Method and device for calculating unsteady seepage field of circular foundation pit of suspension type waterproof curtain

Abstract

The invention provides a calculation method and device for an unsteady-state seepage field of a circular foundation pit of a suspension type waterproof curtain, and belongs to the field of foundation pit engineering.The method comprises the steps that in the diameter direction of the foundation pit, a confined water seepage field is divided into an inside-pit area and an outside-pit area with the suspension type waterproof curtain as the boundary, establishing an axisymmetric two-dimensional seepage geometric model and a seepage control equation of the two regions; in combination with definite solution conditions of the two regions, respectively obtaining water level drawdown expressions containing unknown interface flow of the two regions in the Laplace space; discretizing a common interface of the two regions, constructing an equation set in combination with a continuous condition of water level drop at the interface, and solving to obtain interface flow; and performing inverse transformation on the water level drawdown expression in the Laplace space to obtain the water level drawdown expression in the time domain. According to the method, the transient water level drop of the confined water seepage field of the circular foundation pit provided with the suspension type waterproof curtain at any position can be rapidly and accurately calculated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of foundation pit engineering, and particularly relates to a calculation method and device for unsteady seepage field of a suspension type water-stop curtain circular foundation pit. BACKGROUND

[0002] With the development of urbanization, the population accommodated by cities gradually increases, which brings great pressure on the traffic and life of cities. Therefore, the demand for underground bypass channels, city and industrial sewage treatment cyclone pools, anchor pit in suspension bridge engineering and vertical shaft in water and electricity engineering and the like engineering also correspondingly increases. Due to the great difference in stress characteristics from strip foundation pits, most of such engineering selects circular foundation pits as the excavation scheme.

[0003] In the above engineering, the suspension type water-stop curtain is widely used due to its hindering effect on the seepage of underground water. For the water level drawdown transient solution of the circular foundation pit provided with the suspension type water-stop curtain, on the one hand, it is helpful to understand the distribution of the seepage field of underground water in the circular foundation pit, and on the other hand, it can provide a calculation method and means for the drawdown design and the prediction of underground water level. Therefore, how to determine the water level drawdown transient solution of the circular foundation pit becomes a problem to be solved at present. SUMMARY

[0004] In view of the problems in the prior art, the present application provides a calculation method and device for unsteady seepage field of a suspension type water-stop curtain circular foundation pit.

[0005] The present application provides a calculation method for unsteady seepage field of a suspension type water-stop curtain circular foundation pit, comprising: dividing the whole confined water stratum seepage field into two regular regions of inside and outside the pit along the diameter direction of a target circular foundation pit, taking the suspension type water-stop curtain of the target circular foundation pit as a boundary, and establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit provided with the suspension type water-stop curtain; respectively establishing seepage control equations of the two regular regions according to the two-dimensional axisymmetric seepage geometric model; respectively obtaining water level drawdown expressions of inside and outside the pit in Laplace space containing unknown interface flow by sequentially performing Laplace transform, Fourier transform and inverse Fourier transform on the seepage control equations combined with the definite solution conditions of the two regular regions, the interface flow being unit area flow of the common interface of the two regions; discretely processing the common interface between inside and outside the pit to obtain an expression of the unknown interface flow, and constructing an equation group combined with the water level continuous condition at the common interface, and solving the unknown interface flow; substituting the solved unknown interface flow into the water level drawdown expression, and performing inverse Laplace transform on the water level drawdown expression to obtain water level drawdown expressions of inside and outside the pit in time domain, which are taken as calculation results of the unsteady seepage field of the confined water stratum of the target circular foundation pit.

[0006] According to a method for calculating the unsteady-state seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention, the method for establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with a suspended water-stop curtain comprises: taking the axial direction of the non-complete well at the center of the target circular foundation pit as the Z axis, and taking the radial outward extension direction through the center of the target circular foundation pit as the R axis, to establish a two-dimensional axisymmetric seepage geometric model of the foundation pit with a suspended water-stop curtain.

[0007] According to a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention, the seepage control equations of two regular areas are established respectively based on the two-dimensional axisymmetric seepage geometric model, including:

[0008] ,

[0009] ,

[0010] Where K z and K r are the permeability coefficients of the confined aquifer in the vertical and horizontal directions respectively; 、 are the water level drops at certain locations in the pit area and outside the pit area, respectively. s is the storage coefficient of the confined aquifer, z is the Z-axis coordinate, r is the R-axis coordinate, and t is time.

[0011] According to a calculation method for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention, the fixed solution conditions of the pit area include:

[0012]

[0013] The solution conditions for the area outside the pit include:

[0014]

[0015] Among them, r0 represents the radius of the circular suspended water-stop curtain, B a represents the distance from the lower edge of the water-stop curtain to the bottom of the confined aquifer, B represents the thickness of the confined aquifer, Q is the fixed pumping flow of the incomplete well, represents the interface flow rate, l and d represent the vertical distances from the top and bottom of the pumping well filter section to the bottom of the confined aquifer, respectively.

