Analysis method of nonlinear seepage field in submarine tunnel based on mirror superposition theory

Abstract

The present invention discloses a method for analyzing the nonlinear seepage field of an undersea tunnel based on the mirror image superposition theory, including determining the geological conditions of the undersea tunnel excavation section, the geological conditions being that the undersea tunnel excavation section is located in a homogeneous stratum, treating the homogeneous stratum as being distributed circumferentially around the undersea tunnel section, and determining the inner / outer diameters of each homogeneous stratum to the center of the tunnel section and the permeability coefficients corresponding to each homogeneous stratum; superimposing the potential of the actual undersea tunnel and the virtual undersea tunnel to form the undersea tunnel seepage field, calculating the undersea tunnel seepage field to obtain the surrounding rock seepage field parameters, the grouting ring seepage field parameters and the lining seepage field parameters; predicting the undersea tunnel seepage field based on the surrounding rock seepage field, the grouting ring seepage field and the lining seepage field parameters. The method solves the problem that the existing undersea tunnel seepage field cannot simultaneously consider the nonlinear seepage of the grouting ring and the lining under different seepage conditions, and reduces the safety and applicability before and after the construction of the undersea tunnel.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering, and in particular to a nonlinear seepage field analysis method for a submarine tunnel based on the mirror image superposition theory. Background Art

[0002] The national economy is growing rapidly under the support of a fast and efficient transportation system, and the transportation layout with multiple forms and high technology is becoming increasingly rich. From the perspective of economic development and long-term transportation planning, undersea tunnels are an important form of tunnel transportation. Undersea tunnels are important transportation routes that connect the industrial economy on both sides of the sea area and promote the coordinated development of both sides. However, undersea tunnels still have many problems in terms of structural safety during construction and anti-seepage stability during operation. For example, underestimating the amount of water inflow in the tunnel and the pore pressure on the lining will lead to water inrush in the tunnel and damage to the lining structure, while overestimating it will lead to economic waste. Therefore, it is necessary to predict the tunnel seepage field to ensure its safety, applicability and economy before and after tunnel construction.

[0003] At present, most of the existing analyses of the seepage field of submarine tunnels are based on the individual consideration of the factors affecting the seepage field. It is difficult to reflect the internal stress and displacement distribution of the tunnel surrounding rock and the structural force and deformation characteristics during the construction period under the joint action of the submarine tunnel stress field and seepage field. It is also impossible to jointly predict the nonlinear seepage field of the submarine tunnel based on the different seepage conditions of the grouting ring and lining, which reduces its safety and applicability before and after tunnel construction. Summary of the invention

[0004] The present invention provides a method for analyzing the nonlinear seepage field of a submarine tunnel based on the mirror superposition theory, so as to overcome the problem that the existing submarine tunnel seepage field cannot predict the nonlinear seepage field of the submarine tunnel according to different seepage conditions of the grouting ring and the lining, thereby reducing the problem of its safety and applicability before and after tunnel construction.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for analyzing nonlinear seepage field in submarine tunnels based on mirror superposition theory, including:

[0007] Step S1: determining the geological conditions of the subsea tunnel excavation section, wherein the geological conditions are that the subsea tunnel excavation section is located in a homogeneous stratum, and the homogeneous stratum is located below the seawater, and confirming the dynamic water level at the surface height of the homogeneous stratum;

[0008] The homogeneous stratum includes a surrounding rock layer, a grouting ring layer and a lining layer;

[0009] Step S2: The homogeneous strata are regarded as being distributed circumferentially around the cross section of the submarine tunnel, and the inner / outer diameters of each homogeneous stratum to the center of the tunnel cross section and the permeability coefficients corresponding to each homogeneous stratum are determined;

[0010] The permeability coefficient includes the permeability coefficient of surrounding rock, the permeability coefficient of grouting ring and the permeability coefficient of lining;

[0011] Step S3: With the tunnel axis direction as the z-axis, the horizontal surface of the surrounding rock as the x-axis, and the horizontal surface perpendicular to the surrounding rock as the y-axis, based on the mirror superposition principle, the x-axis is used as a mirror to map the actual submarine tunnel to obtain a virtual submarine tunnel;

[0012] Superimposing the potential of the actual submarine tunnel and the virtual submarine tunnel to obtain a submarine tunnel seepage field model, wherein the submarine tunnel seepage field model includes surrounding rock seepage field, grouting circle seepage field and lining seepage field;

[0013] Step S4: Calculate the surrounding rock seepage field based on Darcy's seepage law to obtain surrounding rock seepage field parameters, wherein the surrounding rock seepage field parameters include water inflow at the cross section of the submarine tunnel, total water head in the surrounding rock area, and pore pressure in the surrounding rock area;

[0014] Step S5: Based on the Hansbo nonlinear seepage model, the seepage field of the grouting circle and the seepage field of the lining are calculated to obtain the seepage parameters of the grouting circle and the seepage parameters of the lining;

[0015] The grouting circle seepage parameters include the grouting circle seepage volume, the grouting circle total water head and the grouting circle pore pressure;

[0016] The lining seepage parameters include lining seepage, lining total water head and lining pore pressure;

[0017] Step S6: Analyze and predict the seepage field of the submarine tunnel according to the surrounding rock seepage parameters, the grouting circle seepage field parameters and the lining seepage field parameters.

[0018] Furthermore, the calculation formula of the dynamic water level at the surface height of the homogeneous stratum is:

[0019] ξ ci =H 0 +H ci cos(w ci tg ci )

[0020] Among them, H 0 represents the average sea level during the analysis period, H ci Indicates the dynamic water level amplitude, w ci represents the dynamic water level cycle, t represents the dynamic water level time, g ci Indicates the phase of the dynamic water level.

