Method and device for calculating unsteady seepage field of suspended water-stop curtain circular foundation pit

Abstract

The application provides a kind of suspended water-stop curtain circular foundation pit unsteady seepage field calculation method and device, belong to foundation pit engineering field, this method includes: along the diameter direction of foundation pit, with suspended water-stop curtain as boundary, the confined water seepage field is divided into two regions inside and outside the pit, the axisymmetric two-dimensional seepage geometric model and the seepage control equation of two regions are established;Combined with the definite condition of two regions, the water level drawdown expression of two regions in Laplace space is obtained respectively, containing unknown interface flow;The common interface of two regions is discretized, and the equation set is constructed by combining the continuous condition of water level drawdown at the interface, and the interface flow is solved;The water level drawdown expression in time domain is obtained by inverse transformation of the water level drawdown expression in Laplace space.This method can quickly and accurately calculate the transient water level drawdown of the confined water seepage field of the suspended water-stop curtain circular foundation pit at any position.

Description

Technical Field

[0001] This invention relates to the field of foundation pit engineering, and in particular to a method and apparatus for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain. Background Technology

[0002] With the development of urbanization, the population that cities can accommodate is gradually increasing, which puts enormous pressure on urban transportation and daily life. Therefore, the demand for projects such as underground bypass tunnels, urban and industrial wastewater treatment cyclone pools, anchorage pits in suspension bridge projects, and vertical shafts in hydropower projects is also increasing. Due to the significant differences in stress characteristics compared to strip pits, most of these projects choose circular pits as the excavation method.

[0003] In the aforementioned projects, suspended cutoff walls are widely used due to their ability to impede groundwater seepage. Determining the transient drawdown of circular foundation pits with suspended cutoff walls is crucial for understanding the groundwater seepage field distribution within such pits. It also provides calculation methods and tools for dewatering design and groundwater level prediction. Therefore, determining the transient drawdown solution for this type of foundation pit is a pressing issue that needs to be addressed. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method and apparatus for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain.

[0005] This invention provides a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain, comprising: dividing the entire seepage field of the confined aquifer into two regular regions, inside and outside the pit, along the diameter direction of the target circular foundation pit and using the suspended water-stop curtain as the boundary; establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain; establishing seepage control equations for the two regular regions based on the two-dimensional axisymmetric seepage geometric model; and performing Laplace transform, Fourier transform, and inverse Fourier transform on the seepage control equations in conjunction with the boundary conditions of the two regular regions, respectively, to obtain... The formula for the drawdown expression in Laplace space, which includes unknown interface flow rates in the areas inside and outside the foundation pit, is as follows: The interface between the two areas is discretized to obtain the expression for the unknown interface flow rate. A system of equations is constructed based on the water level continuity condition at the interface to solve for the unknown interface flow rate. The solved unknown interface flow rate is then substituted back into the drawdown expression, and an inverse Laplace transform is performed to obtain the time-domain drawdown expressions for the areas inside and outside the pit. This result serves as the calculation result for the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0006] According to the present invention, a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain is provided. The step of establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain includes: taking the direction of the axis of the non-complete 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, and establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain.

[0007] According to the present invention, a method for calculating the unsteady seepage field of a suspended cutoff curtain circular foundation pit is provided, wherein the seepage control equations for two regular regions are established based on the two-dimensional axisymmetric seepage geometric model, including:

[0008] ,

[0009] ,

[0010] In the formula, K z and K r These represent the permeability coefficients of confined aquifers in the vertical and horizontal directions, respectively. , S represents the drawdown at a certain location in the pit area and the pit area, respectively. s denoted as the water 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 the present invention, a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain is provided. The boundary conditions for the region within the pit include:

[0012]

[0013] The boundary conditions for the region outside the pit include:

[0014]

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

[0016] According to the present invention, a method for calculating the unsteady seepage field of a circular foundation pit with a suspended cutoff curtain is provided. The expression for the drawdown of the pit's inner and outer regions containing unknown interfacial flow rates in Laplace space includes:

[0017] Area inside the pit:

[0018] ,

[0019] Area outside the pit:

[0020] ,

[0021] in, η0=[S s p] 1 / 2 α(r,n,p)=K1(ηr0)I0(ηr)+I1(ηr0) K0(ηr); n and p represent the Fourier transform parameters, respectively. This represents the drawdown of the pit region in Laplace space; I0 and K0 represent the drawdown of the region outside the pit in Lagrange space; I0 and K0 are the zero-order imaginary argument Bessel functions of the first and second kind, respectively, and I1 and K1 are the first-order imaginary argument Bessel functions of the first and second kind, respectively. This represents the interface flow in the pull space, which is an unknown quantity in the pull space.

