maximum pore diameter of the geotextile considering the action of the external pressure load;

[0059] wherein, λ max-G and A G are calculated according to formula (3.2), (3.3), respectively:

[0060]

[0061]

[0062] wherein K T is the thickness coefficient of geotextile, T g is the thickness of geotextile, p f is the fiber density, d f is the fiber diameter, m g is the areal density of geotextile, D t is the bending fractal dimension, D f is the area fractal dimension, A G is the porous medium cross-sectional area considering the action of external load, l max-G is the maximum pore diameter considering the action of external load, F is the solid volume fraction of geotextile considering the action of normal external load;

[0063] wherein D t , D f are determined according to formula (3.4), (3.5) respectively:

[0064] D f = c · m g T g + d (3.4)

[0065] D t = e · m g T g + f (3.5)

[0066] wherein c, d, e, f are all fitting parameters.

[0067] It should be noted that in S4, the comprehensive prediction model of the modified transverse permeability coefficient of geotextile is obtained according to formula (4.1a):

[0068]

[0069] wherein p is the fluid density; g is the acceleration of gravity; m g is the areal density of geotextile; p f is the fiber density; T g is the thickness of geotextile; m is the viscosity coefficient of fluid; F is the solid volume fraction of geotextile considering the action of normal external load; K T is the thickness coefficient of geotextile; T is a function of the solid volume fraction F of porous medium; P(a) or P(0) is the fiber orientation coefficient; a is the orientation angle of the fiber in the fiber group, a e [0°, 180°]; 0 is the inclination angle of the plane where the jth fiber group is located, 0 e [0°, 180°]; L0 is the characteristic length of capillary, which is taken as the length of geotextile in the direction of fluid; A G is the porous medium cross-sectional area considering the action of external load, l max-GD is the maximum pore diameter considering the action of the external load t D is the bending fractal dimension f D is the area fractal dimension g T g ] is the limit value of the product of the areal density and the thickness of the geotextile; wherein, [mu g T g ] is recommended to be 5*10 -4 kg / m.

[0070] Compared with the prior art, the present application has the following beneficial technical effects:

[0071] (1) The geotextile transverse permeability coefficient resistance model proposed in the present application overcomes the calculation difficulty problem of the existing model under the assumption of three-dimensional distribution of fibers by discussing the random inclined distribution of fibers in the plane parallel to the water flow direction and the random inclined distribution of the plane where the fibers are located relative to the plane of the geotextile. It also avoids the over-simplification limitation under the assumption of two-dimensional distribution of fibers. The present application modifies the existing transverse permeability coefficient resistance model by proposing a fiber orientation coefficient to modify the fluid resistance and fiber length, respectively. The calculation is simple, and the influence of random inclined distribution of fibers can be fully considered, and it has a wider application scenario.

[0072] (2) Through statistical analysis of a large number of geotextile area fractal dimensions and bending fractal dimensions, an empirical formula of fractal dimension is established. Therefore, the geotextile transverse permeability coefficient fractal model proposed in the present application avoids the limitation of relying on high-precision instruments to measure related parameters in the existing fractal model, and can directly calculate and predict the transverse permeability coefficient. In addition, for the above resistance model and fractal model, the present application modifies them by proposing a thickness coefficient to consider the change of the transverse permeability coefficient of the geotextile under the action of the external load, thereby widening the above two models to the calculation scenario of the transverse permeability coefficient of the geotextile under pressure.

[0073] (3) The existing geotextile transverse permeability coefficient resistance model is only applicable to geotextiles with high thickness and large porosity. For geotextiles with low thickness and small porosity, the fractal model is more applicable. Obviously, a single resistance model or fractal model cannot be completely applicable to geotextiles with different thicknesses and porosities. Therefore, the present application combines the resistance model and the fractal model, and uses the product of the areal density and the thickness of the geotextile as the dividing point of the two models, to establish a unified model for predicting the transverse permeability coefficient of geotextiles with different thicknesses and different porosities. This can make geotextiles with different thicknesses and porosities all use the model in the present application for calculation, and the prediction accuracy is high. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1is the schematic diagram for the principle analysis of the random distribution of fibers, wherein the Y axis represents the direction of the same fluid direction, the Z axis represents the direction perpendicular to the plane of the fabric, the X axis represents the direction of the tunnel axis, and the V axis represents the extension direction of the plane of the fibers, f v is the resistance generated by the fibers to the fluid in the plane of the geotextile; p is the resistance generated by the fibers to the fluid perpendicular to the plane of the geotextile.

[0075] Figure 2 is the flow chart for the construction of the comprehensive prediction model of the transverse permeability coefficient of the geotextile of the present application.

[0076] Figure 3 is the schematic diagram for the selection of the boundary value of the demarcation index of the resistance model and the fractal model based on error analysis

[0077] Figure 4 is the schematic diagram for the change of the thickness of the geotextile with the applied load in the thickness test test of the embodiment.

[0078] Figure 5 is the schematic diagram for the change of the thickness coefficient of the geotextile with the applied load in the thickness test test of the embodiment.

[0079] Figure 6 is the fitting schematic diagram of the fitting parameters in the thickness coefficient formula and the surface density of the geotextile in the embodiment.

[0080] Figure 7 is the fitting schematic diagram of the area fractal dimension and the bending fractal dimension in the embodiment.

[0081] Figure 8 is the comparison of the test value of the transverse permeability coefficient and the predicted value of the resistance model in the embodiment.