[0016] According to a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention, the water level drawdown expression containing unknown interface flow in the inner and outer areas of the foundation pit in Laplace space includes:

[0017] Area inside the pit:

[0018] ,

[0019] Exterior region:

[0020] ,

[0021] wherein, η0=[S s p] 1 / 2 , α(r, n, p) = K1(ηr0)I0(ηr) + I1(ηr0) K0(ηr); n, p respectively represent Fourier transform parameters, denotes the drawdown of the interior region in Laplace space; denotes the drawdown of the exterior region in Laplace space; I0, K0 are respectively the zero-order first-type and second-type imaginary Bessel functions, and I1, K1 are respectively the first-order first-type and second-type imaginary Bessel functions; denotes the interface flow in Laplace space, and is an unknown quantity in Laplace space.

[0022] According to the method, the common interface between the interior and exterior regions of the foundation pit is discretized to obtain an expression of unknown interface flow, and the method comprises the following steps:

[0023] B a is discretized into M discrete units, and the length of each unit is Δξ j =ξ j+ −ξ j- , j = 1, 2, 3,..., M, wherein, ξ j+ denotes the upper end longitudinal coordinate of the jth discrete unit, and ξ j- denotes the lower end longitudinal coordinate of the jth discrete unit.

[0024] Suppose that the unit area flow on any independent discrete unit is When the discrete quantity M is large enough, is a constant irrelevant to the coordinate z, the unknown interface flow is represented by a series of discrete constant values , and the related integral expression of is converted into:

[0025] ,

[0026] ,

[0027] wherein, is the midpoint of the jth discrete unit.

[0028] A method for calculating an unsteady seepage field of a suspended water-stop curtain circular foundation pit is provided according to the present application, wherein a set of equations is constructed by using the water level continuity condition at the common interface, and unknown interface flow is solved, and the method comprises the following steps:

[0029] The entire common interface is discretized into M discrete units, and M independent drawdown equalization equations are established, wherein the drawdown equalization equation established on any discrete unit is expressed as:

[0030] ,

[0031] wherein, wherein i represents the corresponding discrete unit number selected by using the drawdown continuity condition of the water level inside and outside the pit, i = 1, 2, …, M; ξ i+ represents the upper end longitudinal coordinate of the i th discrete unit, ξ i- represents the lower end longitudinal coordinate of the i th discrete unit, ξ represents the longitudinal coordinate of the center position of the i th discrete unit, and ;

[0032] According to the drawdown equalization equation corresponding to the above M discrete units, the water level drawdown expression containing unknown interface flow in the Laplace space of the two regions is substituted, and a MxM scale drawdown matrix equation set is constructed by combining the discretization idea and its properties, and is expressed as:

[0033] ,

[0034] wherein X and Y represent a coefficient matrix and a result matrix, respectively;

[0035] ,

[0036] wherein Δξ i represents the distance length from the lower end to the upper end of the i th discrete unit, Δξ j represents the distance length from the lower end to the upper end of the j th discrete unit, and Δξ j = ξ j+ - ξ j- ; F i is a function with n and i as independent variables, ; F j is a function with n and j as independent variables, ; and represent the longitudinal coordinates of the midpoint positions of the i th and j th discrete units, respectively;

[0037] Solving the drawdown matrix equation set can determine the interface flow of the j th discrete unit segment .

[0038] According to the application, a calculation method of a non-steady seepage field of a circular foundation pit is provided, and water level drawdown expressions of pit inside and pit outside areas in a time domain include:

[0039] The water level drawdown expression of the pit inside area is:

[0040]

[0041] The water level drawdown expression of the pit outside area is:

[0042]

[0043] wherein s1 is a drawdown in the pit inside area in the time domain, s2 is a drawdown in the pit outside area in the time domain; respectively represent the drawdown in the pit inside area and the drawdown in the pit outside area in Laplace space, N and w are parameters in the Stehfest algorithm;

[0044] wherein,

[0045] wherein k is a parameter in the Stehfest algorithm, [(w+1) / 2] represents the maximum integer not exceeding (w+1) / 2, and min{w, N / 2} represents the minimum value between w and N / 2.

[0046] The application further provides a calculation device of a non-steady seepage field of a circular foundation pit with a suspended water stop curtain, which includes:

[0047] A model establishing module is configured to divide a whole confined water stratum seepage field into two regular areas of pit inside and pit outside along a diameter direction of a target circular foundation pit and establish a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water stop curtain as a boundary, and establish seepage control equations of the two regular areas according to the two-dimensional axisymmetric seepage geometric model.

[0048] A transformation module is configured to perform Laplace transformation, Fourier transformation and inverse Fourier transformation on the seepage control equations in combination with definite conditions of the two regular areas, and obtain water level drawdown expressions of the pit inside and pit outside areas in Laplace space containing unknown interface flow, wherein the interface flow is unit area flow of a common interface of the two areas.