[0022] According to the present invention, a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain is provided. The method involves discretizing the common interface between the inner and outer regions of the foundation pit to obtain an expression for the unknown interface flow rate, including:

[0023] B a Discretize into M discrete elements, each element having a length of Δξ. j =ξ j+ −ξ j- j=1,2,3,…,M, where ξ j+ ξ represents the upper ordinate of the j-th discrete unit. j- This represents the lower ordinate of the j-th discrete unit;

[0024] Assume the unit area flow rate on any independent discrete unit is When the discrete quantity M is large enough, It is a constant independent of the z-coordinate, representing the unknown interface flow. Through a series of discretized constant values To represent, and will The relevant integral expression is converted to:

[0025] ,

[0026] ,

[0027] in, Let j be the midpoint of the j-th discrete unit.

[0028] According to the present invention, a method for calculating the unsteady seepage field of a circular foundation pit with a suspended cutoff wall is provided. The method involves constructing a set of equations based on the water level continuity condition at the common interface to solve for the unknown interface flow rate.

[0029] The entire common interface is discretized into M discrete cells, and a total of M independent descent equations are established. The descent equation established on any discrete cell is expressed as:

[0030] ,

[0031] Where i represents the corresponding discrete unit index selected by the equation established using the continuous drawdown conditions inside and outside the pit, i=1,2,…,M; ξ i+ ξ represents the upper ordinate of the i-th discrete unit. i- Let represent the ordinate of the lower end of the i-th segment of the common boundary surface. The ordinate represents the center position of the i-th discrete unit. ;

[0032] Based on the aforementioned M discrete units, the corresponding drawdown equations are established. Substituting the drawdown expressions for the two regions in Laplace space with unknown interface flows into these equations, and combining the discretization concept and its properties, a system of M×M drawdown matrix equations is constructed, expressed as:

[0033] ,

[0034] Where X and Y represent the coefficient matrix and the result matrix, respectively;

[0035] ,

[0036] Where, Δξ i Δξ represents the distance from the bottom to the top of the i-th discrete unit. j Δξ represents the distance from the bottom to the top of the j-th discrete unit. j =ξ j+ -ξ j- ;F i Let be a function with n and i as independent variables. ;F j Let be a function with n and j as independent variables. ; Let represent the ordinates of the midpoints of the i-th and j-th discrete segments, respectively.

[0037] Solving the system of equations for the depth reduction matrix will determine the interface flow rate of the j-th discrete unit segment. .

[0038] According to the present invention, a method for calculating the unsteady seepage field of a circular foundation pit is provided, and the expressions for the drawdown in the time domain for the regions inside and outside the pit include:

[0039] Expression for the drawdown of the pit area:

[0040] ,

[0041] Expression for drawdown in the area outside the pit:

[0042] ,

[0043] Where s1 is the drawdown in the pit area under time domain, and s2 is the drawdown in the pit area under time domain; , denoted as the drawdown in the pit area and the drawdown outside the pit area under the Lagrange space, respectively, where N and w are parameters in the Stehfest algorithm;

[0044] in, ;

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

[0046] The present invention also provides a calculation device for the unsteady seepage field of a suspended water-stop curtain circular foundation pit, comprising:

[0047] The model building module is used to divide the entire confined aquifer seepage field into two regular regions, inside and outside the pit, along the diameter direction of the target circular foundation pit and with 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 with the suspended water-stop curtain is established. Based on the two-dimensional axisymmetric seepage geometric model, seepage control equations are established for the two regular regions respectively.