[0082] Figure 9 is the comparison of the test value of the transverse permeability coefficient and the predicted value of the fractal model in the embodiment. DETAILED DESCRIPTION

[0083] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0084] Referring to Figure 1-3 , the present application provides a prediction method for the transverse permeability coefficient of the geotextile of the waterproof layer of a mountain tunnel.

[0085] Geotextile is usually laid between the secondary lining (hereinafter referred to as "secondary lining") and the primary support (hereinafter referred to as "primary support") of a tunnel. When water flows through the primary support and seeps to the secondary lining, it is guided by the geotextile and flows along the tunnel cross-section contour to the tunnel arch foot to achieve waterproofing of the secondary lining and the tunnel. The direction of water flow on the surface of the secondary lining is usually considered to be parallel to the cross-section contour of the secondary lining or parallel to the width direction of the geotextile. The geotextile can be considered to include two parts, one part is a solid waterproof layer attached to the surface of the secondary lining, and the other part is a randomly distributed fiber resistance layer extending outward from the surface of the solid waterproof layer. The more the water flows laterally in the fiber resistance layer, the less the water seeps into the solid waterproof layer (or waterproof board) and the secondary lining, thereby avoiding local accumulation of water.

[0086] For the transverse permeation calculation model of the geotextile, the following assumptions are made: 1) all fiber cross sections are circular and have the same length and diameter; 2) the fiber diameter is much smaller than the fiber length and the fiber spacing, and the geotextile has a large porosity characteristic; 3) all fibers are regularly distributed in several planes parallel to the fluid direction, and the fibers are randomly and randomly distributed in the planes, and the number of fibers in different planes is the same; 4) the planes are randomly and randomly inclined to the plane of the geotextile; 5) the fibers are uniformly inclined to the fluid direction after being subjected to axial external pressure; 6) the fluid only moves in the direction parallel to the plane of the geotextile, and no seepage occurs in the vertical direction; 7) the seepage state is laminar flow with low Reynolds number characteristics.

[0087] S1, establishing a general expression of the thickness coefficient of the geotextile with respect to the applied load

[0088] The ratio of the thickness of the geotextile after the applied load to the initial thickness of the geotextile is defined as the thickness coefficient;

[0089] The actual thickness change of the geotextile under different normal applied loads is measured to obtain a series of thickness coefficient data corresponding to the load of the geotextile, and the thickness coefficient K is fitted by regression analysis method T with respect to the general expression of the applied load;

[0090] It should be noted that in S1, for the geotextile with normal applied load, the applied load will make the thickness of the geotextile smaller, the greater the applied load G, the smaller the thickness T g . Based on the thickness test of the geotextile under the normal applied load, the thickness coefficient K T of the geotextile suitable for the geotextile is established with the applied load G as the parameter, the inventor found in the test process that the thickness coefficient K T and the applied load G have a good negative exponential function relationship, so the regression analysis method is used to fit the general expression of the thickness coefficient with respect to the applied load as a negative exponential function, as shown in formula (1.1):

[0091]

[0092] wherein K T is the thickness coefficient of the geotextile; G is the normal applied load; a, t, y are all fitting parameters, which are related to the areal density μ g of the geotextile.

[0093] S2, establishing a transverse permeability coefficient prediction model considering the effect of normal applied load based on resistance theory

[0094] The solid volume fraction of the geotextile is corrected by using the thickness coefficient obtained in S1, and according to the Russell micro-unit theory, the initial fluid resistance per unit length of any fiber in the water flow direction in any plane parallel to the water flow direction is obtained; according to the random inclined distribution characteristics of the fiber in the plane, the obtained initial fluid resistance is corrected by using the fiber orientation coefficient, so as to obtain the actual fluid resistance per unit length of any fiber in the water flow direction in the plane;

[0095] For the geotextile, the solid volume fraction has a calculation formula:

[0096]

[0097] wherein Φ' is the initial solid volume fraction of the geotextile without being subjected to the normal applied load; μ g is the areal density of the geotextile, ρ f is the fiber density, and T g is the thickness of the geotextile.

[0098] The applied load G will change the solid volume fraction Φ of the geotextile, the greater the applied load G, the smaller the thickness coefficient K T , and the greater the solid volume fraction Φ, so in S2, the solid volume fraction of the geotextile is corrected by using the thickness coefficient to obtain formula (2.1):

[0099]

[0100] wherein Φ is the solid volume fraction of the geotextile considering the effect of the normal applied load.

[0101] Based on the Russell micro-unit theory, in any plane parallel to the water flow direction, when there is an included angle α i between the water flow direction and the fiber, the initial fluid resistance per unit length of any fiber in the water flow direction in the plane is determined according to formula (2.2):

[0102]

[0103] wherein f'(α i) is the initial fluid resistance per unit length of any fiber in the water flow direction in any plane parallel to the water flow direction; μ is the viscosity coefficient of the fluid, v is the average flow velocity of the water flow on the surface of the geotextile; T is a function of the solid volume fraction Ф of the porous medium, wherein α i is the orientation angle of the ith fiber, which is the included angle between the ith fiber and the water flow direction, α i ∈ [0°, 180°]; f v is the resistance of the fiber to the fluid in the plane parallel to the geotextile;

[0104] When the fibers are uniformly distributed, there is no entanglement between the fibers, and the fluid only flows in the uniform area between the fibers, i.e. only laminar flow occurs, but when the fibers are randomly distributed, the entangled fibers will produce small pores / gaps, and when the fluid passes through these pores / gaps, turbulent flow will occur, which will cause irregular changes in the direction of the fluid, which is beneficial to the resistance of the fiber to the fluid. The turbulent flow state is more in line with the actual situation, and the orientation angle α i of each fiber is closer to 0° or 180°, the greater the possibility of producing pores and gaps, the greater the possibility of turbulent flow, and the greater the resistance.

