Mountain tunnel waterproof layer geotextile transverse permeability coefficient prediction method

Abstract

The invention discloses a mountain tunnel waterproof layer geotextile transverse permeability coefficient prediction method which comprises the following steps: correcting the solid volume fraction of a geotextile by adopting a thickness coefficient, correcting the fluid initial resistance borne by fibers and the initial length of the fibers by adopting a fiber orientation coefficient to obtain the total fluid resistance borne by the fibers, and predicting the transverse permeability coefficient of the geotextile. Calculating a permeability coefficient based on a Darcy law, and correcting a transverse permeability coefficient resistance model by adopting a thickness coefficient; a thickness coefficient is adopted to correct the maximum pore diameter and the cross section area, an empirical formula of fractal dimensions is established according to existing data, and then a fractal model for correcting the transverse permeability coefficient is established; the product of the surface density and the thickness of the geotextile serves as a demarcation index, and the two models are combined to form a comprehensive model. The model not only can consider the influence of the disordered fiber distribution and the external load effect on the transverse permeability of the geotextile, but also can be suitable for predicting the transverse permeability coefficient of the geotextile with different thicknesses and surface densities, and is high in prediction precision and strong in applicability.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel waterproofing, and in particular to a method for predicting the lateral permeability coefficient of geotextiles of a mountain tunnel waterproofing layer. Background Art

[0002] In mountain tunnel projects, a composite lining form combining primary support and secondary lining is often used. Between the primary support and the secondary lining, a composite waterproof layer is used to achieve drainage of the tunnel lining. The waterproof board in the composite waterproof layer intercepts the seepage and blocks the seepage outside the secondary lining; the fiber fabric geotextile in the composite waterproof layer leads the seepage to the drainage system of the tunnel arch foot. With the advancement of technology, composite geomembranes have become a feasible solution to replace traditional composite waterproof layers. The fiber fabric of the composite geomembrane is closely combined with the waterproof membrane layer. The fiber fabric also plays a role in lateral penetration, and the waterproof membrane layer replaces the traditional and bulky waterproof board part. Whether it is traditional geotextiles or composite geomembranes, they are all geotextiles. Their lateral permeability has a key impact on the drainage of tunnel structures. The better the lateral permeability, the less likely it is that seepage will accumulate locally, and the smaller the waterproof pressure of the waterproof board.

[0003] At present, the calculation models of the lateral permeability coefficient of fiber fabric geotextiles have been reported, mainly including resistance model, fractal model and random network model. The resistance model combines the fluid resistance theory in porous media with the fiber structure theory of geotextiles to derive the calculation formula of the lateral permeability coefficient; the fractal model uses image processing technology to obtain relevant parameters, and then applies the capillary fluid theory to establish relevant formulas; the random network model derives the calculation formula of the lateral permeability coefficient based on image processing technology and pore distribution probability distribution theory. However, the resistance model is only applicable to geotextile materials with high gram weight and large thickness, and there are problems such as over-simplification of the arrangement and distribution of fibers in the fabric, failure to consider the random angle distribution of fibers, resulting in insufficient prediction accuracy, or the limitation of excessive calculation difficulty due to no simplification of the fiber arrangement and distribution; both the fractal model and the random network model need to obtain the fractal dimension and the maximum pore diameter based on image acquisition and processing technology, which has high requirements for instruments and equipment, and the parameter acquisition process is cumbersome, time-consuming, and insufficient prediction accuracy. In addition, geotextiles in mountain tunnels are often under the pressure field imposed by the secondary lining. The above three models cannot consider the influence of external load on the lateral permeability of geotextiles, and the applicability of composite geomembrane, a new type of geotextile, is also questionable. Therefore, it is necessary to propose a new lateral permeability prediction model and prediction method that can consider the random distribution of fibers, the application of external loads, and is suitable for geotextiles of different thicknesses and surface densities. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method for predicting the lateral permeability coefficient of geotextiles for mountain tunnel waterproofing layers, which can not only consider the influence of random fiber distribution and external load on the lateral permeability of geotextiles, but also be applicable to the prediction of lateral permeability coefficients of geotextiles with different thicknesses and surface densities.