[0048] The transformation module is used to combine the boundary conditions of the two regular regions with the seepage control equation and perform Laplace transform, Fourier transform and inverse Fourier transform in sequence to obtain the water level drawdown expression of the unknown interface flow in the inner and outer regions of the foundation pit under the Laplace space. The interface flow is the unit area flow of the common interface of the two regions.

[0049] The discrete module is used to discretize the common interface between the inner and outer areas of the foundation pit, obtain the expression for the unknown interface flow rate, and construct a set of equations in combination with the water level continuity condition at the common interface to solve for the unknown interface flow rate.

[0050] The calculation module is used to substitute the solved unknown interface flow rate back 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 serve as the calculation results of the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0051] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the calculation method for the unsteady seepage field of the circular foundation pit as described above.

[0052] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the calculation method for the unsteady seepage field of a circular foundation pit as described above.

[0053] The method and apparatus for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by this invention can quickly and accurately calculate the transient water level drawdown at any location of the seepage field in a circular foundation pit with a suspended water-stop curtain. This is beneficial for 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, thereby improving the quality of the project and the construction efficiency. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0055] Figure 1 This is a flowchart illustrating the calculation method for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention.

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

[0057] Figure 3 This is a comparison chart of the calculation results provided by this invention and the calculation results of finite element software;

[0058] Figure 4 This is an analysis diagram of the influence of the change in the insertion depth of the waterstop curtain on the change in the drawdown in the seepage field, provided by the present invention.

[0059] Figure 5 This is a schematic diagram of the structure of the calculation device for the unsteady seepage field of the suspended water-stop curtain circular foundation pit provided by the present invention.

[0060] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0062] The calculation method of this invention can be applied to the design of dewatering for foundation pit excavation, including but not limited to: infrastructure construction such as underground passages, super high-rise buildings, hydropower projects and suspension bridge projects.

[0063] The following is combined Figures 1-6 This invention describes a method and apparatus for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain. Figure 1 This is a flowchart illustrating the calculation method for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention. Figure 1 As shown, the method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention includes:

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

[0065] In some embodiments, establishing a two-dimensional axisymmetric seepage geometric model of a foundation pit equipped with a suspended water-stop curtain includes: taking the direction of the non-complete well axis 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, and establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit equipped with a suspended water-stop curtain.

[0066] Specifically, such as Figure 2 As shown, since the cross-sections taken along any diameter direction of the target circular foundation pit are all the same, and the interface is symmetrical in plane geometry, we take this cross-section for analysis. Taking the vertical direction through the center of the target circular foundation pit on the cross-section as the Z-axis, the radial extension direction through the center of the target circular foundation pit on the cross-section as the R-axis, and the insertion direction of the suspended water-stop curtain as the boundary, the seepage field around the target circular foundation pit is divided into two regular regions, namely the inner region and the outer region, which are the inner region and the outer region. Thus, a two-dimensional seepage geometric model of the foundation pit with the suspended water-stop curtain is established.

[0067] 102. Based on the two-dimensional axisymmetric seepage geometric model, establish seepage control equations for two regular regions respectively.

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

[0069] ,

[0070] ,

[0071] In the formula, K z and K r These represent the permeability coefficients of confined aquifers in the vertical and horizontal directions, respectively. , S represents the drawdown at a certain location in the pit area and the pit area, respectively. s denoted as the water storage coefficient of the confined aquifer, z is the Z-axis coordinate, r is the R-axis coordinate, and t is time.

[0072] 103. Combining the boundary conditions of the two regular regions, the seepage control equation is subjected to Laplace transform, Fourier transform and inverse Fourier transform in sequence to obtain the water level drawdown expression of the unknown interface flow in the inner and outer regions of the foundation pit in Laplace space. The interface flow is the flow per unit area at the common interface of the two regions.

[0073] Based on the properties and rules of the Laplace transform, finite Fourier cosine transform, and their inverse transform, the seepage control equation is subjected to the Laplace transform, Fourier transform, and inverse Fourier transform in sequence, combined with the boundary conditions of the two regions, to obtain the expressions for the drawdown of the two regions inside and outside the foundation pit in Laplace space, which contain unknowns.