[0105] Therefore, the initial fluid resistance of the fiber needs to be corrected. Considering the manufacturing process of the geotextile in actual production, it can be considered that the orientation angle α i of the fiber in the plane is basically in the interval [0°, 180°], and the inventor proposes to give a weight based on the characteristics of the normal distribution to the initial fluid resistance of each fiber in the plane, i.e. the fiber orientation coefficient P i , so as to consider the comprehensive effect of the random distribution of the fiber on the fluid resistance of the fiber. The actual fluid resistance per unit length of any fiber in the water flow direction in any vertical plane parallel to the water flow direction is determined by formula (2.3):

[0106]

[0107] In the formula, f(α i ) is the actual fluid resistance per unit length of any fiber in the water flow direction in any plane parallel to the water flow direction considering the random distribution of the fiber; P(α i ) is the fiber orientation coefficient (indicating the random inclination distribution characteristics of the fiber in the plane).

[0108] For P i , the integral of the normal distribution function can be calculated in numerical software, but based on this method, only the probability of P(α < α i ) can be calculated, i.e. when α i ≤ 90°, the probability satisfies the law of gradually increasing and taking the maximum value 0.5 at 90°; when αi When the fiber orientation angle is >90°, the probability increases and eventually approaches 1 at 180°. However, this does not conform to the concept of normal distribution weights: the probability of the fiber orientation angle being 90° should be the largest and gradually decrease towards the sides.

[0109] Therefore, P i Determine as follows:

[0110]

[0111] Where h is the mathematical expectation of the normal distribution function, σ is the variance of the normal distribution function, and C is the constant in the fiber orientation coefficient formula, which can be calculated by reverse calculation based on data from experiments or existing literature. The recommended value is 1.03.

[0112] When the fiber length is much larger than the fiber diameter, the total resistance F exerted by the fluid on the geotextile can be regarded as the sum of the resistance components exerted by the fluid on each single fiber. i ) and initial fiber length l i0 By multiplying and integrating in the interval [0°, 180°], the total resistance F experienced by all fibers can be obtained.

[0113] Furthermore, any plane parallel to the flow direction is defined as plane j, and all fibers within that plane are defined as group j. Since plane j is randomly and haphazardly tilted relative to the fabric plane, this distribution pattern is identical to that of fibers within a plane and can therefore be considered to conform to normal distribution characteristics. Furthermore, the distribution of fibers within the tilted plane is similar to that within the vertical plane.

[0114] Based on the characteristics that the plane where the fibers are located is randomly and randomly tilted relative to the fabric plane, the fiber orientation coefficient is used to correct the initial length of a single fiber, so that the influence of the random and tilted distribution of the fiber plane on the initial fiber length l0 can be considered.

[0115] Therefore, by multiplying the fiber orientation coefficient by the projection of the initial length l0 of the fiber on the plane, the calculated length of any fiber in the direction of the water flow in any plane parallel to the water flow is obtained as shown in formula (2.4):

[0116] l ij =l0·sinθ j ·P(θ j )(2.4)

[0117] Where, l ij is the calculated length of any fiber in the direction of the fluid in any plane parallel to the water flow; l0 is the initial length of any fiber; P(θ j) is the fiber orientation coefficient (indicating the random tilt distribution characteristics of the fiber plane relative to the fabric plane);

[0118] wherein P j is determined by the following formula:

[0119]

[0120] wherein θ j is the angle between any plane parallel to the water flow and the fabric plane, θ j ∈ [0°, 180°].

[0121] The total fluid resistance of the fibers in the geotextile is calculated according to the actual fluid resistance of the fibers and the calculated length of the fibers. According to the Darcy law, the transverse permeability coefficient based on the resistance theory is obtained. The transverse permeability coefficient obtained is corrected by using the thickness coefficient S1, and the transverse permeability coefficient prediction model based on the resistance theory considering the effect of external load is obtained, which is recorded as K1 model (also can be referred to as "transverse permeability coefficient resistance model");

[0122] The fluid resistance of a single fiber is obtained by multiplying the resistance component f(α i ) of a single fiber and the fiber length l ij . The total fluid resistance F of all fibers in the geotextile is obtained by adding the total number of fibers. The total fluid resistance F is determined by the following formula:

[0123]

[0124] wherein M is the total number of planes j, and N is the total number of fiber groups in the plane j. The above formula can be used to calculate the integral of the normal distribution function in P(θ) and P(α) by using the normcdf function in the numerical calculation software, and then the double integral operation is performed by using the integral function.

[0125] Further, considering that the M and N in the plane of the geotextile are difficult to calculate, the formula (2.9a) is decomposed and equivalently replaced as follows:

[0126]

[0127] Under the assumption that the horizontal initial resistance f v and the initial length l0 of each fiber are the same, the following calculation formula of the total horizontal resistance of the fibers and the total length l of the fibers can be obtained based on the above formula:

[0128]

[0129]

[0130] Therefore, the calculation formula for the total fluid resistance F experienced by all fibers in the geotextile can be simplified as:

[0131]

[0132] In order to avoid the integral calculation of M and N in l, the following method for calculating the total length l of all fibers of geotextiles is given based on the inherent parameters of geotextiles:

[0133] First, calculate the total mass m of the geotextile fiber f , assuming the total length of all fibers in the geotextile is l, then the total mass of the geotextile fibers is m f It can be calculated by the following formula:

[0134]

[0135] Furthermore, the total mass of geotextile fibers m f It can also be calculated based on the volume V of the geotextile. g , surface density μ g and thickness T g Perform the calculation:

[0136]

[0137] By combining the first two equations, we can calculate the total length of all fibers in the geotextile as shown in equation (2.6):

[0138]

[0139] According to the law of conservation of fluid momentum, the pressure change per unit length along the direction of fluid flow, that is, along the horizontal direction of the geotextile, is the pressure gradient ΔP. Therefore, the pressure gradient per unit length of the geotextile per unit volume is equal to the total resistance of the fluid acting on all fibers per unit volume of the geotextile:

[0140]

[0141] Where L is the length of the geotextile along the fluid direction.