[0005] The present application combines the lateral permeability coefficient resistance model and the fractal model, and uses the inherent parameter value of geotextile as the dividing point of the two models, so as to overcome the limitation that the prior art cannot be applied to geotextiles with large and small porosity / thickness at the same time. For the resistance model, it is assumed that the initial orientation of the fiber is divided into the fiber inclination in the plane parallel to the fluid direction, and the overall inclination of the fiber relative to the plane of the geotextile along the plane, and the normal random distribution is considered for the inclination in the two directions respectively, and the three-dimensional calculation is converted into a pseudo-three-dimensional calculation, thereby respectively realizing the correction of the fluid resistance and fiber length considering the random distribution of the fiber. For the fractal model, the inherent parameters of geotextile are used as variables to derive the calculation formulas of the area fractal dimension, the bending fractal dimension and the maximum void diameter, avoiding the limitation that the existing fractal model needs to rely on high-precision instruments to measure the relevant parameters, and the lateral permeability coefficient can be directly calculated and predicted. Finally, a thickness coefficient is proposed to consider the effect of external pressure load on the thickness change of geotextiles, and then consider the effect of external pressure load on solid volume fraction, maximum pore diameter and final lateral permeability, so that the prediction model is suitable for the actual working conditions in which the geotextiles in the composite waterproof layer of the tunnel are often under pressure.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme:

[0007] A method for predicting the lateral permeability coefficient of geotextiles in a mountain tunnel waterproofing layer comprises the following steps:

[0008] S1. Establish a general expression for the thickness factor of geotextiles with respect to the applied load

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

[0010] 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 by regression analysis. T General expressions for imposed loads;

[0011] S2. Establish a lateral permeability prediction model based on resistance theory considering the normal external load

[0012] Use thickness factor K TAfter correcting the solid volume fraction of geotextiles, 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-unit theory;

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

[0015] After calculating the total fluid resistance of the fibers in the geotextile according to 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. 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 denoted as K1 model.

[0016] 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;

[0017] S3. Establish a lateral permeability prediction model based on fractal theory considering the effect of external loads

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

[0019] Use thickness factor K T The calculation model of transverse permeability coefficient based on fractal theory was modified when the fibers were evenly distributed on the surface of geotextiles to obtain the maximum pore diameter and cross-sectional area of ​​geotextiles.

[0020] 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 effect of external load is obtained, which is denoted as K2 model.

[0021] S4. Establish a comprehensive prediction model for geotextile modified lateral permeability coefficient

[0022] Combining the K1 model and the K2 model, we get the comprehensive prediction model of geotextile modified lateral permeability coefficient:

[0023]

[0024] Where K is the lateral permeability coefficient; K1 is the lateral permeability coefficient based on the resistance theory; K2 is the lateral 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 the surface density and thickness of geotextile.

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

[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 is used T According to formula (2.1), the solid volume fraction of geotextile is obtained:

[0029]

[0030] Where, Ф is the solid volume fraction of geotextile under normal external load; μ g is the surface density of geotextile; ρ f is the fiber density; T g is the thickness of the 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 water flow direction is determined according to formula (2.2):

[0032]

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

[0034] in,

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

[0036]

[0037] In the formula, f(α i ) 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(α i ) is the fiber orientation coefficient (indicating the random tilt distribution characteristics of the fibers in the plane);

[0038] Among them, P(α i ) is determined according to the random tilt distribution characteristics of the fibers in the plane as follows:

[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 with a recommended value of 1.03.

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

[0042] l ij =l0·sinθ j ·P(θ j )(2.4)

[0043] In the formula, 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);

[0044] Among them, P(θ j ) is determined according to the random tilt distribution characteristics of the plane relative to the fabric plane as follows:

[0045]

[0046] In the formula, θ j is the angle between any plane parallel to the water flow and the fabric plane, θ j ∈[0°,180°].

[0047] It should be noted that in S2, the total fluid resistance of the fibers in the geotextile is determined according to formula (2.5):

[0048]

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

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

[0051]

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

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

[0054]

[0055] Where K1 is the lateral permeability coefficient based on resistance theory; ρ is the fluid density, g is the gravitational acceleration, 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 fluid; K T is the thickness coefficient of geotextile, T is a function of the solid volume fraction Φ; d f is the fiber diameter.

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

[0057]

[0058] Where: K2 is the lateral permeability coefficient based on 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 curved fractal dimension, D f is the area fractal dimension; A G is the cross-sectional area of ​​geotextile considering the external pressure load; max-G is the maximum pore diameter of geotextile considering external pressure load;

[0059] Among them, λ max-G and A G Calculate according to formula (3.2) and (3.3) respectively:

[0060]

[0061]

[0062] Where: K T is the thickness factor of 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 geotextile, D t is the curved fractal dimension, D f is the area fractal dimension, A G is the cross-sectional area of ​​the porous medium considering the external load, max-G is the maximum pore diameter considering the applied load, Ф is the solid volume fraction of the geotextile when considering the normal applied load;