[0074] 104. Discretize the common interface between the inner and outer areas of the foundation pit to obtain the expression for the unknown interface flow rate. Combine the water level continuity condition at the common interface to construct a set of equations and solve for the unknown interface flow rate.

[0075] 105. Substitute the solved unknown interface flow rate back into the aforementioned drawdown expression, and perform an inverse Laplace transform on the drawdown expression to obtain the drawdown expressions for the areas inside and outside the pit in the time domain, which serve as the calculation results of the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0076] The calculation method for the unsteady seepage field of a circular foundation pit of the present invention can quickly and accurately calculate the transient water level drawdown at any location of the seepage field of a circular foundation pit with a suspended water-stop curtain. This is beneficial for 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, thereby improving the engineering quality and construction efficiency.

[0077] The calculation results of this application can be used to calculate the drawdown at the top of the confined aquifer caused by constant flow pumping. Combined with the initial confined water level, the water head at the top of the confined aquifer can be obtained. By comparing the force transmitted to the confined aquifer by the overlying soil layer, the stability of the circular foundation pit against sudden heave can be verified, ensuring the safety of the foundation pit project. The calculation results of this invention can also be used to estimate the time required to reach a certain drawdown, thereby optimizing the construction time more reasonably.

[0078] In some embodiments, based on the premise that the top and bottom plates of the confined aquifer are both impermeable boundaries and the pumping well is set to pump at a constant flow rate, the boundary condition equations for the pit region are obtained as follows:

[0079]

[0080] The boundary conditions for the region outside the pit include:

[0081]

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

[0083] In some embodiments, the expression for the drawdown of the excavation pit containing unknown interfacial flow in the Laplace space includes:

[0084] Area inside the pit:

[0085] ,

[0086] Area outside the pit:

[0087] ,

[0088] in, η0=[S s p] 1 / 2 α(r, n, p) = K1(ηr0)I0(ηr) + I1(ηr0)K0(ηr); n and p represent the Fourier transform parameters, respectively. This represents the drawdown of the pit region in Laplace space; I0 and K0 represent the drawdown of the region outside the pit in Lagrange space; I0 and K0 are the zero-order imaginary argument Bessel functions of the first and second kind, respectively, and I1 and K1 are the first-order imaginary argument Bessel functions of the first and second kind, respectively. This represents the interface flow in the pull space, which is an unknown quantity in the pull space.

[0089] In some embodiments, the discretization of the common interface between the inner and outer regions of the foundation pit to obtain an expression for the unknown interface flow includes:

[0090] B a Discretize into M discrete elements, each element having a length of Δξ. j =ξ j+ −ξ j- j=1,2,3,…,M, where ξ j+ ξ represents the upper ordinate of the j-th discrete unit. j- This represents the lower ordinate of the j-th discrete unit;

[0091] Assume the unit area flow rate on any independent discrete unit is When the discrete quantity M is large enough, It is a constant independent of the z-coordinate, representing the unknown interface flow. Through a series of discretized constant values To represent, and will The relevant integral expression is converted to:

[0092] ,

[0093] ,

[0094] in, Let j be the midpoint of the j-th discrete unit.

[0095] In some embodiments, based on the principle of mass conservation and continuity between the drawdown and flux on both sides of each discrete unit, a drawdown equation can be established for each discrete unit. Therefore, the step of constructing a set of equations in conjunction with the water level continuity condition at the common interface to solve for the unknown interface flow includes:

[0096] The entire common interface is discretized into M discrete cells, and a total of M independent descent equations are established. The descent equation established on any discrete cell is expressed as:

[0097] ,

[0098] Where i represents the corresponding discrete unit number selected by the equation established using the continuous drawdown conditions inside and outside the pit, i=1,2,…,M; ξ i+ ξ represents the upper ordinate of the i-th discrete unit. i- Let represent the ordinate of the lower end of the i-th segment of the common boundary surface. The ordinate represents the center position of the i-th discrete unit. ;

[0099] Based on the aforementioned M discrete units, the corresponding drawdown equations are established. Substituting the drawdown expressions for the two regions in Laplace space with unknown interface flows into these equations, and combining the discretization concept and its properties, a system of M×M drawdown matrix equations is constructed, expressed as:

[0100] ,

[0101] Where X and Y represent the coefficient matrix and the result matrix, respectively;

[0102] ,

[0103] Where, Δξ i Δξ represents the distance from the bottom to the top of the i-th discrete unit. j Δξ represents the distance from the bottom to the top of the j-th discrete unit. j =ξ j+ -ξ j- ;F i Let be a function with n and i as independent variables. ;F j Let be a function with n and j as independent variables. ; Let represent the ordinates of the midpoints of the i-th and j-th discrete segments, respectively.