[0142] In addition, the pressure gradient can also be calculated according to the basic formula of fluid mechanics:

[0143] ΔP=ρgΔh

[0144] Where ρ is the fluid density, g is the acceleration due to gravity, and Δh is the water level difference between the upper and lower surfaces of the geotextile.

[0145] Combining the above two equations, we can get the total water level difference Δh between the upper and lower surfaces of the geotextile:

[0146]

[0147] According to Darcy's law, the transverse permeability coefficient can be calculated by calculating the fluid flow rate within the unit pressure gradient in the fluid motion direction:

[0148]

[0149] Thus, the transverse permeability coefficient calculation formula of the geotextile based on the resistance theory is obtained, as shown in formula (2.7a):

[0150]

[0151] For the geotextile with an external load, the external load can make the thickness of the geotextile smaller, the greater the external load G, the smaller the thickness T g The volume V g of the geotextile is also smaller.

[0152] Therefore, the thickness coefficient is used to modify formula (2.7a), and the transverse permeability coefficient calculation model based on the resistance theory considering the action of the normal external load is obtained, as shown in formula (2.8) or (2.8a):

[0153]

[0154]

[0155] In the formula, K1 is the transverse permeability coefficient based on the resistance theory.

[0156] It is worth noting that the transverse permeability coefficient model based on the resistance theory is more suitable for geotextile materials with large thickness and large porosity. On the one hand, the transverse permeability coefficient model based on the resistance theory makes the assumption that the fiber length and spacing are much larger than the fiber diameter, that is, the fabric has the characteristics of large porosity, which is consistent with the high porosity characteristics of the geotextile. On the other hand, the transverse permeability coefficient model based on the resistance theory can directly obtain the transverse permeability coefficient based on the macroscopic geotextile parameters, which is also more consistent with the actual situation. However, there are geotextile materials with lower thickness and smaller porosity in actual engineering, and the applicability of the transverse permeability coefficient model based on the resistance theory to this kind of geotextile needs to be discussed. In order to make the model provided by the present application have higher universality, a transverse permeability coefficient calculation model based on the fractal theory is proposed to supplement and revise the above model.

[0157] S3, a transverse permeability coefficient prediction model considering the action of an external load is established based on the fractal theory

[0158] According to the microscopic test data of the geotextile in the prior art, an empirical formula of the fractal dimension about the product of the surface density and the thickness of the geotextile is established;

[0159] Adopting thickness coefficient K T The maximum pore diameter of the geotextile and the cross-sectional area of the geotextile are obtained based on the fractal theory when the fibers are uniformly distributed on the surface of the geotextile.

[0160] A prediction model of the transverse permeability coefficient based on the fractal theory considering the action of an external load is obtained according to the fractal dimension, the maximum pore diameter and the cross-sectional area of the geotextile, and is denoted as K2 model (also referred to as “fractal model of the transverse permeability coefficient” for short).

[0161] When the fibers are uniformly distributed on the surface of the geotextile, the seepage flow of a fluid flowing through a capillary tube with a length of L t (λ) and a diameter of λ is obtained based on the fractal theory and the modified Hagen-Poiseulle equation as follows:

[0162]

[0163] The total flow Q of all capillary tubes with a cross-sectional area of A is:

[0164]

[0165] Further, since the geotextile material is a porous medium with fractal characteristics, the number of pores N on the cross section and the diameter λ of the pores satisfy the following scaling relationship:

[0166]

[0167] In the formula, λ is the pore diameter, λ is the maximum pore diameter, f(λ) is the pore diameter distribution density function, N(λ) is the number of pores with a pore diameter greater than λ, D f is the area fractal dimension of the pores. The derivative of the above formula with respect to the pore diameter λ is:

[0168]

[0169] Substituting the above formula into the calculation formula of the total flow Q gives:

[0170]

[0171] Based on the Pitchumani model, there is an exponential relationship between L t (λ) and the pore diameter λ as follows:

[0172]

[0173] In the formula, D t is the bending fractal dimension of the pores, D t = 1 represents that the capillary tube channel is straight, and D t=2 represents that the capillary channel is completely curved and fills the entire plane, and L0 is the characteristic length of the capillary, that is, the distance through which the fluid passes.

[0174] Therefore, the following can be obtained:

[0175]

[0176] In view of the bending fractal dimension D t and the area fractal dimension D f are values in the interval [1, 2], D t +3-D f is a value greater than 1, and in the porous medium, generally:

[0177]

[0178] Therefore, the simplified calculation formula of the total flow Q is:

[0179]

[0180] Based on the Darcy law, the calculation model of the transverse permeability coefficient based on the fractal theory when the fibers are uniformly distributed on the surface of the geotextile is obtained as follows:

[0181]

[0182] For the maximum pore diameter λ max , the random network theory based on Poisson Polyhedron can be used to obtain:

[0183]

[0184] In view of the fact that the cross section of the geotextile can be regarded as being composed of pores and fibers, the calculation formula of the cross section area A can be obtained based on the solution of the porosity:

[0185]

[0186] In the formula, Ф is the solid volume fraction of the geotextile.