[0063] Among them, D t , D f Determine according to formula (3.4) and (3.5) respectively:

[0064] D f =c·μ g T g +d (3.4)

[0065] D t =e·μ g T g +f (3.5)

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

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

[0068]

[0069] Where: ρ is the fluid density; g is the gravitational acceleration; μ g is the surface density of geotextile; ρ f is the fiber density; T g is the thickness of the geotextile; μ is the viscosity coefficient of the fluid; Ф is the solid volume fraction of the geotextile when considering the normal external load; K T is the thickness coefficient of 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, α∈[0°,180°]; θ is the inclination angle of the plane where the jth fiber group is located, θ∈[0°,180°]; L0 is the characteristic length of the capillary, which is taken as the length of the geotextile in the fluid direction; A G is the cross-sectional area of ​​the porous medium considering the external load, max-GD is the maximum pore diameter considering the external load; t is the curved fractal dimension, D f is the area fractal dimension; [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.

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

[0071] (1) The geotextile lateral permeability resistance model proposed in the present invention discusses the random directional tilt distribution of fibers in a plane parallel to the water flow direction and the random directional tilt distribution of the fiber plane relative to the fabric plane, thereby overcoming the calculation difficulty of the existing model under the assumption of three-dimensional fiber distribution and avoiding the limitation of over-simplification under the assumption of two-dimensional fiber distribution. The present invention proposes a fiber orientation coefficient to correct the fluid resistance and fiber length respectively, and corrects the existing lateral permeability resistance model by considering the normal external load and fiber orientation. The calculation is simple and the influence of the random directional tilt distribution of fibers can be fully considered, so it has a wider range of application scenarios.

[0072] (2) By statistically analyzing a large number of geotextile area fractal dimensions and bending fractal dimensions, an empirical formula for fractal dimensions is established. Therefore, the fractal model of geotextile lateral permeability coefficient proposed in the present invention avoids the limitation of existing fractal models that rely on high-precision instruments to measure relevant parameters, and can directly calculate and predict the lateral permeability coefficient. In addition, for the above-mentioned resistance model and fractal model, the present invention modifies them by proposing a thickness coefficient to consider the change of the geotextile lateral permeability coefficient under the action of an external load, thereby expanding the above-mentioned two models to the calculation scenario of the geotextile lateral permeability coefficient under pressure.

[0073] (3) The existing resistance model for the lateral permeability coefficient of geotextiles is only applicable to geotextiles with high thickness and large porosity. For geotextiles with low thickness and small porosity, the fractal model will be more applicable. Obviously, a single resistance model or fractal model cannot be fully applicable to geotextiles with different thicknesses and porosities. Therefore, the present invention proposes to combine the resistance model with the fractal model, and use the product of the geotextile surface density and thickness as the dividing point between the two models to establish a unified model for predicting the lateral permeability coefficient of geotextiles with different thicknesses and different porosities. This allows geotextiles with different thicknesses and porosities to be calculated using the model in the present invention, and the prediction accuracy is relatively high. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1Schematic diagram of the analysis of the fiber random distribution principle, where the Y axis represents the direction of the fluid, the Z axis represents the direction perpendicular to the fabric plane, the X axis represents the tunnel axis direction, and the V axis represents the extension direction of the fiber plane. v f is the resistance of the fiber to the fluid parallel to the plane of the geotextile; p It is the resistance of the fibers to the fluid perpendicular to the plane of the geotextile.

[0075] Figure 2 The present invention is a flow chart for constructing a comprehensive prediction model for the lateral permeability coefficient of geotextiles.

[0076] Figure 3 Schematic diagram for selecting boundary values ​​of resistance model and fractal model based on error analysis

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

[0078] Figure 5 It is a schematic diagram of the variation of the thickness coefficient of geotextile with the applied load in the thickness test experiment of the embodiment.

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

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

[0081] Figure 8 Comparison between the experimental value of the lateral permeability coefficient in the embodiment and the value predicted by the resistance model.

[0082] Fig. 9 Comparison between the experimental value of the lateral permeability coefficient in the embodiment and the value predicted by the fractal model. DETAILED DESCRIPTION

[0083] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0084] See also Figure 1-3 The present invention provides a method for predicting the lateral permeability coefficient of geotextiles in a mountain tunnel waterproofing layer.