[0104] Solving the system of equations for the depth reduction matrix will determine the interface flow rate of the j-th discrete unit segment. .

[0105] Solve the system of equations based on the depth-of-motion matrix. The expression is:

[0106] ,

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

[0108] In some embodiments, the expressions for the drawdown of the in-pit and out-of-pit regions in the time domain include:

[0109] Expression for the drawdown of the pit area:

[0110] ,

[0111] Expression for drawdown in the area outside the pit:

[0112] ,

[0113] Where s1 is the drawdown in the pit area under time domain, and s2 is the drawdown in the pit area under time domain; denoted as the drawdown in the pit area and the drawdown outside the pit area under the Lagrange space, respectively, where 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 taking the largest integer not exceeding (w+1) / 2; min{w,N / 2} represents taking the minimum value between w and N / 2.

[0116] Will Substituting back, the expressions for the drawdown of the two regions of the target circular foundation pit under the pull-out space are obtained as follows:

[0117] ,

[0118] ,

[0119] The Stehfest algorithm is used to perform the inverse Laplace transform, which converts the drawdown expressions of the two regions in the Laplace space to the drawdown expressions in the time domain, resulting in the drawdown expressions of the pit region in the time domain as s1 and s2 above.

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

[0121] A specific example is the analysis of the impact of the change in the insertion depth of the cutoff curtain in the circular foundation pit of a vortex pool in a steel plant on the change in the drawdown in the seepage field. The relevant foundation pit engineering parameters are shown in Table 1:

[0122] Table 1. Design parameters for dewatering of a circular foundation pit in a steel plant's vortex pool.

[0123]

[0124] Based on the specific dimensions and other parameters of the project, the water level drawdown in the two areas inside and outside the circular foundation pit was obtained using the calculation method of this application, and compared with the calculation results of finite element software. The comparison results are as follows. Figure 3 As shown. By Figure 3 It is evident that the calculation results of this application have high accuracy and can be used as a benchmark for numerical model calibration, providing 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. In the seepage field of the circular foundation pit with the suspended water-stop curtain, the influence of Ba on the drawdown inside the pit decreases as Ba increases.

[0126] Therefore, the calculation results of this application can be used to study and analyze the effect of the change in the insertion depth of the cutoff curtain on the change in the drawdown of the seepage field, and thus provide services for engineering design.

[0127] The following describes the calculation device for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the present invention. The calculation device for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain described below can be referred to in correspondence with the calculation method for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain described above.

[0128] Figure 5 This is a schematic diagram of the structure of the calculation device for the unsteady seepage field of the suspended water-stop curtain circular foundation pit provided by the present invention, as shown in the figure. Figure 5 As shown, the calculation device for the unsteady seepage field of the suspended cutoff wall circular foundation pit includes: a model building module 501, a transformation module 502, a discretization module 503, and a calculation module 504. The model building module 501 is used to divide the entire confined aquifer seepage field into two regular regions—inside and outside the pit—along the diameter direction of the target circular foundation pit, with the suspended cutoff wall as the boundary. A two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended cutoff wall is established. Based on the two-dimensional axisymmetric seepage geometric model, seepage control equations are established for the two regular regions. The transformation module 502 is used to perform Laplace transform, Fourier transform, and inverse Fourier transform on the seepage control equations, combining the boundary conditions of the two regular regions, to obtain the results for the inner and outer regions of the foundation pit in Laplace space. The unknown interface flow rate is expressed as the drawdown expression, where the interface flow rate is the flow rate per unit area at the common interface between the two regions. The discretization module 503 is used to discretize the common interface between the inner and outer regions of the foundation pit to obtain the expression for the unknown interface flow rate, and construct a set of equations in combination with the water level continuity condition at the common interface to solve for the unknown interface flow rate. The calculation module 504 is used to substitute the solved unknown interface flow rate back into the drawdown expression, and perform an inverse Laplace transform on the drawdown expression to obtain the drawdown expressions for the inner and outer regions in the time domain, which are used as the calculation results of the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0129] The apparatus embodiments provided in this invention are for implementing the above-described method embodiments. For specific processes and details, please refer to the above-described method embodiments, which will not be repeated here.