[0187] The fractal model described above is the prior art, which is described in document 1.

[0188] Document 1: Ji Lianying. Permeability of non-woven geotextile [D]. Donghua University, 2010.

[0189] The prediction model provided by the present application needs to consider the influence of the external load G on the transverse permeability of the geotextile, and therefore the calculation formula of the maximum pore diameter λ max and the cross section area A needs to be modified. The external load G will make the thickness T gThe decrease in the thickness T of the geotextile will also change the solid volume fraction Ф of the geotextile, but since Ф is also related to the thickness T of the geotextile g , the key to the change of Ф due to the applied load also falls on the thickness T of the geotextile g .

[0190] Therefore, the thickness coefficient K T is introduced to modify the response of the applied load G on the geotextile. max The maximum pore diameter λ max-G and the cross-sectional area A of the geotextile in the model are modified to obtain the maximum pore diameter λ G and the cross-sectional area A considering the effect of the applied load, and then combined with the modified solid volume fraction Ф in S2, the calculation model of the lateral permeability coefficient based on the fractal theory considering the effect of the applied load can be obtained as formula (3.1):

[0191]

[0192] In the formula, K2 is the lateral permeability coefficient based on the fractal theory; L0 is the characteristic length of the capillary, which is taken as the length of the geotextile in the direction of water flow; D t is the bending fractal dimension, D f is the area fractal dimension; A G is the cross-sectional area of the geotextile considering the effect of the external pressure load; λ max-G is the maximum pore diameter of the geotextile considering the effect of the external pressure load.

[0193] In the formula, the maximum pore diameter λ max-G and the cross-sectional area A G are calculated according to formulas (3.2)-(3.4), respectively:

[0194]

[0195]

[0196] In the formula, K T is the thickness coefficient of the geotextile, T g is the thickness of the geotextile, ρ f is the fiber density, d f is the fiber diameter, μ g is the surface density of the geotextile, D t is the bending fractal dimension, A G is the cross-sectional area of the porous medium considering the effect of the applied load, D f is the area fractal dimension, λ max-G is the maximum pore diameter considering the effect of the applied load, and Ф is the solid volume fraction of the geotextile considering the effect of the normal applied load.

[0197] The above modified formula is substituted into the following formula (3.4) to obtain a calculation model of the transverse permeability coefficient based on the fractal theory considering the effect of the applied load:

[0198]

[0199] For the bending fractal dimension D t and the area fractal dimension D f , the inventors collected existing micro-observation test data of geotextiles (Table 6-1 and Table 6-3 of Literature 1, Table 4-1 of Literature 2), and obtained the calculated values of D t , D f according to the electron microscope test results), taking the product of the surface density μ g of the geotextile and the thickness T g of the fabric as the independent variable, and taking the bending fractal dimension D t and the area fractal dimension D f as the dependent variable, respectively, it was found that D t or D f had a good linear relationship with μ g T g , so that D t , D f could be determined according to formula (3.5) and (3.6), respectively:

[0200] D f = c·μ g T g + d (3.5)

[0201] D t = e·μ g T g + f (3.6)

[0202] In the formula, c, d, e, and f are fitting parameters.

[0203] In specific embodiments, the four parameters c, d, e, and f obtained by the inventors are 10.4, 1.9, -31.2, and 1.2, respectively.

[0204] Literature 1: Ji, L. Y. Permeability of nonwoven geotextiles [D]. Donghua University, 2010.

[0205] Literature 2: Lu, H. J. Theoretical study on vertical permeability of needle-punched geotextiles [D]. Donghua University, 2012.

[0206] The measured and calculated values of D f are 1.94, 1.932, 1.92, and 1.926, and the measured and calculated values of D t are 1.18, 1.23, 1.16, and 1.25.

[0207] S4. Establish a comprehensive prediction model for geotextile modified lateral permeability coefficient

[0208] By combining the K1 model and the K2 model, we can obtain the comprehensive prediction model of geotextile modified lateral permeability coefficient:

[0209]

[0210] Where K is the lateral permeability coefficient; μ g is the surface density of geotextile; T g is the thickness of geotextile; [μ g T g ] is the limit value of the product of the surface density and thickness of geotextile.

[0211] Specifically: the product of the surface density and thickness of the geotextile is used as the demarcation index of the K1 model obtained in S2 and the K2 model obtained in S3; the limit value of the demarcation index is determined according to the error between the lateral permeability test results in the prior art and the predicted results of the theoretical model; the critical value is used as the upper limit of the demarcation index in the K1 model or the lower limit of the demarcation index in the K2 model; the K1 model in S2 and the K2 model in S3 are combined to obtain a comprehensive prediction model for the modified lateral permeability coefficient of geotextiles.