[0085] Geotextiles are usually laid between the secondary lining of the tunnel (hereinafter referred to as "secondary lining") and the initial support (hereinafter referred to as "primary support"). After the water flow outside the tunnel penetrates through the primary support and leaks into the secondary lining, it is guided by the geotextile and flows along the cross-sectional contour of the tunnel to the arch foot of the tunnel 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-sectional contour of the secondary lining, or parallel to the width direction of the geotextile. Geotextiles can be considered to include two parts, one is a solid waterproof layer that is close to the surface of the secondary lining, and the other is a fiber barrier layer that extends outward from the surface of the solid waterproof layer and is distributed in random directions. The more water seeps laterally in the fiber barrier layer, the less water will penetrate into the solid waterproof layer (or waterproof board) and the secondary lining, which can avoid local accumulation of water.

[0086] For the lateral permeability calculation model of geotextiles, the present invention makes the following assumptions: 1) All fiber cross-sections are circular, and the length and diameter are the same; 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 neatly distributed in several groups on 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 relative to the fabric plane; 5) After being subjected to axial external pressure, the inclination angles of the fibers are consistent and inclined toward the fluid direction; 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 a low Reynolds number characteristic.

[0087] S1. Establish a general expression for the thickness factor of geotextiles with respect to the applied load

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

[0089] 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 by regression analysis. T General expressions for imposed loads;

[0090] It should be noted that in S1, for geotextiles with normal external load, the external load will reduce the thickness of the geotextile. The larger the external load G, the greater the thickness T g Based on the thickness test of geotextiles under normal external load, the thickness coefficient K suitable for geotextiles with external load G as parameter is established. T The inventors found during the experiment that the thickness coefficient K T There is a good negative exponential function relationship with the external load G, so the regression analysis method is used to fit the negative exponential function to obtain the general expression of the thickness coefficient with respect to the external load as shown in formula (1.1):

[0091]

[0092] 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 related to the surface density μ of geotextile g There is a linear relationship.

[0093] S2. Establish a lateral permeability prediction model based on resistance theory considering the normal external load

[0094] The solid volume fraction of the geotextile is corrected by the thickness coefficient obtained by S1, and 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-unit theory; according to the random tilt distribution characteristics of the fiber in the plane, the fiber orientation coefficient is used to correct the obtained initial resistance, and the actual fluid resistance per unit length of any fiber in the plane in the water flow direction is obtained;

[0095] For porous media such as geotextiles, the solid volume fraction is calculated by the formula:

[0096]

[0097] Where Φ' is the initial solid volume fraction of the geotextile when it is not subjected to normal external load; μ g is the surface density of geotextile, ρ f is the fiber density, T g is the thickness of geotextile.

[0098] The applied load G will change the solid volume fraction Ф of the geotextile. The larger the applied load G, the greater the thickness coefficient K. T The smaller it is, the larger the solid volume fraction Ф is. Therefore, in S2, the solid volume fraction of geotextile is corrected by the thickness coefficient to obtain formula (2.1):

[0099]

[0100] Where Ф is the solid volume fraction of the geotextile when considering the normal external load.

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

[0102]

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

[0104] When the fibers are evenly distributed, there will be no entanglement between the fibers, and the fluid will only flow in the uniform area between the fibers, that is, only laminar flow will occur. However, when the fibers are randomly distributed, the entangled fibers will produce tiny pores / gaps. When the fluid passes through these pores / gaps, turbulence will occur. Turbulence will cause irregular changes in the direction of the fluid, which is conducive to the blocking effect of the fibers on the fluid. The turbulent state is more in line with the actual situation. The orientation angle α of each fiber i The closer it is to 0° or 180°, the greater the possibility of pores and gaps, the greater the possibility of turbulence, and the greater the resistance.

[0105] Therefore, it is necessary to correct the initial resistance of the fluid to the fiber. Considering the manufacturing process of geotextiles in actual production, it can be considered that the orientation angle α of the fiber in the plane i The values ​​in the interval [0°, 180°] are basically in accordance with the normal distribution. The inventor proposes to assign a weight based on the normal distribution characteristics to the initial fluid resistance of each fiber in the plane, namely, the fiber orientation coefficient P i , in order to consider the comprehensive effect of fiber random distribution 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 according to formula (2.3):

[0106]

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

[0108] For P i , can be calculated by solving the integral of the normal distribution function in numerical software, but this method can only calculate P(α<α i ), that is, when α i When α ≤90°, the probability gradually increases and reaches a maximum value of 0.5 at 90°.i When the fiber orientation angle is >90°, the probability increases and finally approaches 1 at 180°. However, this does not conform to the concept of normal distribution weight: the probability of the fiber orientation angle being 90° should be the largest and the probability gradually decreases on both sides.