[0021] Furthermore, in step S4, the surrounding rock seepage field parameters are calculated based on Darcy's seepage law, specifically:

[0022] Step S4.1: The cross-sectional center of the actual submarine tunnel is defined as the sink, and the cross-sectional center of the virtual submarine tunnel is defined as the source. Then the distances from any point M(x, y) on the submarine tunnel calculation cross-sectional area to the source and sink are:

[0023]

[0024] Among them, r 1 represents the distance from any point M(x,y) to the sink; r 2 represents the distance from any point M(x,y) to the source; h represents the distance from the sink to the horizontal surface of the surrounding rock;

[0025] Step S4.2: The seepage pattern of the soil conforms to Darcy seepage:

[0026]

[0027] Where i represents the hydraulic gradient of the surrounding rock; k represents the permeability coefficient; v represents the seepage velocity of the surrounding rock;

[0028] When the submarine tunnel is a single-hole circular tunnel, the flow rate flowing through each section of the tunnel is:

[0029] Q s =2πrv (3)

[0030] Where: Q s represents the water inflow of the calculated section of the surrounding rock layer; r represents the distance from any point of the calculated section to the center of the submarine tunnel. Substituting formula (2) into formula (3), we get We can get:

[0031]

[0032] Where: Indicates the total water head of the surrounding rock layer; Q s Indicates the water inflow of the calculated section of the surrounding rock layer; k s represents the permeability coefficient of the surrounding rock; r represents the distance from any point of the calculation section to the center of the submarine tunnel;

[0033] Integrating formula (4) yields:

[0034]

[0035] Where: C represents the integral constant; Q s Indicates the water inflow of the calculated section of the surrounding rock layer; k s represents the permeability coefficient of the surrounding rock; r represents the distance from any point on the calculation section to the center of the circle;

[0036] Step S4.3: The total water head of the surrounding rock layer is obtained from the water momentum of any point in the mirror normal plane according to the principle of potential superposition. The calculation formula is:

[0037]

[0038] Where: Indicates the total water head of the surrounding rock layer; Q sj represents the seepage volume of the jth tunnel, and takes a positive value when it flows in and a negative value when it flows out; r j represents the distance from any point on the calculated section to the center point of the jth tunnel; C 1 represents the value of a constant to be determined;

[0039] When 1 =r 2 time; that is, y = h, So we can get:

[0040]

[0041] When 1 =r g When r g >>h, then r 2 =2h:

[0042]

[0043] Where: r g Indicates the radius of the grouting circle; h gt represents the total water head at the outer boundary of the grouting circle; ξ ci represents the dynamic water level at the surface height of the homogeneous stratum; h represents the distance from the sink to the horizontal surface of the surrounding rock; It represents the total water head of the seepage field in the submarine tunnel;

[0044] Step S4.4: According to formula (1) to formula (8), the seepage volume in the surrounding rock of the submarine tunnel, the water head in the surrounding rock of the submarine tunnel and the pore pressure distribution function in the surrounding rock of the submarine tunnel can be obtained as follows:

[0045]

[0046] Where: represents the total water head of the surrounding rock area in the xy coordinate system; p s (x,y) represents the pore pressure in the surrounding rock area in the xy coordinate system; h s represents the position head of the surrounding rock area; β represents the ratio of the radius of the grouting circle to the distance from the sink to the horizontal surface of the surrounding rock, and β = r g / 2h; γ w Indicates the weight of water; ci The dynamic water level represents the height of action on the surface of a homogeneous stratum;

[0047] Furthermore, in step S5, the grouting circle seepage field and the lining seepage field are calculated based on the Hansbo nonlinear seepage model to obtain the grouting circle seepage parameters and the lining seepage parameters, specifically:

[0048] Step S5.1: Hansbo nonlinear seepage model is

[0049]

[0050]

[0051] Where: k 0s represents the permeability coefficient of the curve segment of the nonlinear seepage model; k 0 It is expressed as the permeability coefficient of the straight line segment; m represents the nonlinear parameter; i 0 represents the first critical hydraulic gradient; i l represents the second critical hydraulic gradient;

[0052] Step S5.2: Define the fluid as incompressible and the seepage direction is perpendicular to the y-axis. The continuity equation of the fluid seepage in the grouting circle is expressed as:

[0053]

[0054] Decompose the velocity vector in the seepage field:

[0055] u=v i cosθ,v=v i sinθ,v i =k 0s i m (13)

[0056] Where: u represents the seepage velocity in the x-axis direction; v represents the seepage velocity in the y-axis direction; v i represents the seepage velocity in any direction; i m represents the hydraulic gradient to the power of m; k os represents the permeability coefficient of the curve segment of the nonlinear seepage model; θ represents the angle between the seepage velocity in any direction and the x-axis direction;

[0057] Step S5.3: Based on the fact that the hydraulic gradient direction of the seepage is the same as the streamline direction, the hydraulic gradient can be expressed as:

[0058]

[0059] According to the radial seepage condition of circular cross section of submarine tunnel, it can be obtained that:

[0060]

[0061] Where: It is expressed as the total water head; i represents the hydraulic gradient of the surrounding rock; r represents the distance from any point of the calculation section to the center of the circle;

[0062] Substituting formulas (10), (11), (13), (14), and (15) into formula (12) for simplification, we can obtain the nonlinear continuity equation of the fluid in the polar coordinate form of the grouting ring and the lining under the radial seepage condition of the submarine tunnel:

[0063] The nonlinear continuity equation of the fluid in the grouting circle in polar coordinate form is:

[0064]

[0065] Where: Indicates the total water head in the grouting circle; m g Represents the first nonlinear parameter of the grouting area; i lg Represents the second nonlinear parameter of the grouting area; r 1g Indicates the distance from any point in the grouting area to the actual tunnel center;

[0066] The nonlinear continuity equation of the fluid in the lining polar coordinate form is:

[0067]

[0068] Where: Indicates the total water head in the lining area; m l represents the nonlinear parameter of the first lining zone; i ll represents the nonlinear parameter of the second lining area; r 2l It indicates the distance from any point in the lining area to the actual center of the tunnel;