[0212] As mentioned before, the lateral permeability coefficient prediction model based on resistance theory (K1 model) is more suitable for geotextiles with high thickness and large porosity. For geotextiles with low thickness and small porosity, the lateral permeability coefficient prediction model based on fractal theory (K2 model) is more suitable. g and thickness T g The boundary of the two models (K1 model and K2 model) is divided by multiplying the product of , and the final comprehensive prediction model of lateral permeability coefficient is obtained as shown in formula (4.1a):

[0213]

[0214] Where: K is the lateral permeability coefficient; ρ is the fluid density, g is the acceleration of gravity, μ g is the surface density of geotextile, ρ f is the fiber density, T g is the thickness of geotextile, μ is the viscosity coefficient of the fluid; Ф is the solid volume fraction of geotextile when considering the normal external load, K Tis the thickness coefficient of the geotextile, T is a function of the solid volume fraction Φ of the porous medium, P(α) or P(θ) is the fiber orientation coefficient, α is the orientation angle of the fiber in the fiber group, which is the angle between the fiber and the water flow direction, α∈[0°,180°]; θ is the plane inclination angle of the jth fiber group, which is the angle between the plane where the fiber group is located and the fabric plane, θ∈[0°,180°]; L0 is the characteristic length of the capillary, which is the length of the geotextile in the fluid direction, D t is the curved fractal dimension, A G D is the cross-sectional area of ​​the porous medium considering the external load. f is the area fractal dimension, λ max-G is the maximum pore diameter considering the external load; [μ g T g ] is the limit value of the product of the surface density and thickness of geotextile; where [μ g T g ] It is recommended to take 5×10 -4 kg / m.

[0215] For the limit value [μ g T g ], the inventors collected existing lateral permeability test data (Chapter 4, Section 4.2 of Document 1, Chapters 3 and 4 of Document 3, Section 2 of Document 4), used the corresponding geotextile parameter values ​​and the resistance model and fractal model established by the inventors, and calculated the theoretical values ​​of the lateral permeability coefficient of the two models respectively, and compared them with the lateral permeability test values ​​and calculated the error values, thereby obtaining the theoretical values ​​of the lateral permeability coefficient of the two models with μ g T g The error distribution of Figure 3 Obviously, if 2% is taken as the error acceptance value, the resistance model is g T g >5×10 -4 kg / m3 is more accurate, and μ g T g <5×10 -4 kg / m has poor accuracy; the fractal model has poor accuracy in μ g T g <5×10 -4 kg / m3 is more accurate, and μ g T g >5×10 -4 kg / m3 has poor accuracy. Therefore, [μ g T g ]=5×10 -4 kg / m was used as the model limit value under the 2% error acceptance value.

[0216] Document 3: Daitingting. Horizontal permeability of short fiber needled geotextile [D]. Central Plains College of Engineering, 2011.

[0217] Document 4: Du Zhaohua, et al. Theoretical model and application of transverse seepage of composite waterproof layer in mountain tunnel [J]. Highway Traffic Science and Technology, 2019, 36(7): 98-105.

[0218] After the K1 model and the K2 model are combined into one model, the values of the two models at the critical point may not be equal, and if necessary, can be obtained μ g T g =[μ g T g ] when the endpoint values of the two models, and then according to the endpoint values of the K1 model and the K2 model, the prediction values are corrected, so that K becomes continuous, as follows:

[0219]

[0220] Among them,

[0221] The geotextile is composed of fibers and contains a large number of pores, so most of the geotextiles are actually high-porosity and high-thickness materials, which are more suitable for the application scenarios of the resistance model. However, there are still a small number of low-porosity and low-thickness geotextiles, such as low-thickness geotextiles and composite geotextiles. For these geotextiles, the calculation accuracy of the resistance model is low, so the present application introduces the idea of partitioning, thereby combining the transverse permeability coefficient prediction models suitable for geotextile materials with different porosities and thicknesses into one model for systematic prediction.

[0222] Specific embodiments; see Figure 1-9 ;

[0223] The present application provides a kind of mountain tunnel waterproof layer geotextile transverse permeability coefficient prediction model, its general expression is:

[0224]

[0225] In the expression, it mainly includes two unknown parameters, one is thickness coefficient K T , which can be measured by thickness test based on normal external load, which is related to the characteristics of geotextile product, and the second is the parameter T related to the solid volume fraction of geotextile Ф and the transverse permeability coefficient K, which is measured by the transverse permeability test of geotextile based on normal external load. Therefore, this embodiment mainly carries out transverse permeability test, and the reliability of the model is verified by comparing the test results with the model calculation results. But before using the model to calculate the transverse permeability coefficient, the thickness coefficient K of the geotextile used in this embodiment needs to be determined.T .

[0226] The face density μ g is 100 g / m 2 , 200 g / m 2 , 300 g / m 2 , 400 g / m 2 , and the thickness T g is 1.3, 2.2, 3.1, 3.7 mm. The geotextile has a length of 20 cm, a fiber density ρ f of 1.38*10 3 kg / m 3 , and a fiber diameter d f of 0.025 mm. The fluid is water, the density ρ is 1000 kg / m 3 , and the viscosity coefficient μ is 1*10 -3 kg / (m·s). The normal applied load G2 of the transverse permeation test is 2, 5, 10, 20, 30, 40, 50 kPa.