[0109] Therefore, P i Determine by the following formula:

[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 fluid direction is defined as plane j, and all fibers in the plane are defined as the jth group of fibers. Since plane j is randomly and randomly tilted relative to the fabric plane, the distribution mode is the same as the distribution mode of the fibers in the plane, so it can also be considered to conform to the normal distribution characteristics, and the distribution of fibers in the inclined plane is similar to that in 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 tilt 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] In the formula, 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] Among them, P j Determine as follows:

[0119]

[0120] In the formula, 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 based on the actual fluid resistance of the fibers and the calculated fiber length. Based on this, the lateral permeability coefficient based on the resistance theory is obtained according to Darcy's law. The lateral permeability coefficient obtained by S1 is corrected to obtain a lateral permeability coefficient prediction model based on the resistance theory that takes into account the effect of external loads, which is recorded as K1 model (also referred to as "lateral permeability coefficient resistance model").

[0122] By taking the resistance component f(α i ) and fiber length l ij Multiply the fluid resistance of a single fiber and add the total number of fibers to get the total fluid resistance F of all fibers in the geotextile, which can be determined by the following formula:

[0123]

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

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

[0126]

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

[0128]

[0129]

[0130] Therefore, the calculation formula for the total fluid resistance F of 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 is a calculation method for the total length l of all fibers of geotextiles based on the inherent parameters of geotextiles:

[0133] First, calculate the total mass of the geotextile fiber m f , assuming that 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, the total length of all fibers in the geotextile can be obtained 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 in a unit volume is equal to the total resistance of the fluid acting on all fibers in the 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 be calculated according to the basic formula of fluid mechanics:

[0143] ΔP=ρgΔh

[0144] Where ρ is the fluid density, g is the acceleration of 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 lateral permeability coefficient can be calculated by calculating the fluid flow rate per unit pressure gradient in the direction of fluid movement:

[0148]

[0149] The calculation formula of the lateral permeability coefficient of geotextiles based on resistance theory is obtained as shown in formula (2.7a):

[0150]

[0151] For geotextiles with external loads, the external load will reduce the thickness of the geotextile. The greater the external load G, the greater the thickness T g The smaller the volume V of the geotextile g Also smaller.

[0152] Therefore, by using the thickness coefficient to modify formula (2.7a), we can obtain the lateral permeability calculation model based on resistance theory that takes into account the normal external load, such as formula (2.8) or (2.8a):

[0153]

[0154]

[0155] Where K1 is the lateral permeability coefficient based on resistance theory.

[0156] It is worth noting that the lateral permeability coefficient model based on resistance theory is more suitable for geotextile materials with large thickness and large porosity. On the one hand, the lateral permeability coefficient model based on 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 geotextiles. On the other hand, the lateral permeability coefficient model based on resistance theory can directly obtain the lateral permeability coefficient based on the macroscopic geotextile parameters, which is also more consistent with reality. However, in actual engineering, there are geotextile materials with lower thickness and smaller porosity. The applicability of the lateral permeability coefficient model based on resistance theory to this kind of geotextile is questionable. In order to make the model provided by the present invention more universal, a lateral permeability coefficient calculation model based on fractal theory is proposed to supplement and revise the above model.

[0157] S3. Establish a lateral permeability prediction model based on fractal theory considering the effect of external loads

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

[0159] Use thickness factor K T The calculation model of transverse permeability coefficient based on fractal theory was modified when the fibers were evenly distributed on the surface of geotextiles to obtain the maximum pore diameter and cross-sectional area of ​​geotextiles.

[0160] According to the fractal dimension, maximum pore diameter and cross-sectional area of ​​geotextiles, a lateral permeability coefficient prediction model based on fractal theory considering the effect of external load is obtained, which is recorded as K2 model (also referred to as "lateral permeability coefficient fractal model");

[0161] When the fibers are evenly distributed on the surface of the geotextile, based on the fractal theory and the modified Hagen-Poiseulle equation, it can be obtained that the fluid flows through a length L t (λ), the seepage flow rate of the capillary with a diameter of λ is:

[0162]

[0163] The total flow rate Q through all capillaries with a cross-sectional area of ​​A is:

[0164]

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

[0166]

[0167] Where 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, and D f is the area fractal dimension of the pore. The above formula is derived for the pore diameter λ to obtain:

[0168]

[0169] Substituting the above formula into the calculation formula of total flow Q, we can get:

[0170]

[0171] Based on the Pitchumani model, for L in the formula t (λ) has an exponential relationship with the pore diameter λ:

[0172]

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

[0174] Therefore, we can obtain:

[0175]

[0176] Given the curved fractal dimension D t and area fractal dimension D f are all values ​​in the interval [1,2], then D t +3-D f is a value greater than 1, and in porous media it is generally:

[0177]

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

[0179]

[0180] Based on Darcy's law, the calculation model of the lateral permeability coefficient based on fractal theory when the fibers are evenly distributed on the surface of geotextiles can be obtained as follows:

[0181]

[0182] For the maximum pore diameter λ max , can be obtained based on the random network theory proposed by Poisson Polyhedron:

[0183]

[0184] Since the cross section of geotextiles can be regarded as composed of pores and fibers, the calculation formula of the cross-sectional area A can be obtained based on the solution of the porosity:

[0185]

[0186] Where Ф is the solid volume fraction of geotextile.