[0049] A discretization module is configured to discretize the common interface between the pit inside and pit outside areas, obtain an expression of the unknown interface flow, and construct an equation group in combination with a water level continuity condition at the common interface to solve the unknown interface flow.

[0050] ​​​​The computing module is used for back substitution of the solved unknown interface flow into the water level drawdown expression, and Laplace inverse transformation of the water level drawdown expression, so as to obtain the water level drawdown expression of the pit and pit area in the time domain, as the calculation result of the non-steady state seepage field of the target circular foundation pit confined water stratum.

[0051] The application further provides an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the calculation method of the non-steady state seepage field of the circular foundation pit according to any one of the above.

[0052] The application further provides a non-transitory computer readable storage medium, which stores a computer program, and the computer program is executable on the processor to implement the calculation method of the non-steady state seepage field of the circular foundation pit according to any one of the above.

[0053] The application provides a calculation method and device for the non-steady state seepage field of the suspended water stop curtain circular foundation pit, which can quickly and accurately calculate the transient water level drawdown of the seepage field of the suspended water stop curtain circular foundation pit at any position, and is beneficial to determining the influence of the insertion depth of the water stop curtain, the length and position of the filter pipe section of the pumping well on the seepage field, so as to improve the engineering quality and construction efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the present application or prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0055] Figure 1 It is a flowchart of the calculation method for the non-steady state seepage field of the suspended water stop curtain circular foundation pit provided by the present application;

[0056] Figure 2 It is a schematic diagram of the axisymmetric two-dimensional simplified seepage geometry model of the target suspended water stop curtain circular foundation pit provided by the present application;

[0057] Figure 3 It is a comparison diagram of the calculation result and the finite element software calculation result provided by the present application;

[0058] Figure 4 It is an analysis diagram of the influence of the change of the insertion depth of the water stop curtain on the change of the water level drawdown in the seepage field provided by the present application;

[0059] Figure 5 It is a structural schematic diagram of the calculation device for the non-steady state seepage field of the suspended water stop curtain circular foundation pit provided by the present application;

[0060] Figure 6 Figure 1 is a structural schematic diagram of an electronic device provided by the present application. DETAILED DESCRIPTION

[0061] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be clearly and completely described below with reference to the drawings in the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present application.

[0062] The calculation method of the present application can be applied to the design of foundation pit excavation and dewatering, including but not limited to: underground passages, super high-rise buildings, water and electricity engineering and suspension bridge engineering and other infrastructure construction.

[0063] The calculation method of the present application will be described below. Figures 1-6 The present application provides a calculation method and device for unsteady seepage field of a suspended water-stop curtain circular foundation pit. Figure 1 Figure 1 is a flow schematic diagram of the calculation method for unsteady seepage field of a suspended water-stop curtain circular foundation pit provided by the present application, as shown in Figure 1 The calculation method for unsteady seepage field of a suspended water-stop curtain circular foundation pit provided by the present application comprises the following steps:

[0064] 101. Along the diameter direction of the target circular foundation pit, the entire confined water stratum seepage field is divided into two regular areas of inside and outside the pit by taking the suspended water-stop curtain of the target circular foundation pit as the boundary, and a two-dimensional axisymmetric seepage geometric model of the foundation pit provided with the suspended water-stop curtain is established.

[0065] In some embodiments, the establishment of the two-dimensional axisymmetric seepage geometric model of the foundation pit provided with the suspended water-stop curtain comprises: taking the direction of the non-complete well axis through the center of the target circular foundation pit as the Z axis, and taking the radial extension direction through the center of the target circular foundation pit as the R axis, to establish the two-dimensional axisymmetric seepage geometric model of the foundation pit provided with the suspended water-stop curtain.

[0066] Specifically, as shown in Figure 2 Based on the fact that the cross section taken along any diameter direction of the target circular foundation pit is the same, and the interface has symmetry in plane geometry, the cross section is analyzed, the vertical direction of the center of the target circular foundation pit on the cross section is taken as the Z axis, the radial extension direction of the center of the target circular foundation pit on the cross section is taken as the R axis, and the insertion direction of the suspended water-stop curtain is taken as the boundary, to divide the seepage field around the target circular foundation pit into two regular areas of inside and outside the pit, i.e. the inside area and the outside area, thereby establishing the two-dimensional seepage geometric model of the foundation pit provided with the suspended water-stop curtain.

[0067] 102. According to the two-dimensional axisymmetric seepage geometry model, seepage control equations of the two regular regions are respectively established.

[0068] For example, based on the two-dimensional seepage geometry model and the groundwater dynamics theory, the seepage control equations corresponding to the two regions are respectively established, including the following:

[0069]

[0070]

[0071] In the formula, K z and K r respectively represent the permeability coefficients of the confined aquifer in the vertical direction and the horizontal direction; S s and S s are the water level drawdowns at a certain position in the pit region and the pit region, respectively, Sis the water storage coefficient of the confined aquifer, z is the Z-axis coordinate, r is the R-axis coordinate, and t is the time.