[0069] Step S5.4: Solve formula (16) and formula (17) by separation of variables method, and substitute boundary condition (18) to obtain the total water head of the grouting circle and the total water head of the lining:

[0070]

[0071] Where: h gt Indicates the water head outside the grouting area; h lt Indicates the water head outside the lining area; h 0t Indicates the water head inside the lining area; r 0 Indicates the inner radius of the lining; r l represents the outer radius of the submarine tunnel excavated inside the rock mass; r represents the distance from any point on the calculated section to the center of the circle;

[0072] Total water head of grouting ring for:

[0073]

[0074] Total head in lining area for:

[0075]

[0076] Step S5.5: Integrate formula (19) and formula (20) to obtain the seepage of the grouting ring and the seepage of the lining:

[0077] Seepage volume of grouting ring Q g :

[0078]

[0079] Lining seepage Q l for:

[0080]

[0081] Step S5.6: Convert formula (19) and formula (20) into rectangular coordinates to obtain the total water head H of the grouting circle in the xy coordinate system: g(x,y) The total water head H in the lining area in the xy coordinate system l(x,y) :

[0082] Total water head H of grouting circle in xy coordinate system of seepage field in submarine tunnel g(x,y) The calculation formula is:

[0083]

[0084] Total water head H in the lining area of ​​the submarine tunnel seepage field in the xy coordinate system l(x,y ) is calculated as:

[0085]

[0086]

[0087] Where: p lt represents the pore pressure at the outer boundary of the lining; p 0t represents the pore pressure at the inner boundary of the lining area; h gt Represents the water head outside the grouting area; r 0 Indicates the inner radius of the lining; r l represents the outer radius of the submarine tunnel excavated inside the rock mass; γ w represents the gravity of water; h represents the distance from the sink to the horizontal surface of the surrounding rock; x represents the distance from any point on the calculation section of the submarine tunnel to the y axis; y represents the distance from any point on the calculation section of the submarine tunnel to the x axis; A 1 Represents the first variable parameter of the grouting ring; A 2 Represents the second variable parameter of the grouting ring; A 3 Represents the third variable parameter of the grouting ring; A 4Represents the fourth variable parameter of the grouting ring; A 5 Represents the fifth variable parameter of the grouting ring; A 6 Represents the first variable parameter of the lining; A 7 A represents the second variable parameter of the lining; 8 A represents the third variable parameter of the lining; 9 A represents the fourth variable parameter of the lining; 10 The fifth variable parameter representing the lining;

[0088] Step S5.7: According to the total head function of submarine tunnel seepage equal to the sum of pressure head function and position head function, the pore pressure of grouting circle and lining pore pressure are obtained, and the calculation formula is:

[0089]

[0090] Where: H (x,y) It is expressed as the total water head of the seepage field of the submarine tunnel in the xy coordinate system; P (x,y) represents the pore pressure of the submarine tunnel seepage field in the xy coordinate system; γ w Indicates the weight of water;

[0091] The calculation formula of pore pressure in grouting ring is:

[0092]

[0093] The calculation formula of lining pore pressure is:

[0094]

[0095] Furthermore, in step S6, the seepage field of the submarine tunnel is analyzed and predicted according to the surrounding rock seepage parameters, the grouting ring seepage field parameters and the lining seepage field parameters, specifically:

[0096] Step S6.1: Analyze the seepage mode of the grouting ring and the lining based on the seepage continuity condition and obtain the water head h outside the grouting area gt The water head outside the lining area h lt ;

[0097] The seepage continuity condition is that the surrounding rock seepage is equal to the grouting ring seepage and equal to the lining seepage;

[0098] Step S6.2: If both the grouting ring and the lining are Hansbo nonlinear seepage curve segments, that is, m g >1,i≤i lg ;m l >1,i≤i ll Under the condition, then from formula (9), formula (21) and formula (22), we can get

[0099]

[0100] If the lining is a Hansbo nonlinear seepage curve segment and the grouting circle is a Hansbo nonlinear seepage straight line segment, that is, m g >1,i≤i lg ;m l >1,i>i ll Under the condition; from formula (9), formula (21) and formula (22), we can get

[0101]

[0102] If the grouting ring and the lining are both Hansbo nonlinear seepage straight line segments, that is, m g =1;m l =1, from formula (9), formula (21) and formula (22) we can get

[0103]

[0104] Step S6.3: Calculate the water head h outside the grouting area according to formulas (29), (30) and (31): gt The water head outside the lining area h lt ;

[0105] h gt With h lt Substituting back into the calculation formulas of surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters, the surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters under current seepage conditions are obtained;

[0106] The seepage field of the submarine tunnel is predicted according to the surrounding rock seepage field parameters, the grouting circle seepage field parameters and the lining seepage field parameters under the current seepage conditions.

[0107] Beneficial effects: The present invention provides a method for analyzing the nonlinear seepage field of an undersea tunnel based on the mirror superposition theory. By simultaneously analyzing the seepage field of the undersea tunnel under different seepage modes of the grouting ring and the lining, the change of the seepage field of the undersea tunnel under the condition of water level fluctuation is more completely and accurately described, and the influence of the amplitude, period and phase of the dynamic water level on the seepage field of the undersea tunnel can be studied. The water inflow, pore pressure and water head of the surrounding rock, grouting ring and lining in the undersea tunnel can be calculated more accurately, which improves the accuracy of the prediction of the nonlinear seepage field of the undersea tunnel and reduces the problems of safety and applicability before and after the tunnel construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0109] Figure 1 It is a flowchart of the steps of the nonlinear seepage field analysis method of a submarine tunnel based on the mirror image superposition theory of the present invention;

[0110] Figure 2 It is a flowchart of the nonlinear seepage field analysis method of a submarine tunnel based on the mirror image superposition theory of the present invention;

[0111] Figure 3 It is a simplified calculation model of the submarine tunnel seepage field for analyzing the nonlinear seepage field of the submarine tunnel based on the mirror image superposition theory of the present invention;