[0187] The above-mentioned fractal model is a prior art and is described in Document 1.

[0188] Literature 1: Ji Lianying. Research on the permeability properties of nonwoven geotextiles[D]. Donghua University, 2010.

[0189] The prediction model provided by the present invention needs to consider the influence of the external load G on the lateral permeability of the geotextile, so it is necessary to max The calculation formula of cross-sectional area A is modified. The applied load G will increase the thickness T of the geotextile. gdecreases, the solid volume fraction Ф of geotextiles will also change. However, since Ф is also related to the fabric thickness T g Therefore, the key to the change of Ф due to the applied load also lies in the fabric thickness T g The response to the external load G.

[0190] Therefore, the thickness factor K is used T The maximum pore diameter λ of the geotextile in this model max , cross-sectional area A, and the maximum pore diameter λ after considering the influence of the external load is obtained. max-G and cross-sectional area A G , combined with the corrected solid volume fraction Φ in S2, we can obtain the lateral permeability calculation model based on fractal theory considering the external load, as shown in formula (3.1):

[0191]

[0192] Where: K2 is the lateral permeability coefficient based on 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 curved fractal dimension, D f is the area fractal dimension; A G is the cross-sectional area of ​​geotextile considering the external pressure load; max-G It is the maximum pore diameter of geotextile considering the external pressure load.

[0193] Among them, the maximum pore diameter λ max-G and cross-sectional area A G Calculate according to formula (3.2)-(3.4) respectively:

[0194]

[0195]

[0196] In the formula: In the formula: K T is the thickness factor of geotextile, T g is the thickness of geotextile, ρ f is the fiber density, d f is the fiber diameter, μ g is the surface density of geotextile, 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, and Ф is the solid volume fraction of the geotextile when considering the normal external load.

[0197] Substituting the above modified formulas into the formula (3.4), the lateral permeability calculation model based on fractal theory considering the external load is obtained:

[0198]

[0199] For the curved fractal dimension D t and area fractal dimension D f The inventor collected the existing geotextile microscopic observation test data (Table 6-1 and Table 6-3 of Document 1, Table 4-1 of Document 2), and obtained D according to the electron microscope test results. t , D f The calculated value of geotextile surface density μ g , fabric thickness T g The product of is the independent variable, and the curved fractal dimension D t and area fractal dimension D f Fitting the dependent variable, we find that D t or D f With μ g T g has a good linear relationship, so D t , D f It can 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] Where c, d, e, and f are all fitting parameters.

[0203] In a specific embodiment, the inventors fitted and obtained four parameters c, d, e, and f as 10.4, 1.9, -31.2, and 1.2, respectively.

[0204] Literature 1: Ji Lianying. Research on the permeability properties of nonwoven geotextiles[D]. Donghua University, 2010.

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

[0206] Inventor's experimental data: D f The measured calculated values ​​are 1.94, 1.932, 1.92, 1.926, D t The measured calculated values ​​are 1.18, 1.23, 1.16, and 1.25.

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

[0208] Combining the K1 model and the K2 model, we get 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 , thereby obtaining the final lateral permeability comprehensive prediction model as shown in formula (4.1a):

[0213]

[0214] Where: K is the lateral permeability coefficient; ρ is the fluid density, g is the gravitational acceleration, 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 taken as 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, respectively calculated the theoretical values ​​of the lateral permeability coefficient of the two models, and compared them with the lateral permeability test values ​​and calculated the error values, thus 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 acceptable error 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; 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] Reference 3: Dai Tingting. Research on horizontal permeability of staple fiber needle-punched geotextile[D]. Zhongyuan University of Technology, 2011.

[0217] Reference 4: Du Zhaohua et al. Theoretical model and application of lateral seepage of composite waterproof layer in mountain tunnels[J]. Journal of Highway and Transportation Research and Development, 2019, 36(7): 98-105.