[0072] 103. The seepage control equations are combined with the two regular regions to perform Laplace transform, Fourier transform and inverse Fourier transform in sequence to obtain water level drawdown expressions of the inner and outer regions of the foundation pit containing unknown interface flow in the Laplace space, and the interface flow is the unit area flow of the common interface of the two regions.

[0073] According to the properties and rules of Laplace transform, finite Fourier cosine transform and inverse transform, the seepage control equations are combined with the two regions to perform Laplace transform, Fourier transform and inverse Fourier transform in sequence to obtain water level drawdown expressions of the inner and outer regions of the foundation pit containing unknown quantities in the Laplace space.

[0074] 104. The common interface between the inner and outer regions of the foundation pit is discretized to obtain an expression of the unknown interface flow, and an equation group is constructed by combining the water level continuity condition at the common interface to solve the unknown interface flow.

[0075] 105. The solved unknown interface flow is substituted into the water level drawdown expression, and the water level drawdown expression is inverse Laplace transformed to obtain the water level drawdown expressions of the inner and outer regions of the foundation pit in the time domain, which are the calculation results of the unsteady seepage field of the confined water stratum of the target circular foundation pit.

[0076] The circular foundation pit unsteady seepage field calculation method can quickly and accurately calculate the transient water level drawdown of the seepage field of the circular foundation pit with a suspended waterproof curtain at any position, which is beneficial to determine the influence of the insertion depth of the waterproof curtain, the length and position of the filter pipe section of the pumping well on the seepage field, thereby improving the engineering quality and construction efficiency.

[0077] The water level drawdown caused by constant flow pumping at the top of the confined aquifer can be calculated by using the calculation result of the application, and the water head at the top of the confined aquifer is further obtained in combination with the initial confined water level, and the stability calculation of the circular foundation pit against sudden gushing is completed by comparing the force transmitted by the overlying soil layer of the confined aquifer on the pit, so as to ensure the safety of the foundation pit engineering, and the required time to reach a certain drawdown can also be estimated by using the calculation result of the application, and the construction time is further optimized more reasonably.

[0078] In some embodiments, based on the premise assumption condition that the top and bottom plates of the confined aquifer are both impervious boundaries and the pumping well is set to constant flow pumping, the pit area constant solution condition equation is obtained as follows:

[0079]

[0080] The pit area constant solution condition equation is obtained as follows:

[0081]

[0082] Wherein, r0 represents the radius of the circular suspended water stop curtain, B a represents the distance from the lower edge of the water stop curtain to the bottom plate of the confined aquifer, B represents the thickness of the confined aquifer, Q is the constant pumping flow of the incomplete well, represents the interface flow, and l and d respectively represent the vertical distance from the top end and bottom end of the filter pipe section of the pumping well to the bottom plate of the confined aquifer.

[0083] In some embodiments, the water level drawdown expression of the pit area inside and outside the Laplace space under the interface flow contains unknowns, which includes:

[0084] The pit area inside and outside the Laplace space under the interface flow contains unknowns, which includes:

[0085] ,

[0086] The pit area inside and outside the Laplace space under the interface flow contains unknowns, which includes:

[0087] ,

[0088] Wherein, η0=[S s p] 1 / 2 , α(r, n, p)=K1(ηr0)I0(ηr)+I1(ηr0) K0(ηr); n, p respectively represent Fourier transform parameters, represents the drawdown of the pit area inside the Laplace space; represents the drawdown of the pit area outside the Laplace space; I0, K0 are respectively the zero-order first-type and second-type imaginary Bessel functions, and I1, K1 are respectively the first-order first-type and second-type imaginary Bessel functions; denotes the interface flux in the Lagrangian space, which is an unknown variable in the Lagrangian space.

[0089] In some embodiments, the discretization processing on the common interface between the inner and outer regions of the foundation pit is performed to obtain an expression of the unknown interface flux, including:

[0090] B a is discretized into M discrete units, and the length of each unit is Δξ j =ξ j+ −ξ j- , j = 1, 2, 3, …, M, wherein, ξ j+ denotes the upper end longitudinal coordinate of the jth discrete unit, and ξ j- denotes the lower end longitudinal coordinate of the jth discrete unit.

[0091] It is assumed that the unit area flux on any independent discrete unit is When the discrete quantity M is large enough, is a constant independent of the coordinate z, and the unknown interface flux is represented by a series of discrete constant values , and the related integral expression of is converted to:

[0092] ,

[0093] ,

[0094] wherein, is the midpoint of the jth discrete unit.