[0130] The calculation device for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided in this embodiment of the invention has the same implementation principle and technical effect as the aforementioned calculation method embodiment for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain. For the sake of brevity, any parts not mentioned in the calculation device embodiment for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain can be referred to the corresponding content in the aforementioned calculation method embodiment for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain.

[0131] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 6 As shown, the electronic device may include: a processor 601, a communication interface 602, a memory 603, and a communication bus 604. The processor 601, communication interface 602, and memory 603 communicate with each other via the communication bus 604. The processor 601 can call logical instructions in the memory 603 to execute a calculation method for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain. This method includes: dividing the entire confined aquifer seepage field into two regular regions—inside and outside the pit—along the diameter direction of the target circular foundation pit, with the suspended water-stop curtain as the boundary; establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain; establishing seepage control equations for the two regular regions based on the two-dimensional axisymmetric seepage geometric model; and performing Laplace transform, Fourier transform, and... on the seepage control equations in conjunction with the boundary conditions of the two regular regions. Inverse Fourier transform is used to obtain the water level drawdown expressions for the unknown interface flow rates in the inner and outer regions of the foundation pit in Laplace space, where the interface flow rate is the flow rate per unit area at the common interface between the two regions. The common interface between the inner and outer regions of the foundation pit is discretized to obtain the expression for the unknown interface flow rate. A system of equations is constructed based on the water level continuity condition at the common interface to solve for the unknown interface flow rate. The solved unknown interface flow rate is substituted back into the water level drawdown expression, and an inverse Laplace transform is performed on the water level drawdown expression to obtain the water level drawdown expressions for the inner and outer regions of the pit in the time domain. These expressions are used as the calculation results for the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0132] Furthermore, the logical instructions in the aforementioned memory 603 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the calculation method for the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain provided by the above methods. The method includes: dividing the entire seepage field of the confined aquifer into two regular regions, inside and outside the pit, along the diameter direction of the target circular foundation pit and with the suspended water-stop curtain of the target circular foundation pit as the boundary; establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain; establishing seepage control equations for the two regular regions according to the two-dimensional axisymmetric seepage geometric model; and applying the seepage control equations to the two regular regions. The equations, combined with the boundary conditions of two regular regions, are subjected to Laplace transform, Fourier transform, and inverse Fourier transform in sequence to obtain the water level drawdown expressions in Laplace space for the regions inside and outside the foundation pit containing unknown interface flows. The interface flows are the unit area flows at the common interface between the two regions. The common interface between the regions inside and outside the foundation pit is discretized to obtain the expression for the unknown interface flows. A system of equations is constructed based on the water level continuity condition at the common interface to solve for the unknown interface flows. The solved unknown interface flows are substituted back into the water level drawdown expressions, and the inverse Laplace transform is performed on the water level drawdown expressions to obtain the water level drawdown expressions for the regions inside and outside the pit in the time domain. These expressions serve as the calculation results for the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0134] Furthermore, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, this computer program implements a method for calculating the unsteady seepage field of a circular foundation pit with a suspended water-stop curtain, as provided by the methods described above. This method includes: dividing the entire confined aquifer seepage field into two regular regions—inside and outside the pit—along the diameter direction of the target circular foundation pit and using the suspended water-stop curtain as a boundary; establishing a two-dimensional axisymmetric seepage geometric model of the foundation pit with the suspended water-stop curtain; establishing seepage control equations for the two regular regions based on the two-dimensional axisymmetric seepage geometric model; and combining the seepage control equations with the boundary conditions of the two regular regions. The Laplace transform, Fourier transform, and inverse Fourier transform are performed sequentially to obtain the water level drawdown expressions in Laplace space for the unknown interface flow rates in the areas inside and outside the foundation pit. The interface flow rate is the flow rate per unit area at the common interface between the two areas. The common interface between the areas inside and outside the foundation pit is discretized to obtain the expression for the unknown interface flow rate. An equation system is constructed based on the water level continuity condition at the common interface to solve for the unknown interface flow rate. The solved unknown interface flow rate is substituted back 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 expressions for the areas inside and outside the pit in the time domain. This is used as the calculation result of the unsteady seepage field of the confined aquifer in the target circular foundation pit.