[0218] After K1 model and K2 model are combined into one model, their values ​​at the critical point may not be equal. If necessary, μ can be obtained. g T g =[μ g T g ] are the endpoint values ​​of the two models, and then the predicted values ​​of the K1 model and the K2 model are corrected according to the endpoint values ​​to make K continuous, as shown in the following formula:

[0219]

[0220] in,

[0221] Geotextiles are composed of fibers and contain a large number of pores. Therefore, in fact, most geotextiles are high-porosity and high-thickness materials, which are more in line with 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 geomembranes. For these geotextiles, the calculation accuracy of the resistance model is low. Therefore, the present invention introduces the idea of ​​zoning, thereby integrating the lateral permeability coefficient prediction models applicable to geotextile materials of different porosities and thicknesses into one model for systematic prediction.

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

[0223] The present invention provides a prediction model for the lateral permeability coefficient of geotextiles in a mountain tunnel waterproofing layer, and its general expression is:

[0224]

[0225] This expression mainly contains two types of unknown parameters, one of which is the thickness coefficient K T , which can be measured by a thickness test based on a normal external load, and is related to the characteristics of the geotextile product; the second is a parameter T related to the solid volume fraction Φ of the geotextile and the lateral permeability coefficient K, which is measured by a lateral permeability test of the geotextile based on a normal external load. Therefore, this embodiment mainly conducts lateral permeability tests, measures the lateral permeability coefficient of the geotextile, and compares the test results with the model calculation results to verify the reliability of this model. However, before using this model to calculate the lateral permeability coefficient, it is necessary to determine the thickness coefficient K of the geotextile used in this embodiment.T .

[0226] Using surface density μ g 100g / m 2 , 200g / m 2 , 300g / m 2 , 400g / m 2 , thickness T g Thickness test and lateral penetration test were carried out for geotextiles with thickness of 1.3, 2.2, 3.1 and 3.7 mm. The length of geotextile was 20 cm and the fiber density was ρ f 1.38×10 3 kg / m 3 , fiber diameter d f The fluid is water, and the density ρ is 1000 kg / m 3 , the viscosity coefficient μ is 1×10 -3 kg / (m·s). The normal external load G2 of the lateral penetration test is 2, 5, 10, 20, 30, 40, and 50 kPa.

[0227] Before analyzing the lateral permeability coefficient, a thickness test of the geotextile under normal external load was carried out. The external load G1 was 2, 5, 10, 30, 50, 70, and 100 kPa. The test was carried out in a graded pressurization manner. The test results are as follows: Figure 4 , obviously the thickness coefficient K T There is a good negative exponential function relationship with the external load G. Therefore, the thickness coefficient K of geotextiles with four different surface densities was obtained by regression analysis. T The expression between the external load G is:

[0228]

[0229] In addition, the inventors also found that the fitting parameters in the above expression are related to the geotextile surface density μ g There is a good linear relationship. In order to calculate the thickness coefficient K of different geotextiles T Unified, the thickness coefficient K T The fitting parameters such as a, y, t and geotextile surface density μ g (g / m 3 ) is fitted, 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 factor K T The formula can be summarized as:

[0234]

[0235] Fiber orientation coefficient P(α i ) and P(θ j ) can objectively reflect the random distribution of fibers in geotextiles. In view of the fact that the manufacturing process of geotextiles often makes the fiber bundles appear vertical or nearly vertical, this embodiment considers that the distribution probability of the fiber orientation angle is approximately centered on the symmetry axis α. i =90° or π / 2 and gradually decreases to both sides, 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 is basically α i It falls in the interval [0°, 180°] or [0, π], so based on the 3σ principle, we can determine σ = 30° or π / 6.

[0236] The integral term in the formula The normcdf function in the numerical calculation software can be used to calculate the normal distribution function integral of P(θ) and P(α), and then the integral function is used to perform double integration operations. For the constant C in the formula of P(θ) and P(α), the inventor extracted the penetration test data in the literature and calculated that C is 1.03.

[0237] To determine the parameter T in the model, it is necessary to determine the solid volume fraction Φ of the geotextile. The solid volume fraction Φ will continue to change under the normal external load G, and its specific value is calculated according to formula (2.1). For the lateral permeability test of geotextiles, when the surface density μ g 100, 200, 300, 400g / m 2 When the thickness coefficient K is T As shown in Table 2 and the solid volume fraction Ф as shown in Table 3.