[0095] In some embodiments, based on the drawdown and flux on both sides of each discrete unit satisfying the mass conservation and continuity principle, a drawdown equation can be established on each discrete unit, and therefore, the equation group is constructed by combining the water level continuity condition at the common interface to solve the unknown interface flux, including:

[0096] The entire common interface is discretized into M discrete units, and M independent drawdown equation is established, and the drawdown equation established on any discrete unit is represented as:

[0097] ,

[0098] wherein, i denotes the corresponding discrete unit serial number selected by the equation established by using the drawdown continuity condition of the water level inside and outside the pit, i = 1, 2, …, M; ξ i+ denotes the upper end longitudinal coordinate of the ith discrete unit, and ξ i- denotes the lower end longitudinal coordinate of the ith small common interface, denotes the longitudinal coordinate of the center position of the ith discrete unit, ;

[0099] Based on the above M discrete units, the corresponding drawdown equations are established. The water level drawdown expressions with unknown interface flow in the two regions in Laplace space are substituted into the equations. Combining the discretization idea and its properties, an M×M scale drawdown matrix equation system is constructed, which is expressed as:

[0100] ,

[0101] Among them, X and Y express the coefficient matrix and result matrix respectively;

[0102] ,

[0103] Among them, Δξ i Represents the distance from the bottom to the top of the i-th discrete unit, Δξ j Represents the distance from the bottom to the top of the jth discrete unit, Δξ j =ξ j+ -ξ j- ; F i is a function with n and i as independent variables, ; F j is a function with n and j as independent variables, ; Respectively represent the ordinates of the midpoints of the i-th and j-th discrete segments;

[0104] Solving the depth reduction matrix equations can determine the interface flow of the jth discrete unit segment .

[0105] Solve the equation system according to the reduced matrix equation , the expression is:

[0106] ,

[0107] Among them, G is the inverse matrix of the coefficient matrix X, G ij Represents the element corresponding to the i-th row and j-th column in the matrix G.

[0108] In some embodiments, the expressions for the water level drawdown in the pit and the area outside the pit in the time domain include:

[0109] The water level drop expression in the pit area is:

[0110] ,

[0111] The water level drop expression outside the pit area is:

[0112] ,

[0113] Among them, s1 is the depth reduction of the pit area in the time domain, and s2 is the depth reduction of the pit area in the time domain; They represent the depth reduction of the inner pit area and the outer pit area under the pull-type space, respectively. N and w are parameters in the Stehfest algorithm.

[0114] in, ;

[0115] Where k is a parameter in the Stehfest algorithm, [(w+1) / 2] represents the maximum integer not exceeding (w+1) / 2, and min{w,N / 2} represents the minimum value between w and N / 2.

[0116] Will Back-substitution yields the expression for the water level drawdown in the two areas of the target circular foundation pit in the pull-type space:

[0117] ,

[0118] ,

[0119] The Stehfest algorithm is used to implement the inverse Pull transform, and the water level drawdown expressions of the two areas in the Pull space are converted to the water level drawdown expressions in the time domain. The water level drawdown expressions of the pit areas in the time domain are obtained as s1 and s2 mentioned above.

[0120] In combination with the above embodiment, the solution in the time domain is used as the calculation result of the target circular foundation pit seepage field, and the calculation results of this application are compared with the calculation results of the finite element software to verify the correctness of the calculation results of this application.

[0121] For example, in analyzing the effect of the insertion depth of the water-stop curtain in a circular foundation pit of a cyclone pool in a steel plant on the change in the water level drop in the seepage field, the relevant foundation pit engineering parameters are shown in Table 1:

[0122] Table 1 Engineering parameters for the dewatering design of a circular foundation pit for a cyclone pool in a steel plant

[0123]

[0124] Based on the specific dimensions and other parameters of the project, the water level drop in the two areas inside and outside the circular foundation pit was obtained by the calculation method of this application, and compared with the calculation results of the finite element software. The comparison is as follows Figure 3 As shown. Figure 3 It can be seen that the calculation results of this application are highly accurate and can be used as a benchmark for numerical model calibration, providing an engineering reference for foundation pit dewatering design research.

[0125] pass Figure 4It can be seen that due to the different insertion depths of the suspended water-stop curtain, the drawdown of the confined water level inside and outside the pit is affected to different degrees, and the influence of Ba on the drawdown inside the pit in the seepage field of the circular pit provided with the suspended water-stop curtain decreases with the increase of Ba.

[0126] Therefore, the calculation results of the present application can be used to analyze the influence of the change of the insertion depth of the water-stop curtain on the drawdown of the water level in the seepage field, thereby serving the engineering design.

[0127] The suspended water-stop curtain circular pit unsteady seepage field calculation device provided by the present application is described below, and the suspended water-stop curtain circular pit unsteady seepage field calculation device described below can be correspondingly referred to the suspended water-stop curtain circular pit unsteady seepage field calculation method described above.