[0227] Before analyzing the transverse permeation coefficient, the thickness test under the normal applied load of the geotextile is carried out, the applied load G1 is 2, 5, 10, 30, 50, 70, 100 kPa, and the test is carried out in a stepwise manner, and the test results are as follows Figure 4 Obviously, the thickness coefficient K T has a good negative exponential function relationship with the applied load G. Therefore, the expression between the thickness coefficient K T and the applied load G of the geotextile with four different face densities is fitted by using the regression analysis method:

[0228]

[0229] In addition, the inventors have found that the fitting parameters in the above expression have a good linear relationship with the face density μ g of the geotextile. In order to unify the thickness coefficients K T of different geotextiles, the fitting parameters a, y, t, etc. in the thickness coefficient K T are further fitted with the face density μ g (g / m 3 ) of the geotextile, and the following calculation formula can be obtained:

[0230] a=0.0012·μ g -0.88

[0231] y=0.0011·μ g -0.24

[0232] t=-0.0003·μg -10.93

[0233] Therefore, the thickness coefficient K T The formula can be summarized as:

[0234]

[0235] The fiber orientation coefficient P(α i ) and P(θ j ) can objectively reflect the random distribution of fibers in geotextiles. Since the manufacturing process of geotextiles often makes the fiber bundle perpendicular or nearly perpendicular, this embodiment considers that the distribution probability of the fiber orientation angle gradually decreases on both sides of the symmetry axis α i = 90° or π / 2, so the mathematical expectation h is 90° or π / 2. For the variance σ, in this embodiment, it is required that the fiber orientation angle α i falls within the interval [0°, 180°] or [0, π], so based on the 3σ principle, σ = 30° or π / 6 can be determined.

[0236] The integral term in the formula The integral of the normal distribution function in P(θ) and P(α) can be calculated using the normcdf function in numerical calculation software, and then the integral function is used for double integration. For the constant C in the formula of P(θ) and P(α), the inventors calculated C to be 1.03 by extracting the data of the permeability test in the literature.

[0237] To determine the parameter T in the model, the solid volume fraction Ф of the geotextile needs to be determined. The solid volume fraction Ф will change continuously under the action of the normal external load G, and its specific value is calculated according to formula (2.1). For the transverse permeability test of geotextiles, when the areal density μ g is 100, 200, 300, 400 g / m 2 , under the action of different external loads G, the thickness coefficient K T is as shown in Table 2, and the solid volume fraction Ф is as shown in Table 3.

[0238] Table 2 Thickness coefficient

[0239]

[0240] Table 3 Solid volume fraction

[0241]

[0242] For the transverse permeability coefficient prediction model based on the fractal theory, for the bending fractal dimension D t and the area fractal dimension D f, reference to the existing geotextile microscopic observation test data, with the product of the geotextile surface density μ g , fabric thickness T g as the variable, linear fitting of the bending fractal dimension D t and the area fractal dimension D f , obtains:

[0243] D f = 10.4·μ g T g +1.9

[0244] D t =-31.2·μ g T g +1.2

[0245] So far, the parameters in the model proposed by the application have been determined, and the comparison chart of the calculated values of the resistance model (K1 model) and the fractal model (K2 model) and the transverse permeation test results is as shown in Figure 8-9 . The error between each point on each curve can be calculated from Figure 8-9 , and the average error of the same surface density and thickness under different applied loads is obtained, as shown in Table 4.

[0246] Table 4 Error between calculated values of individual models and experimental values

[0247] μ g T g (kg / m)]]> 0.00013 0.00044 0.00093 0.00148 Error-resistance model 0.051 0.038 0.019 0.011 Error-Fractal Model 0.009 0.018 0.041 0.049

[0248] It can be found that the calculation error of the resistance model for geotextiles with μ g T g <5×10 -4 kg / m is greater than that for geotextiles with μ g T g >5×10 -4 , and the calculation error of the fractal model for geotextiles with μ g T g >5×10 -4 kg / m is greater than that for geotextiles with μ g T g <5×10 -4 kg / m. The above results show that the resistance model has poor applicability in the low μ g T g interval, and the fractal model has poor applicability in the high μ g T g interval, so the limit value [μ g T g ]=5×10 - 4The method of taking 6×10 g T g ] as a demarcation point, combining the high-precision interval of the resistance model and the fractal model respectively, can make the two models well predict the transverse permeability coefficient in their respective applicable intervals. Of course, according to the results in Table 4, [μ -4 kg / m is also possible.

[0249] When the model of the application is applied to predict the transverse permeability coefficient of the waterproof layer of the geotextile in an actual mountain tunnel project, only the type of the geotextile used in the project (determining the corresponding parameters) and the surrounding rock pressure acting on the geotextile need to be investigated, and the thickness coefficient of the geotextile is determined through the thickness test under the action of the normal external load, and then the model can be used to predict the permeability coefficient, which is very convenient and reliable.

[0250] The above description is only used to illustrate the technical solutions of the application and not to limit the application, and the modifications or replacements of the technical solutions made by other skilled persons in the art should be covered in the scope of the claims of the application as long as they do not deviate from the connotation of the technical solutions of the application.