[0238] Table 2 Thickness coefficient

[0239]

[0240] Table 3 Solid volume fraction

[0241]

[0242] For the lateral permeability prediction model based on fractal theory, for the bending fractal dimension D t and area fractal dimension D f, referring to the existing geotextile microscopic observation test data, the geotextile surface density μ g , fabric thickness T g The product of the variables is the bending fractal dimension D t and area fractal dimension D f The linear fit of , we get:

[0243] D f =10.4·μ g T g +1.9

[0244] D t =-31.2 μ g T g +1.2

[0245] At this point, the parameters in the model proposed by the present invention have been determined, and the calculated values ​​of the resistance model (K1 model) and the fractal model (K2 model) are compared with the results of the lateral penetration test as shown in the figure below: Figure 8-9 .Depend on Figure 8-9 The error between each point on each curve can be calculated by taking the average error value of the same surface density and thickness under different applied loads, as shown in Table 4.

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

[0247] <![CDATA[μ g T g (kg / m)]]> 0.00013 0.00044 0.00093 0.00148 Error-Drag 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 resistance model for μ g T g <5×10 -4 The calculation error of kg / m geotextile is greater than that of μ g T g >5×10 -4 The calculation error of geotextiles, fractal model for μ g T g >5×10 -4 The calculation error of kg / m geotextile is greater than that of μ g T g <5×10 -4 kg / m geotextile calculation error. The above results show that the resistance model is g T g The applicability is poor in the range, and the fractal model has poor applicability in high μ g T g The applicability of the interval is poor, so the present invention proposes a limit value [μ g T g ]=5×10 - 4kg / m as the demarcation point, and the method of combining the high-precision intervals of the resistance model and the fractal model respectively, can make the two models predict the lateral permeability coefficient well within their respective applicable ranges. Of course, according to the results in Table 4, [μ g T g ] Take 6×10 -4 kg / m is also acceptable.

[0249] When applying the model described in the present invention to predict the lateral permeability coefficient of the geotextile of the waterproof layer in an actual mountain tunnel project, it is only necessary to investigate the type of geotextile used in the project (determine its corresponding parameters) and the size of the surrounding rock pressure it is subjected to, and determine the thickness coefficient of the geotextile through a thickness test under normal external load. 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 solution of the present invention and is not intended to limit it. Any modification or replacement of the technical solution made by other technicians in this professional field should be included in the scope of the claims of the present invention as long as it does not deviate from the connotation of the technical solution of the present invention.

Claims

1. A method for predicting the lateral permeability coefficient of geotextiles in mountain tunnel waterproofing layers, characterized by: The steps include: S1. Establish a general expression for the thickness factor 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 geotextiles 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 by regression analysis. T General expressions for imposed loads; S2. Establish a lateral permeability prediction model based on resistance theory considering the normal external load Use thickness factor K T After correcting the solid volume fraction of geotextiles, 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-unit theory; The obtained initial resistance is corrected by using the fiber orientation coefficient to obtain the actual fluid resistance per unit length of any fiber in the plane in the water flow direction; The initial length of the fiber is corrected by using the fiber orientation coefficient to obtain the calculated length of the fiber in the plane in the direction of water flow; After calculating the total fluid resistance of the fibers in the geotextile according to 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. 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 denoted as 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 prediction model based on fractal theory considering the effect of external loads According to the microscopic test data of geotextiles in the prior art, an empirical formula of fractal dimension is established about the product of geotextile surface density and thickness; Use thickness factor K T The calculation model of transverse permeability coefficient based on fractal theory was modified when the fibers were evenly distributed on the surface of geotextiles 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 effect of external load is obtained, which is denoted as K2 model. S4. Establish a comprehensive prediction model for geotextile modified lateral permeability coefficient Combining the K1 model and the K2 model, we get the comprehensive prediction model of geotextile modified lateral permeability coefficient: Wherein, K is the lateral permeability coefficient; K1 is the lateral permeability coefficient based on the resistance theory; K2 is the lateral permeability coefficient based on the 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, characterized in that: 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: In the formula, 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, characterized in that: 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, characterized in that: In S2, the initial fluid resistance per unit length of any fiber in any plane parallel to the water flow direction is determined according to 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 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, characterized in that: In S2, the actual fluid resistance per unit length of any fiber in any plane parallel to the water flow direction in 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, characterized in that: In S2, the calculated length of any fiber in any plane parallel to the water flow in the direction of the water flow is as follows: lij=l0·sinθj·P(θj) (2.4) Where, lij is the calculated length of any fiber in the plane parallel to the water flow in the direction of the fluid; 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, characterized in that: 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 fiber; α is the orientation angle of the fiber 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; Among them, 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, characterized in that: In S2, the lateral permeability 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, characterized in that: In S3, the lateral permeability 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 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, characterized in that: 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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