[0135] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0136] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the unsteady seepage field of a suspended water-stop curtain circular foundation pit, characterized in that, Comprise: Along the direction of the target circular foundation pit diameter, with the target circular foundation pit hanging waterproof curtain as the boundary, the whole confined water stratum seepage field is divided into two regular areas of pit and pit, and a two-dimensional axisymmetric seepage geometry model of the pit provided with the hanging waterproof curtain is established; According to the two-dimensional axisymmetric seepage geometry 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 determined condition, and Laplace transform, Fourier transform and inverse Fourier transform are carried out in turn, and the water level drawdown expression of the two areas containing unknown interface flow in Laplace space is obtained, and the interface flow is the unit area flow of the common interface of the two areas; The common interface between the pit and the pit is discretized to obtain the expression of the unknown interface flow, and an equation group is constructed by combining the water level continuous condition at the common interface, and the unknown interface flow is solved; The solved unknown interface flow is substituted into the water level drawdown expression, and the inverse Laplace transform is carried out on the water level drawdown expression to obtain the water level drawdown expression of the pit and the pit in time domain, which is the calculation result of the target circular foundation pit confined water stratum unsteady seepage field; The two-dimensional axisymmetric seepage geometry model of the pit provided with the hanging waterproof curtain, comprising: ； ； wherein K z and K r represent the vertical and horizontal permeability coefficients of the confined aquifer, respectively; , are the water level drawdowns at a certain location in the pit and outside the pit, respectively, S 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. The water level drawdown expression of the two areas containing unknown interface flow in Laplace space, comprising: The pit area: ； The pit area: ； wherein η0=[S s p] 1 / 2 , a(r, n, p) = K1(ηr0)I0(ηr) + I1(ηr0) K0(ηr); n, p represent Fourier transform parameters, respectively, denotes the drawdown in the in-hole region in Laplace space; denotes the drawdown in the out-of-hole region in Laplace space; I0, K0 are the zeroth order first kind and second kind imaginary Bessel functions, respectively, and I1, K1 are the first order first kind and second kind imaginary Bessel functions, respectively; denotes the interfacial flux in Laplace space, and is an unknown in Laplace space; where r0 represents the radius of the circular suspended water-stop curtain, B a where r0 represents the radius of the circular suspended water-stop curtain, B a where r0 represents the radius of the circular suspended water-stop curtain, B 2. The method according to claim 1, wherein, The two-dimensional axisymmetric seepage geometry model of the pit provided with the hanging waterproof curtain, comprising: The two-dimensional axisymmetric seepage geometry model of the pit provided with the hanging waterproof curtain is established.

3. The method according to claim 2, wherein, The pit area determined condition includes: The pit area determined condition includes: wherein represents the interfacial flux.

4. The method according to claim 3, wherein, The common interface between the pit and the pit is discretized to obtain the expression of the unknown interface flow, comprising: B a discretized into M discrete units, each unit having a length of Δξ j =ξ j+ −ξ j- , j = 1, 2, 3, …, M, where ξ j+ represents the upper end longitudinal coordinate of the jthdiscrete unit, and ξ j- represents the lower end longitudinal coordinate of the jthdiscrete unit. Assume that the unit area flux on any independent discrete element is When the discrete number M is large enough, is a constant independent of coordinate z, and the unknown interface flux is expressed by a series of discrete constant values , and the relevant integral expression of is converted to: ； ； wherein, is the midpoint of the jth discrete unit.