[0112] Figure 4 It is a schematic diagram of the mirror method of the nonlinear seepage field analysis method of the submarine tunnel based on the mirror superposition theory of the present invention;

[0113] Figure 5 The invention discloses a Hansbo nonlinear seepage model for analyzing the nonlinear seepage field of a submarine tunnel based on the mirror image superposition theory. DETAILED DESCRIPTION

[0114] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0115] This embodiment provides a method for analyzing the nonlinear seepage field of a submarine tunnel based on the mirror superposition theory. Figure 1 to Figure 2 As shown, it includes: step S1: determining the geological conditions of the submarine tunnel excavation section, the geological conditions being that the submarine tunnel excavation section is located in a homogeneous stratum, and the homogeneous stratum is located below seawater, and confirming the dynamic water level of the surface action height of the homogeneous stratum;

[0116] Step S2: According to the basic assumption theory, the homogeneous strata are regarded as being distributed annularly around the section of the submarine tunnel, and the inner / outer diameters of each homogeneous stratum to the center of the tunnel section and the permeability coefficients corresponding to each homogeneous stratum are determined; the homogeneous strata include surrounding rock layers, grouting ring layers and lining layers; the permeability coefficients include surrounding rock permeability coefficients, grouting ring permeability coefficients and lining permeability coefficients; the surrounding rock layer is a saturated, homogeneous, continuous and isotropic semi-infinite rock medium, and the semi-infinite rock medium is to assume that the rock mass is infinite, and the influence of the lower boundary is not considered;

[0117] Step S3: taking the tunnel axis direction as the z-axis, the horizontal surface of the surrounding rock as the x-axis, and the horizontal surface perpendicular to the surrounding rock as the y-axis, based on the mirror superposition principle, the x-axis is used as a mirror to map the actual submarine tunnel to obtain a virtual submarine tunnel; superimposing the potential of the actual submarine tunnel and the virtual submarine tunnel to obtain a submarine tunnel seepage field model, wherein the submarine tunnel seepage field model includes the surrounding rock seepage field, the grouting ring seepage field, and the lining seepage field;

[0118] Step S4: Calculate the surrounding rock seepage field based on Darcy's seepage law to obtain surrounding rock seepage field parameters, wherein the surrounding rock seepage field parameters include water inflow at the cross section of the submarine tunnel, total water head in the surrounding rock area, and pore pressure in the surrounding rock area;

[0119] Step S5: Based on the Hansbo nonlinear seepage model, the grouting circle seepage field and the lining seepage field are calculated to obtain the grouting circle seepage parameters and the lining seepage parameters; the grouting circle seepage parameters include the grouting circle seepage amount, the grouting circle total water head and the grouting circle pore pressure; the lining seepage parameters include the lining seepage amount, the lining total water head and the lining pore pressure;

[0120] Step S6: Analyze and predict the seepage field of the submarine tunnel according to the surrounding rock seepage parameters, the grouting circle seepage field parameters and the lining seepage field parameters.

[0121] The invention provides a method for analyzing the nonlinear seepage field of a submarine tunnel based on the mirror image superposition theory, which solves the problem that the existing submarine tunnel calculation method cannot simultaneously consider the situation that both the grouting ring and the lining are nonlinear seepage, and introduces the Hansbo nonlinear seepage model, which can consider the situation that the seepage mode enters the linear seepage when the water pressure is too high, so that the different seepage modes of the grouting ring and the lining under different water pressure conditions can be discussed in different situations, thereby more completely and accurately describing the change of the seepage field of the submarine tunnel under the condition of water level fluctuation, and can study the influence of the amplitude, period and phase of the dynamic water level on the seepage field of the submarine tunnel, solve the tunnel water inflow and the pore pressure borne by the grouting ring and the lining, so that the simulation of the nonlinear seepage field of the submarine tunnel is more real and reliable, which is convenient for better selection of the grouting ring and the lining materials in actual situations, improves the accuracy of the prediction of the nonlinear seepage field of the submarine tunnel, and reduces the problems of safety and applicability before and after the tunnel construction.

[0122] In a specific embodiment, the calculation formula of the dynamic water level at the surface height of the homogeneous formation is:

[0123] ξ ci =H 0 +H ci cos(w ci tg ci )

[0124] Among them, H 0 represents the average sea level during the analysis period, H ci Indicates the dynamic water level amplitude, w ci represents the dynamic water level cycle, t represents the dynamic water level time, g ci Indicates the phase of the dynamic water level;

[0125] like Figure 3 As shown in the simplified schematic diagram of the submarine tunnel under the action of dynamic water level, the ground is taken as the potential zero surface, a lining area is arranged outside the submarine tunnel, a grouting area is arranged between the lining area and the surrounding rock layer, and H is set 0 is the average water level during the analysis period, h 1 is the highest water level, h 2 is the lowest water level, and a hole with an outer radius of r is excavated inside the rock mass. l The distance from the tunnel center to the ground surface is h, and the surrounding rock permeability is k. s ; The inner radius of the lining is r 0 ; The permeability coefficient is k l ; The radius of the grouting circle is r g ; The permeability coefficient is k g .

[0126] In a specific embodiment, in step S4, the surrounding rock seepage field is calculated based on Darcy's seepage law to obtain the surrounding rock seepage field parameters, specifically:

[0127] like Figure 4 As shown in the figure, the solution of the surrounding rock seepage field belongs to the semi-infinite plane problem. The influence of the boundary of the semi-infinite plane on the seepage field can be regarded as taking the boundary (the plane where the top of the surrounding rock is located) as a mirror to map the actual tunnel. The position of the actual tunnel symmetrical to the boundary is imaged as a virtual tunnel. The actual tunnel and the virtual tunnel are superimposed with potential, and the resulting seepage field is equal to the seepage field formed by considering the boundary influence, and the mapped boundary remains as an equipotential line.