[0128] Figure 5 is a structural schematic diagram of the suspended water-stop curtain circular pit unsteady seepage field calculation device provided by the present application, as Figure 5 shown, the suspended water-stop curtain circular pit unsteady seepage field calculation device comprises a model establishing module 501, a transformation module 502, a discretization module 503 and a calculation module 504. Among them, the model establishing module 501 is used to divide the entire confined water stratum seepage field into two regular areas of inside and outside the pit along the diameter direction of the target circular pit, and establish a two-dimensional axisymmetric seepage geometric model of the pit provided with the suspended water-stop curtain, and establish seepage control equations of the two regular areas according to the two-dimensional axisymmetric seepage geometric model; the transformation module 502 is used to transform the seepage control equations combined with the definite condition of the two regular areas, and sequentially perform Laplace transform, Fourier transform and inverse Fourier transform, to obtain the water level drawdown expression of the interface flow containing unknowns between the inside and outside of the pit in the Laplace space, and the interface flow is the unit area flow of the common interface between the two areas; the discretization module 503 is used to discretize the common interface between the inside and outside of the pit, to obtain the expression of the unknown interface flow, and construct an equation group combined with the water level continuous condition at the common interface, to solve the unknown interface flow; the calculation module 504 is used to substitute the solved unknown interface flow into the water level drawdown expression, and perform Laplace inverse transform on the water level drawdown expression, to obtain the water level drawdown expression of the inside and outside of the pit in the time domain, as the calculation result of the unsteady seepage field of the confined water stratum of the target circular pit.

[0129] The device embodiment provided by the embodiment of the present application is used to realize the above-mentioned method embodiments, and the specific process and detailed content are referred to the above-mentioned method embodiments, which will not be described here.

[0130] The implementation principle and the technical effects of the device for calculating the unsteady seepage field of the suspended water-stop curtain circular foundation pit are the same as those of the method for calculating the unsteady seepage field of the suspended water-stop curtain circular foundation pit, and for brevity, the part of the device for calculating the unsteady seepage field of the suspended water-stop curtain circular foundation pit that is not mentioned in the foregoing description can be referred to the corresponding content in the method for calculating the unsteady seepage field of the suspended water-stop curtain circular foundation pit.

[0131] Figure 6 is a structural schematic diagram of an electronic device provided by the present application, as Figure 6 shown, the electronic device can include a processor (processor) 601, a communications interface (Communications Interface) 602, a memory (memory) 603 and a communications bus 604, wherein the processor 601, the communications interface 602, the memory 603 complete the communication between each other through the communications bus 604. The processor 601 can call the logic instructions in the memory 603 to execute the method for calculating the unsteady seepage field of the suspended water-stop curtain circular foundation pit, which comprises: dividing the entire confined water stratum seepage field into two regular areas of inside and outside the pit along the diameter direction of the target circular foundation pit, and taking the suspended water-stop curtain of the target circular foundation pit as the boundary; a two-dimensional axisymmetric seepage geometric model of the foundation pit provided with the suspended water-stop curtain is established; according to the two-dimensional axisymmetric seepage geometric model, the seepage control equations of the two regular areas are respectively established; the seepage control equations are combined with the two regular areas of the definite condition, and Laplace transform, Fourier transform and inverse Fourier transform are sequentially performed to obtain the water level drawdown expression of the inside and outside areas of the pit containing unknown interface flow in the Laplace space, the interface flow is the unit area flow of the common interface of the two areas; the common interface between the inside and outside areas of the pit is discretized to obtain the expression of the unknown interface flow, and an equation group is constructed by combining the water level continuity condition at the common interface to solve the unknown interface flow; the solved unknown interface flow is substituted into the water level drawdown expression, and the inverse Laplace transform is performed on the water level drawdown expression to obtain the water level drawdown expression of the inside and outside areas of the pit in the time domain, which is the calculation result of the unsteady seepage field of the confined water stratum of the target circular foundation pit.

[0132] Moreover, the logic instructions in the memory 603 described above can be realized in the form of a software function unit and sold or used as an independent product, which can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application or the part of the prior art that contributes essentially or the part of the technical solutions can be embodied in the form of a software product, which is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0133] In another aspect, the present application also provides a computer program product, which comprises a computer program, the computer program can be stored on a non-transitory computer readable storage medium, and the computer program can be executed by a processor to enable a computer to execute the calculation method of the unsteady seepage field of a suspended water stop curtain circular foundation, which comprises the following steps: dividing the entire confined water stratum seepage field into two regular areas of inside and outside the foundation along the diameter direction of the target circular foundation and bounded by the suspended water stop curtain of the target circular foundation, establishing a two-dimensional axisymmetric seepage flow geometric model of the foundation provided with the suspended water stop curtain; establishing seepage flow control equations of the two regular areas according to the two-dimensional axisymmetric seepage flow geometric model; performing Laplace transform, Fourier transform and inverse Fourier transform on the seepage flow control equations combined with the definite conditions of the two regular areas, respectively, to obtain water level drawdown expressions of the inside and outside areas of the foundation containing unknown interface flow in the Laplace space, the interface flow being the unit area flow of the common interface of the two areas; discretizing the common interface between the inside and outside areas of the foundation to obtain an expression of the unknown interface flow, and constructing an equation group combined with the water level continuity condition at the common interface to solve the unknown interface flow; substituting the solved unknown interface flow into the water level drawdown expression, and performing inverse Laplace transform on the water level drawdown expression to obtain water level drawdown expressions of the inside and outside areas of the foundation in the time domain, which are the calculation results of the unsteady seepage field of the confined water stratum of the target circular foundation.