Claims

1. A method for predicting the lateral permeability coefficient of geotextiles for mountain tunnel waterproofing, characterized by: The steps include: S1. Establish a general expression for the thickness coefficient of geotextiles with respect to the applied load The ratio of the thickness of the geotextile after the load is applied to its initial thickness is defined as the thickness factor; The actual thickness change of geotextile under different normal external loads was measured to obtain a series of thickness coefficient data corresponding to the geotextile and the load. The thickness coefficient K was fitted using regression analysis. T General expressions for applied loads; S2. Establish a lateral permeability coefficient prediction model based on resistance theory considering the effect of normal external load Using thickness coefficient K T After correcting the solid volume fraction of the geotextile, the initial fluid resistance per unit length of any fiber in any plane parallel to the water flow direction is obtained according to the Russell micro-element theory. The initial resistance is corrected using the fiber orientation coefficient to obtain the actual fluid resistance per unit length of any fiber in the plane in the direction of water flow; The initial length of the fiber is corrected using the fiber orientation coefficient to obtain the calculated length of the fiber in the plane in the direction of water flow; After the total fluid resistance of the fibers in the geotextile is calculated based on the actual fluid resistance of the fibers and the calculated fiber length, the lateral permeability coefficient based on the resistance theory is obtained according to Darcy's law, and the thickness coefficient K is used. T The lateral permeability coefficient is corrected to obtain a lateral permeability coefficient prediction model based on resistance theory that takes into account the effect of external loads, which is recorded as the K1 model. The fiber orientation coefficient is determined according to the random tilt distribution characteristics of the fibers in the plane and the random tilt distribution characteristics of the plane relative to the fabric plane; S3. Establish a lateral permeability coefficient prediction model based on fractal theory considering the effect of external loads Based on the microscopic test data of geotextiles in the prior art, an empirical formula of fractal dimension is established as the product of geotextile surface density and thickness. Using thickness coefficient K T The calculation model of lateral permeability coefficient based on fractal theory when the fibers are uniformly distributed on the surface of geotextiles is modified to obtain the maximum pore diameter and cross-sectional area of ​​geotextiles. According to the fractal dimension, maximum pore diameter and cross-sectional area of ​​geotextiles, a fractal theory-based prediction model of lateral permeability coefficient considering the external load is obtained, which is denoted as K2 model. S4. Establish a comprehensive prediction model for geotextile modified lateral permeability coefficient By combining the K1 model and the K2 model, we can obtain the comprehensive prediction model of geotextile modified lateral permeability coefficient: Where K is the lateral permeability coefficient; K1 is the lateral permeability coefficient based on resistance theory; K2 is the lateral permeability coefficient based on resistance theory; μg is the surface density of the geotextile; Tg is the thickness of the geotextile; [μgTg] is the limit value of the product of the surface density and thickness of the geotextile.

2. The prediction method according to claim 1, wherein: In S1, the thickness coefficient K T The general expression of external pressure load is obtained by fitting according to formula (1.1) using regression analysis method: Where K T is the thickness coefficient of geotextile; G is the normal external load; a, t, y are all fitting parameters.

3. The prediction method according to claim 2, wherein: In S2, the thickness coefficient K is used T According to formula (2.1), the solid volume fraction of geotextile is obtained: Where Ф is the solid volume fraction of the geotextile under normal external compressive load; μg is the surface density of the geotextile; ρf is the fiber density; Tg is the thickness of the geotextile.

4. The prediction method according to claim 3, wherein: In S2, the initial resistance of any fiber per unit length in the direction of water flow in any plane parallel to the direction of water flow is determined by formula (2.2): Where f'(αi) is the initial resistance of the fluid per unit length in the direction of water flow on any fiber in any plane parallel to the direction of water flow; μ is the viscosity coefficient of the fluid, and v is the average flow velocity of water flowing on the surface of the geotextile; T is a function related to the solid volume fraction Φ; αi is the orientation angle of the i-th fiber in the plane, αi∈[0°,180°]; in, 5. The prediction method according to claim 4, wherein: In S2, the actual fluid resistance per unit length of any fiber in any plane parallel to the water flow direction is determined according to formula (2.3): Where f(αi) is the actual fluid resistance per unit length of any fiber in any plane parallel to the fluid direction in the direction of water flow; P(αi) is the fiber orientation coefficient; Wherein, P(αi) is determined according to the random tilt distribution characteristics of the fibers in the plane as follows: Where h is the mathematical expectation of the normal distribution function, σ is the variance of the normal distribution function, and C is a constant.

6. The prediction method according to claim 5, wherein: In S2, the calculated length of any fiber in the direction of water flow in any plane parallel to the water flow is as follows: lij=l0·sinθj·P(θj) (2.4) Where lij is the calculated length of any fiber in the direction of the fluid in any plane parallel to the water flow; l0 is the initial length of any fiber; P(θj) is the fiber orientation coefficient; Wherein, P(θj) is determined according to the random tilt distribution characteristics of the plane relative to the fabric plane as follows: Where θj is the angle between any plane parallel to the water flow and the fabric plane, θj∈[0°,180°].

7. The prediction method according to claim 6, wherein: In S2, the total fluid resistance of the fibers in the geotextile is determined according to formula (2.5): Where l is the total length of geotextile fibers; α is the orientation angle of the fibers in the plane where the fiber group is located; θ is the plane inclination angle of the plane where the fiber group is located; P(α) and P(θ) are both fiber orientation coefficients; Where l is determined according to formula (2.6): Where df is the fiber diameter and Vg is the volume of the geotextile.

8. The prediction method according to claim 7, wherein: In S2, the lateral permeability coefficient prediction model based on resistance theory considering the normal external pressure load is obtained according to formula (2.8a): Where ρ is the fluid density, g is the acceleration due to gravity, and μ is the viscosity coefficient of the fluid.

9. The prediction method according to claim 8, wherein: In S3, the lateral permeability coefficient prediction model based on fractal theory considering the external pressure load is obtained according to formula (3.1): Where: L0 is the characteristic length of the capillary; Dt is the bending fractal dimension, Df is the area fractal dimension; A G is the cross-sectional area of ​​geotextile considering the external pressure load; G is the maximum pore diameter of geotextile considering the external pressure load; Among them, λmax- G and A G Calculate according to formula (3.2) and (3.3) respectively: Where Dt and Df are determined according to formula (3.4) and (3.5) respectively: Df=c·μgTg+d (3.4) Dt=e·μgTg+f (3.5) Where c, d, e, and f are all fitting parameters.

10. The prediction method according to claim 9, wherein: In S4, the comprehensive prediction model of geotextile modified lateral permeability coefficient is obtained according to formula (4.1a): Where: [μgTg] is the limit value of the product of the surface density and thickness of the geotextile.

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