[0128] Step S4.1: The cross-sectional center of the actual submarine tunnel is defined as the sink, and the cross-sectional center of the virtual submarine tunnel is defined as the source. Then the distances from any point M(x, y) on the submarine tunnel calculation cross-sectional area to the source and sink are:

[0129]

[0130] Among them, r 1 represents the distance from any point M(x,y) to the sink; r 2 represents the distance from any point M(x,y) to the source; h represents the distance from the sink to the horizontal surface of the surrounding rock;

[0131] Step S4.2: The seepage pattern of the soil conforms to Darcy seepage:

[0132]

[0133] Where i represents the hydraulic gradient of the surrounding rock; k represents the permeability coefficient; v represents the seepage velocity of the surrounding rock;

[0134] When the submarine tunnel is a single-hole circular tunnel, the flow rate flowing through each section of the tunnel is:

[0135] Q s =2πrv (3)

[0136] Where: Q s represents the water inflow of the calculated section of the surrounding rock layer; r represents the distance from any point of the calculated section to the center of the submarine tunnel. Substituting formula (2) into formula (3), we get We can get:

[0137]

[0138] Where: Indicates the total water head of the surrounding rock layer; Q s Indicates the water inflow of the calculated section of the surrounding rock layer; k s represents the permeability coefficient of the surrounding rock; r represents the distance from any point of the calculation section to the center of the submarine tunnel;

[0139] Integrating formula (4) yields:

[0140]

[0141] Where: C represents the integral constant; Q s Indicates the water inflow of the calculated section of the surrounding rock layer; k s represents the permeability coefficient of the surrounding rock; r represents the distance from any point on the calculation section to the center of the circle;

[0142] Step S4.3: The total water head of the surrounding rock layer is obtained from the water momentum of any point in the mirror normal plane according to the principle of potential superposition. The calculation formula is:

[0143]

[0144] Where: Indicates the total water head of the surrounding rock layer; Q sj represents the seepage volume of the jth tunnel, and takes a positive value when it flows in and a negative value when it flows out; r j represents the distance from any point on the calculated section to the center point of the jth tunnel; C 1 represents the value of a constant to be determined;

[0145] When 1 =r 2 time; that is, y = h, So we can get:

[0146]

[0147] When 1 =r g When r g >>h, then r 2 =2h:

[0148]

[0149] Where: r g Indicates the radius of the grouting circle; h gt represents the total water head at the outer boundary of the grouting circle; ξ ci represents the dynamic water level at the surface height of the homogeneous stratum; h represents the distance from the sink to the horizontal surface of the surrounding rock; It represents the total water head of the seepage field in the submarine tunnel;

[0150] Step S4.4: According to formula (1) to formula (8), the seepage volume in the surrounding rock of the submarine tunnel, the water head in the surrounding rock of the submarine tunnel and the pore pressure distribution function in the surrounding rock of the submarine tunnel can be obtained as follows:

[0151]

[0152] Where: represents the total water head of the surrounding rock area in the xy coordinate system; p s(x,y) represents the pore pressure in the surrounding rock area in the xy coordinate system; h s represents the position head of the surrounding rock area; β represents the ratio of the radius of the grouting circle to the distance from the sink to the horizontal surface of the surrounding rock, and β = r g / 2h; γ w Indicates the weight of water; ci The dynamic water level represents the height of action on the surface of a homogeneous stratum;

[0153] In a specific embodiment, Figure 5 As shown, in step S5, the seepage field of the grouting circle and the seepage field of the lining are calculated based on the Hansbo nonlinear seepage model to obtain the seepage parameters of the grouting circle and the seepage parameters of the lining, which are specifically:

[0154] Step S5.1: The grouting ring and lining are low permeability media, and their internal seepage mode will deviate from Darcy seepage, which is consistent with non-Darcy seepage. The Hansbo nonlinear seepage model is introduced; the Hansbo nonlinear seepage model is

[0155]

[0156]

[0157] Where: k 0s represents the permeability coefficient of the curve segment of the nonlinear seepage model; k 0 It is expressed as the permeability coefficient of the straight line segment; m represents the nonlinear parameter; i 0 represents the first critical hydraulic gradient; i l represents the second critical hydraulic gradient; where i 0 with i l All are fixed values ​​set by experimental measurement;

[0158] Step S5.2: Define the fluid as incompressible and the seepage direction is perpendicular to the y-axis. The continuity equation of the fluid seepage in the grouting circle is expressed as:

[0159]

[0160] Decompose the velocity vector in the seepage field:

[0161] u=v i cosθ,v=v i sinθ,v i =k 0s i m (13)

[0162] Where: u represents the seepage velocity in the x-axis direction; v represents the seepage velocity in the y-axis direction; v i represents the seepage velocity in any direction; i mrepresents the hydraulic gradient to the power of m; k os represents the permeability coefficient of the curve segment of the nonlinear seepage model; θ represents the angle between the seepage velocity in any direction and the x-axis direction;

[0163] Step S5.3: Based on the fact that the hydraulic gradient direction of the seepage is the same as the streamline direction, the hydraulic gradient can be expressed as:

[0164]

[0165] According to the radial seepage condition of circular cross section of submarine tunnel, it can be obtained that:

[0166]

[0167] Where: It is expressed as the total water head; i represents the hydraulic gradient of the surrounding rock; r represents the distance from any point of the calculation section to the center of the circle;

[0168] Substituting formulas (10), (11), (13), (14), and (15) into formula (12) for simplification, we can obtain the nonlinear continuity equation of the fluid in the polar coordinate form of the grouting ring and the lining under the radial seepage condition of the submarine tunnel:

[0169] The nonlinear continuity equation of the fluid in the grouting circle in polar coordinate form is:

[0170]

[0171] Where: Indicates the total water head in the grouting circle; m g Represents the first nonlinear parameter of the grouting area; i lg Represents the second nonlinear parameter of the grouting area; r 1g Indicates the distance from any point in the grouting area to the actual tunnel center;

[0172] The nonlinear continuity equation of the fluid in the lining polar coordinate form is:

[0173]

[0174] Where: Indicates the total water head in the lining area; m l represents the nonlinear parameter of the first lining zone; i ll represents the nonlinear parameter of the second lining area; r 2l It indicates the distance from any point in the lining area to the actual center of the tunnel;

[0175] Step S5.4: Solve formula (16) and formula (17) by separation of variables method, and substitute boundary condition (18) to obtain the total water head of the grouting circle and the total water head of the lining:

[0176]

[0177] Where: h gt Indicates the water head outside the grouting area; h lt Indicates the water head outside the lining area; h 0t Indicates the water head inside the lining area; r 0 Indicates the inner radius of the lining; r l represents the outer radius of the submarine tunnel excavated inside the rock mass; r represents the distance from any point on the calculated section to the center of the circle;

[0178] Total water head of grouting ring for:

[0179]

[0180] Total head in lining area for:

[0181]

[0182] Step S5.5: Integrate formula (19) and formula (20) to obtain the seepage of the grouting ring and the seepage of the lining:

[0183] Seepage volume of grouting ring Q g :

[0184]

[0185] Lining seepage Q l for:

[0186]

[0187] Step S5.6: Convert formula (19) and formula (20) into rectangular coordinates to obtain the total water head H of the grouting circle in the xy coordinate system: g(x,y) The total water head H in the lining area in the xy coordinate system l(x,y) :

[0188] Total water head H of grouting circle in xy coordinate system of seepage field in submarine tunnel g(x,y) The calculation formula is:

[0189]

[0190] Total water head H in the lining area of ​​the submarine tunnel seepage field in the xy coordinate system l(x,y ) is calculated as:

[0191]

[0192]

[0193] Where: p ltrepresents the pore pressure at the outer boundary of the lining; p 0t represents the pore pressure at the inner boundary of the lining area; h gt Represents the water head outside the grouting area; r 0 Indicates the inner radius of the lining; r l represents the outer radius of the submarine tunnel excavated inside the rock mass; γ w represents the gravity of water; h represents the distance from the sink to the horizontal surface of the surrounding rock; x represents the distance from any point on the calculation section of the submarine tunnel to the y axis; y represents the distance from any point on the calculation section of the submarine tunnel to the x axis; A 1 Represents the first variable parameter of the grouting ring; A 2 Represents the second variable parameter of the grouting ring; A 3 Represents the third variable parameter of the grouting ring; A 4 Represents the fourth variable parameter of the grouting ring; A 5 Represents the fifth variable parameter of the grouting ring; A 6 Represents the first variable parameter of the lining; A 7 A represents the second variable parameter of the lining; 8 A represents the third variable parameter of the lining; 9 A represents the fourth variable parameter of the lining; 10 The fifth variable parameter representing the lining;

[0194] Step S5.7: According to the total head function of submarine tunnel seepage equal to the sum of pressure head function and position head function, the pore pressure of grouting circle and lining pore pressure are obtained, and the calculation formula is:

[0195]

[0196] Where: H (x,y) It is expressed as the total water head of the seepage field of the submarine tunnel in the xy coordinate system; P (x,y) represents the pore pressure of the submarine tunnel seepage field in the xy coordinate system; γ w Indicates the weight of water;

[0197] The calculation formula of pore pressure in grouting ring is:

[0198]

[0199] The calculation formula of lining pore pressure is:

[0200]

[0201] In a specific embodiment, in step S6, the seepage field of the submarine tunnel is analyzed and predicted according to the surrounding rock seepage parameters, the grouting ring seepage field parameters and the lining seepage field parameters, specifically:

[0202] Step S6.1: Analyze the seepage mode of the grouting ring and the lining based on the seepage continuity condition and obtain the water head h outside the grouting area gt The water head outside the lining area h lt ;

[0203] The seepage continuity condition is that the surrounding rock seepage is equal to the grouting ring seepage and equal to the lining seepage;

[0204] Step S6.2: If both the grouting ring and the lining are Hansbo nonlinear seepage curve segments, that is, m g >1,i≤i lg ;m l >1,i≤i ll Under the condition, then from formula (9), formula (21) and formula (22), we can get

[0205]

[0206] If the lining is a Hansbo nonlinear seepage curve segment and the grouting circle is a Hansbo nonlinear seepage straight line segment, that is, m g >1,i≤i lg ;m l >1,i>i ll Under the condition; from formula (9), formula (21) and formula (22), we can get

[0207]

[0208] If the grouting ring and the lining are both Hansbo nonlinear seepage straight line segments, that is, m g =1;m l =1, from formula (9), formula (21) and formula (22) we can get

[0209]

[0210] Step S6.3: Calculate the water head h outside the grouting area according to formulas (29), (30) and (31): gt The water head outside the lining area h lt ;

[0211] h gt With h lt Back-substitute into the calculation formulas of surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters to obtain surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters under current seepage conditions; predict the seepage field of the submarine tunnel according to the surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters under the current seepage conditions.