5. The method according to claim 4, wherein, The equation group is constructed by combining the water level continuous condition at the common interface, and the unknown interface flow is solved, comprising: The whole common interface is discretized into M discrete units, and M independent drawdown equation equations are established, and the drawdown equation equation established on any discrete unit is expressed as: ； wherein i represents the discrete element number selected by the equation of the continuous condition of water level drawdown inside and outside the pit, i = 1, 2, …, M; ξ i+ represents the upper end longitudinal coordinate of the i th discrete element, ξ i- represents the lower end longitudinal coordinate of the i th discrete element, represents the longitudinal coordinate of the center position of the i th discrete element, ; According to the drawdown equation equations corresponding to the above M discrete units, the water level drawdown expression of the two areas containing unknown interface flow in Laplace space is substituted, and combined with the discretization idea and its properties, a MxM scale drawdown matrix equation group is constructed, expressed as: ； Wherein, X, Y respectively express the coefficient matrix and the result matrix; ； 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, Δξ j = ξ j+ - ξ j- ; F i is a function of n, i as arguments, ; F j is a function of n, j as arguments, ; respectively represent the longitudinal coordinate at the midpoint position of the i-th, j-th discrete segment. Solving the drawdown matrix equation system determines the interface flow of the jth discrete element section .

6. The method according to claim 5, wherein, The water level drawdown expression of the pit and the pit in time domain, comprising: The water level drawdown expression of the pit area: ， The water level drawdown expression of the pit area: ， Wherein, s1 is the drawdown of the in-pit area in time domain, s2 is the drawdown of the out-pit area in time domain; Respectively represent the drawdown of the in-pit area and the out-pit area in the draw space, N, w are both parameters in the Stehfest algorithm; wherein ; Wherein, k is the parameter in Stehfest algorithm, [(w+1) / 2] represents the maximum integer not exceeding (w+1) / 2; min{w,N / 2} represents the minimum value between w and N / 2.

7. A device for calculating the unsteady seepage field of a suspended water-stop curtain circular foundation pit, characterized in that, Comprise: The model establishing module is configured to divide the whole confined water stratum seepage field into two regular areas of inside and outside the pit along the direction of the target circular pit diameter, and establish a two-dimensional axisymmetric seepage geometric model of the pit provided with the suspended water-stop curtain, according to the two-dimensional axisymmetric seepage geometric model, the seepage control equations of the two regular areas are established respectively; The transformation module is configured to perform Laplace transformation, Fourier transformation and inverse Fourier transformation on the seepage control equations combined with the definite condition of the two regular areas, respectively, to obtain water level drawdown expressions of the inside and outside areas of the pit containing unknown interface flow in the Laplace space, the interface flow being unit area flow of the common interface of the two areas; The discrete module is configured to discretize the common interface between the inside and outside areas of the pit to obtain an 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 is configured to substitute the solved unknown interface flow into the water level drawdown expression, and perform inverse Laplace transformation 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 target circular pit confined water stratum; The seepage control equations of the two regular areas according to the two-dimensional axisymmetric seepage geometric model include: ； ； wherein K z and K r represent the vertical and horizontal permeability coefficients of the confined aquifer, respectively; 、 are the water level drawdowns at a certain location in the pit and outside the pit, respectively, S 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. The water level drawdown expression of the inside area of the pit includes: The water level drawdown expression of the outside area of the pit includes: ； The processor implements the calculation method of the unsteady seepage field of the suspended water-stop curtain circular pit according to any one of claims 1 to 6 when executing the program. ； wherein, η0=[S s p] 1 / 2 , a(r, n, p) = K1(ηr0)I0(ηr) + I1(ηr0) K0(ηr); n, p represent Fourier transform parameters, respectively, denotes the drawdown of the in-pit region in Laplace space; denotes the drawdown of the out-pit region in Laplace space; I0, K0 are the zeroth order first kind, second kind of Bessel function of imaginary argument, respectively, and I1, K1 are the first order first kind, second kind of Bessel function of imaginary argument, respectively; denotes the interface flux in Laplace space, and is an unknown in Laplace space; where r0 represents the radius of the circular suspended water-stop curtain, B a where r0 represents the radius of the circular suspended water-stop curtain, B a where r0 represents the radius of the circular suspended water-stop curtain, B 8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, ​

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