[0134] In yet another aspect, the present application also provides a non-transitory computer readable storage medium having stored thereon a computer program, which, when executed by a processor, implements the method for calculating the unsteady seepage field of a suspended water-stop curtain circular foundation pit provided by the above method, and the method comprises: dividing the entire confined water stratum seepage field into two regular areas of inside and outside the pit along the diameter direction of the target circular foundation pit and bounded by the suspended water-stop curtain of the target circular foundation pit, and establishing a two-dimensional axisymmetric seepage flow geometric model of the pit provided with the suspended water-stop curtain; according to the two-dimensional axisymmetric seepage flow geometric model, establishing seepage flow control equations of the two regular areas respectively; performing Laplace transform, Fourier transform and inverse Fourier transform on the seepage flow control equations in combination with the definite conditions of the two regular areas, to obtain water level drawdown expressions of the inside and outside areas of the pit containing unknown interface flow in the Laplace space, wherein the interface flow is the unit area flow of the common interface of the two areas; performing discretization processing on the common interface between the inside and outside areas of the pit to obtain an expression of the unknown interface flow, and combining the water level continuity condition at the common interface to construct an equation group, and solving the unknown interface flow; substituting the solved unknown interface flow into the water level drawdown expression, and performing Laplace inverse transform on the water level drawdown expression to obtain water level drawdown expressions of the inside and outside areas of the pit in the time domain, as the calculation result of the unsteady seepage field of the confined water stratum of the target circular foundation pit.

[0135] The device embodiments described above are merely illustrative, wherein the units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e., can be located in one place or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0136] Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software and necessary general hardware platforms, and of course can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes a plurality of instructions to make a computer device (which can be a personal computer, server, or network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0137] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain, characterized in that: include: Along the diameter direction of the target circular foundation pit, with the target circular foundation pit's suspended water-stop curtain as the boundary, the entire confined water stratum seepage field is divided into two regular areas, inside the pit and outside the pit. A two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain is established. According to the two-dimensional axisymmetric seepage geometry model, the seepage control equations of two regular regions are established respectively; The seepage control equation is combined with the boundary conditions of the two regular regions, and Laplace transform, Fourier transform and inverse Fourier transform are performed in sequence to obtain the water level drawdown expressions containing unknown interface flow in the inner and outer regions of the foundation pit in Laplace space, where the interface flow is the flow per unit area of ​​the common interface between the two regions; The public interface between the inner and outer areas of the foundation pit is discretized to obtain the expression of the unknown interface flow. The equation group is constructed based on the water level continuity condition at the public interface to solve the unknown interface flow. The solved unknown interface flow is substituted back into the water level drawdown expression, and the water level drawdown expression is subjected to an inverse Laplace transform to obtain the water level drawdown expressions in the time domain for the areas inside and outside the pit, which are used as the calculation results of the unsteady-state seepage field of the confined water stratum in the target circular foundation pit.

2. The method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain according to claim 1 is characterized in that: The method of establishing a two-dimensional axisymmetric seepage geometry model of a foundation pit provided with a suspended water-stop curtain comprises: With the axis direction of the incomplete well passing through the center of the target circular foundation pit as the Z axis and the radial outward extension direction passing through the center of the target circular foundation pit as the R axis, a two-dimensional axisymmetric seepage geometric model of the foundation pit equipped with a suspended water-stop curtain is established.

3. The method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain according to claim 2 is characterized in that: According to the two-dimensional axisymmetric seepage geometric model, the seepage control equations of two regular regions are established respectively, including: Where K z and K r are the permeability coefficients of the confined aquifer in the vertical and horizontal directions respectively; 、 are the water level drops at certain locations in the pit area and outside the pit area, respectively. s is the storage coefficient of the confined aquifer, z is the Z-axis coordinate, r is the R-axis coordinate, and t is time.

4. The method for calculating the unsteady seepage field of a circular base of a suspended water-stop curtain according to claim 3 is characterized in that: The definite solution conditions for the area in the pit include: The solution conditions for the area outside the pit include: Among them, r0 represents the radius of the circular suspended water-stop curtain, B a represents the distance from the lower edge of the water-stop curtain to the bottom of the confined aquifer, B represents the thickness of the confined aquifer, Q is the fixed pumping flow of the incomplete well, represents the interface flow rate, l and d represent the vertical distances from the top and bottom of the pumping well filter section to the bottom of the confined aquifer, respectively.