[0212] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing nonlinear seepage field in submarine tunnels based on the mirror superposition theory, characterized in that: include: Step S1: determining the geological conditions of the subsea tunnel excavation section, wherein the geological conditions are that the subsea tunnel excavation section is located in a homogeneous stratum, and the homogeneous stratum is located below the seawater, and confirming the dynamic water level at the surface height of the homogeneous stratum; The homogeneous stratum includes a surrounding rock layer, a grouting ring layer and a lining layer; Step S2: The homogeneous strata are regarded as being distributed circumferentially around the cross section of the submarine tunnel, and the inner / outer diameters of each homogeneous stratum to the center of the tunnel cross section and the permeability coefficients corresponding to each homogeneous stratum are determined; The permeability coefficient includes the permeability coefficient of surrounding rock, the permeability coefficient of grouting ring and the permeability coefficient of lining; Step S3: With the tunnel axis direction as the z-axis, the horizontal surface of the surrounding rock as the x-axis, and the horizontal surface perpendicular to the surrounding rock as the y-axis, based on the mirror superposition principle, the x-axis is used as a mirror to map the actual submarine tunnel to obtain a virtual submarine tunnel; Superimposing the potential of the actual submarine tunnel and the virtual submarine tunnel to obtain a submarine tunnel seepage field model, wherein the submarine tunnel seepage field model includes surrounding rock seepage field, grouting circle seepage field and lining seepage field; Step S4: Calculate the surrounding rock seepage field based on Darcy's seepage law to obtain surrounding rock seepage field parameters, wherein the surrounding rock seepage field parameters include water inflow of the submarine tunnel section, total water head in the surrounding rock area, and pore pressure in the surrounding rock area; Step S5: Based on the Hansbo nonlinear seepage model, the seepage field of the grouting circle and the seepage field of the lining are calculated to obtain the seepage parameters of the grouting circle and the seepage parameters of the lining; The grouting circle seepage parameters include the grouting circle seepage volume, the grouting circle total water head and the grouting circle pore pressure; The lining seepage parameters include lining seepage, lining total water head and lining pore pressure; Step S6: Analyze and predict the seepage field of the submarine tunnel according to the surrounding rock seepage parameters, the grouting circle seepage field parameters and the lining seepage field parameters.

2. The nonlinear seepage field analysis method for submarine tunnels based on the mirror image superposition theory according to claim 1 is characterized in that: The calculation formula of the dynamic water level at the surface height of the homogeneous stratum is: ξ ci =H0+H ci cos(w ci t-g ci ) Where H0 represents the average sea level during the analysis period, H ci Indicates the dynamic water level amplitude, w ci represents the dynamic water level cycle, t represents the dynamic water level time, g ci Indicates the phase of the dynamic water level.

3. The nonlinear seepage field analysis method for submarine tunnels based on the mirror image superposition theory according to claim 1 is characterized in that: In step S4, the surrounding rock seepage field parameters are calculated based on Darcy's seepage law, specifically: Step S4.1: The cross-sectional center of the actual submarine tunnel is defined as the sink, and the cross-sectional center of the virtual submarine tunnel is defined as the source. Then the distances from any point M(x, y) on the submarine tunnel calculation cross-sectional area to the source and sink are: Among them, r1 represents the distance from any point M(x,y) to the sink; r2 represents the distance from any point M(x,y) to the source; h represents the distance from the sink to the horizontal surface of the surrounding rock; Step S4.2: The seepage pattern of the soil conforms to Darcy seepage: Where i represents the hydraulic gradient of the surrounding rock; k represents the permeability coefficient; v represents the seepage velocity of the surrounding rock; When the submarine tunnel is a single-hole circular tunnel, the flow rate flowing through each section of the tunnel is: Q s =2πrv (3) Where: Q s represents the water inflow of the calculated section of the surrounding rock layer; r represents the distance from any point of the calculated section to the center of the submarine tunnel. Substituting formula (2) into formula (3), we get We can get: Where: Indicates the total water head of the surrounding rock layer; Q s Indicates the water inflow of the calculated section of the surrounding rock layer; k s represents the permeability coefficient of the surrounding rock; r represents the distance from any point of the calculation section to the center of the submarine tunnel; Integrating formula (4) yields: Where: C represents the integral constant; Q s Indicates the water inflow of the calculated section of the surrounding rock layer; k s represents the permeability coefficient of the surrounding rock; r represents the distance from any point on the calculation section to the center of the circle; Step S4.3: The total water head of the surrounding rock layer is obtained from the water momentum of any point in the mirror normal plane according to the principle of potential superposition. The calculation formula is: Where: Indicates the total water head of the surrounding rock layer; Q sj represents the seepage volume of the jth tunnel, and takes a positive value when it flows in and a negative value when it flows out; r j represents the distance from any point on the calculated section to the center point of the jth tunnel; C1 represents the value of the undetermined constant; When r1=r2; that is, y=h, So we can get: When r1=r g When r g >>h, then r2=2h: Where: r g Indicates the radius of the grouting circle; h gt represents the total water head at the outer boundary of the grouting circle; ξ ci represents the dynamic water level at the surface height of the homogeneous stratum; h represents the distance from the sink to the horizontal surface of the surrounding rock; It represents the total water head of the seepage field in the submarine tunnel; Step S4.4: According to formula (1) to formula (8), the seepage volume in the surrounding rock of the submarine tunnel, the water head in the surrounding rock of the submarine tunnel and the pore pressure distribution function in the surrounding rock of the submarine tunnel can be obtained as follows: Where: represents the total water head of the surrounding rock area in the xy coordinate system; p s (x,y) represents the pore pressure in the surrounding rock area in the xy coordinate system; h s represents the position head of the surrounding rock area; β represents the ratio of the radius of the grouting circle to the distance from the sink to the horizontal surface of the surrounding rock, and β = r g / 2h; γ w Indicates the weight of water; ci The dynamic water level represents the height of action on the surface of a homogeneous stratum; 4. The nonlinear seepage field analysis method for submarine tunnels based on the mirror superposition theory according to claim 1 is characterized in that: In step S5, the seepage field of the grouting circle and the seepage field of the lining are calculated based on the Hansbo nonlinear seepage model to obtain the seepage parameters of the grouting circle and the seepage parameters of the lining, which are specifically: Step S5.1: Hansbo nonlinear seepage model is Where: k 0s represents the permeability coefficient of the curve segment of the nonlinear seepage model; k0 represents the permeability coefficient of the straight line segment; m represents the nonlinear parameter; i0 represents the first critical hydraulic gradient; i l represents the second critical hydraulic gradient; Step S5.2: Define the fluid as incompressible and the seepage direction is perpendicular to the y-axis. The continuity equation of the fluid seepage in the grouting circle is expressed as: Decompose the velocity vector in the seepage field: u=v i cosθ,v=v i sinθ,v i =k 0s i m (13) Where: u represents the seepage velocity in the x-axis direction; v represents the seepage velocity in the y-axis direction; v i represents the seepage velocity in any direction; i m represents the hydraulic gradient to the power of m; k os represents the permeability coefficient of the curve segment of the nonlinear seepage model; θ represents the angle between the seepage velocity in any direction and the x-axis direction; Step S5.3: Based on the fact that the hydraulic gradient direction of the seepage is the same as the streamline direction, the hydraulic gradient can be expressed as: According to the radial seepage condition of circular cross section of submarine tunnel, it can be obtained that: Where: It is expressed as the total water head; i represents the hydraulic gradient of the surrounding rock; r represents the distance from any point of the calculation section to the center of the circle; Substituting formulas (10), (11), (13), (14), and (15) into formula (12) for simplification, we can obtain the nonlinear continuity equation of the fluid in the polar coordinate form of the grouting ring and the lining under the radial seepage condition of the submarine tunnel: The nonlinear continuity equation of the fluid in the grouting circle in polar coordinate form is: Where: Indicates the total water head in the grouting circle; m g Represents the first nonlinear parameter of the grouting area; i lg Represents the second nonlinear parameter of the grouting area; r 1g Indicates the distance from any point in the grouting area to the actual tunnel center; The nonlinear continuity equation of the fluid in the lining polar coordinate form is: Where: Indicates the total water head in the lining area; m l represents the nonlinear parameter of the first lining zone; i ll represents the nonlinear parameter of the second lining area; r 2l It indicates the distance from any point in the lining area to the actual center of the tunnel; Step S5.4: Solve formula (16) and formula (17) by separation of variables method, and substitute boundary condition (18) to obtain the total water head of the grouting circle and the total water head of the lining: Where: h gt Indicates the water head outside the grouting area; h lt Indicates the water head outside the lining area; h 0t represents the water head inside the lining area; r0 represents the inner radius of the lining; r l represents the outer radius of the submarine tunnel excavated inside the rock mass; r represents the distance from any point on the calculated section to the center of the circle; Total water head of grouting ring for: Total head in lining area for: Step S5.5: Integrate formula (19) and formula (20) to obtain the seepage of the grouting ring and the seepage of the lining: Seepage volume of grouting ring Q g : Lining seepage Q l for: Step S5.6: Convert formula (19) and formula (20) into rectangular coordinates to obtain the total water head H of the grouting circle in the xy coordinate system: g(x,y) The total water head H in the lining area in the xy coordinate system l(x,y) : Total water head H of grouting circle in xy coordinate system of seepage field in submarine tunnel g(x,y) The calculation formula is: Total water head H in the lining area of ​​the submarine tunnel seepage field in the xy coordinate system l(x,y ) is calculated as: Where: p lt represents the pore pressure at the outer boundary of the lining; p 0t represents the pore pressure at the inner boundary of the lining area; h gt represents the water head outside the grouting area; r0 represents the inner radius of the lining; r l represents the outer radius of the submarine tunnel excavated inside the rock mass; γ w represents the weight of water; h represents the distance from the sink to the horizontal surface of the surrounding rock; x represents the distance from any point on the calculation section of the submarine tunnel to the y axis; y represents the distance from any point on the calculation section of the submarine tunnel to the x axis; A1 represents the first variable parameter of the grouting ring; A2 represents the second variable parameter of the grouting ring; A3 represents the third variable parameter of the grouting ring; A4 represents the fourth variable parameter of the grouting ring; A5 represents the fifth variable parameter of the grouting ring; A6 represents the first variable parameter of the lining; A7 represents the second variable parameter of the lining; A8 represents the third variable parameter of the lining; A9 represents the fourth variable parameter of the lining; A 10 The fifth variable parameter representing the lining; Step S5.7: According to the total head function of submarine tunnel seepage equal to the sum of pressure head function and position head function, the pore pressure of grouting circle and lining pore pressure are obtained, and the calculation formula is: Where: H (x,y) It is expressed as the total water head of the seepage field of the submarine tunnel in the xy coordinate system; P (x,y) represents the pore pressure of the submarine tunnel seepage field in the xy coordinate system; γ w Indicates the weight of water; The calculation formula of pore pressure in grouting ring is: The calculation formula of lining pore pressure is:

5. The nonlinear seepage field analysis method for submarine tunnels based on the mirror image superposition theory according to claim 1 is characterized in that: In step S6, the seepage field of the submarine tunnel is analyzed and predicted according to the surrounding rock seepage parameters, the grouting ring seepage field parameters and the lining seepage field parameters, specifically: Step S6.1: Analyze the seepage mode of the grouting ring and the lining based on the seepage continuity condition and obtain the water head h outside the grouting area gt The water head outside the lining area h lt ; The seepage continuity condition is that the surrounding rock seepage is equal to the grouting ring seepage and equal to the lining seepage; Step S6.2: If both the grouting ring and the lining are Hansbo nonlinear seepage curve segments, that is, m g >1,i≤i lg ;m l >1,i≤i ll Under the condition, then from formula (9), formula (21) and formula (22), we can get If the lining is a Hansbo nonlinear seepage curve segment and the grouting circle is a Hansbo nonlinear seepage straight line segment, that is, m g >1,i≤i lg ;m l >1,i>i ll Under the condition; from formula (9), formula (21) and formula (22), we can get If the grouting ring and the lining are both Hansbo nonlinear seepage straight line segments, that is, m g =1;m l =1, from formula (9), formula (21) and formula (22) we can get Step S6.3: Calculate the water head h outside the grouting area according to formulas (29), (30) and (31): gt The water head outside the lining area h lt ; h gt With h lt Substituting back into the calculation formulas of surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters, the surrounding rock seepage field parameters, grouting circle seepage field parameters and lining seepage field parameters under current seepage conditions are obtained; The seepage field of the submarine tunnel is predicted according to the surrounding rock seepage field parameters, the grouting circle seepage field parameters and the lining seepage field parameters under the current seepage conditions.

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