5. The method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain according to claim 3 is characterized in that: The water level drawdown expression for the unknown interface flow in the inner and outer areas of the foundation pit in the Laplace space includes: Area inside the pit: Area outside the pit: in, η0=[S s p] 1 / 2 ,α(r,n,p)=K1(ηr0)I0(ηr)+I1(ηr0) K0(ηr); n, p represent the Fourier transform parameters, represents the drawdown of the pit area in Lagrangian space; represents the depth reduction of the outer area of ​​the pit in Lagrangian space; I0 and K0 are zero-order Bessel functions of the first and second kinds of imaginary quantities, respectively; I1 and K1 are first-order Bessel functions of the first and second kinds of imaginary quantities, respectively; It represents the interface flow in the pull-type space and is an unknown quantity in the pull-type space.

6. The method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain according to claim 5 is characterized in that: The discretization process of the common interface between the inner and outer areas of the foundation pit is performed to obtain the expression of the unknown interface flow, including: B a Discretize into M discrete units, the length of each unit is Δξ j =ξ j+ −ξ j- , j = 1, 2, 3, ..., M, where ξ j+ represents the upper ordinate of the jth discrete unit, ξ j- Indicates the lower ordinate of the jth discrete unit; Assume that the flow rate per unit area on any independent discrete unit is , when the discrete number M is large enough, is a constant that is independent of the coordinate z and converts the unknown interface flow Through a series of discretized constant values To express, and The relevant integral expression is converted to: in, is the midpoint of the jth discrete unit.

7. The method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain according to claim 6 is characterized in that: The method of constructing a set of equations based on the water level continuity condition at the common interface to solve the unknown interface flow rate includes: The entire public interface is discretized into M discrete units, and a total of M independent depth reduction equations are established. The depth reduction equation established on any discrete unit is expressed as: Where i represents the corresponding discrete unit number selected by the equation established using the continuous condition of water level drop inside and outside the pit, i=1, 2,…, M; ξ i+ represents the upper ordinate of the i-th discrete unit, ξ i- represents the lower ordinate of the common boundary surface of the i-th segment, Represents the ordinate of the center position of the i-th discrete unit, ; Based on the above M discrete units, the corresponding drawdown equations are established. The water level drawdown expressions with unknown interface flow in the two regions in Laplace space are substituted into the equations. Combining the discretization idea and its properties, an M×M scale drawdown matrix equation system is constructed, which is expressed as: Among them, X and Y express the coefficient matrix and result matrix respectively; Among them, Δξ i Represents the distance from the bottom to the top of the i-th discrete unit, Δξ j Represents the distance from the bottom to the top of the jth discrete unit, Δξ j =ξ j+ -ξ j- ; F i is a function with n and i as independent variables, ; F j is a function with n and j as independent variables, ; Respectively represent the ordinates of the midpoints of the i-th and j-th discrete segments; Solving the depth reduction matrix equations can determine the interface flow of the jth discrete unit segment .

8. The method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain according to claim 3 is characterized in that: The expressions for the water level drawdown in the pit and outside the pit in the time domain include: The water level drop expression in the pit area is: ， The water level drop expression in the area outside the pit is: ， Among them, s1 is the depth reduction of the pit area in the time domain, and s2 is the depth reduction of the pit area in the time domain; They represent the depth reduction of the inner pit area and the outer pit area under the pull-type space, respectively. N and w are parameters in the Stehfest algorithm. in, ; Where k is a parameter in the Stehfest algorithm, [(w+1) / 2] represents the maximum integer not exceeding (w+1) / 2, and min{w,N / 2} represents the minimum value between w and N / 2.

9. A device for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain, characterized in that: include: A model building module is used to divide the seepage field of the entire confined water stratum into two regular areas, inside and outside the pit, along the diameter direction of the target circular foundation pit and with the target circular foundation pit suspended water-stop curtain as the boundary, establish a two-dimensional axisymmetric seepage geometry model of the foundation pit with the suspended water-stop curtain, and establish the seepage control equations for the two regular areas based on the two-dimensional axisymmetric seepage geometry model; a transformation module for sequentially performing Laplace transform, Fourier transform, and inverse Fourier transform on the seepage control equation in combination with the boundary conditions of the two regular regions, to obtain water level drawdown expressions for the inner and outer regions of the foundation pit containing unknown interface flow in Laplace space, where the interface flow is the flow per unit area of ​​the common interface between the two regions; The discrete module is used to discretize the common interface between the inner and outer areas of the foundation pit, obtain the expression of the unknown interface flow, and construct the equation system based on the water level continuity condition at the common interface to solve the unknown interface flow; The calculation module is used to substitute the solved unknown interface flow into the water level drawdown expression, and perform an inverse Laplace transform on the water level drawdown expression to obtain the water level drawdown expressions in the time domain for the areas inside and outside the pit, which are used as the calculation results of the unsteady-state seepage field of the confined water stratum in the target circular foundation pit.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, it implements the calculation method of the unsteady seepage field of the circular foundation pit with a suspended water-stop curtain as described in any one of claims 1 to 8.

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