Analytical method for water inflow of suspended water-stop curtain in circular foundation pit of confined water layer

Abstract

The present invention discloses an analytical method for water inflow of a suspended water-stop curtain in a circular foundation pit of a confined water layer. The method applies the principle of groundwater dynamics to solve the water inflow of a circular foundation pit with a suspended water-stop curtain in a confined water layer, introduces the seepage influence coefficient of the foundation pit, and proposes a method for determining the same. The main implementation steps include S1, solving the seepage flow rate outside the foundation pit; S2, solving the seepage flow rate inside the foundation pit; S3, determining the water inflow of the foundation pit; The method establishes a calculation model for the water inflow of a suspended water-stop curtain foundation pit in a confined water stratum, adopts numerical simulation forward and reverse analysis fitting to obtain a key parameter: a calculation formula for the seepage influence coefficient, and verifies the analytical solution of the method through a large number of supplementary numerical simulations of verification conditions. The calculation results are in good agreement, indicating the correctness and rationality of the analytical model of the method.

Description

Technical Field

[0001] The invention relates to a method for analyzing water inflow of a suspended water-stop curtain, and in particular to a method for analyzing water inflow of a suspended water-stop curtain in a circular foundation pit of a pressurized water layer, and belongs to the technical field of water inflow analysis of a water-stop curtain at the bottom of a deep foundation pit. Background Art

[0002] In recent years, with the continuous growth of the national economy and the continuous improvement of urbanization, more and more super-high-rise buildings and large-scale underground complexes have appeared in cities, resulting in a sharp increase in the number of deep foundation pits. There is often a confined water layer at the bottom of a deep foundation pit. When the water head of the confined water layer is high, it is necessary to take dewatering and pressure reduction measures to avoid sudden surges at the bottom of the pit and the overall floating of the structure. Among the existing groundwater pressure reduction measures, the "wall-well" interception and drainage pressure reduction system composed of a pumping well and a suspended water-stop curtain is widely used because of its good water control effect and simple and fast construction. In the design process of the "wall-well" system, in order to reasonably design the total pumping volume or total drainage volume of the pressure relief well group, it is necessary to accurately calculate the water inflow in the suspended curtain foundation pit under different pit bottom water head design values. At present, domestic and foreign scholars have used theoretical derivation, numerical simulation, indoor model test and other research methods to study the water inflow in the suspended curtain foundation pit. Wang Junhui et al. analyzed the seepage characteristics of the two areas of bypass and non-bypass in the seepage field under the influence of the suspended water-stop curtain, modified the large well method formula and derived the calculation formula for the water inflow of groundwater and confined water under the condition of the water-stop curtain. Zhang Zhihong et al. derived the calculation formula for the water inflow of a circular foundation pit with a suspended water-stop curtain in a deep groundwater layer based on the distribution law of the flow network inside and outside the foundation pit and the principle of groundwater dynamics. Li Ying et al. equivalent the area of ​​the suspended curtain foundation pit to a large-diameter confined complete well with water entering the well wall, derived a simplified formula for calculating the water inflow of the foundation pit interception and drainage decompression, and compared it with the numerical calculation results to verify that the simplified formula has a high accuracy when the curtain insertion ratio is greater than 0.6 and the ratio of the foundation pit radius to the confined aquifer thickness is less than 2.0. Xiao Mingzhao et al. established a three-dimensional seepage finite element model by analyzing the hydrogeological conditions of the foundation pit of the Wuhan Yangtze River Tunnel Wuchang shield shaft, and performed numerical simulation calculations on the dewatering process of the deep foundation pit with a suspended water-stop curtain. Under the condition of a certain total pumping volume of the foundation pit, the relationship between the insertion depth of the water-stop curtain and the water head value inside and outside the foundation pit was quantitatively analyzed. Li Guangming and others relied on the foundation pit dewatering project of a subway transfer station in Tianjin to invert the formation parameters of the numerical model through the on-site pumping test data, and then used the finite difference method to numerically simulate the water inflow in the pit during the dewatering process of the hanging curtain foundation pit. Zhang Bangpei, Zhang Qinxi and others explored the influence of the curtain insertion depth on the water inflow in the foundation pit through indoor model box experiments, and proposed a reasonable value range for the insertion depth of the water-stop curtain, providing a reference for the design parameters of the water-stop curtain in actual projects.

[0003] However, there is a large error between the existing theoretical analytical solution for the water inflow of the hanging curtain foundation pit and the actual situation and numerical simulation results. It has good accuracy only within certain specific r0 / M and L / M ranges (where r0 is the radius of the circular foundation pit, L is the insertion depth of the water-stopping curtain, and M is the thickness of the confined aquifer). The reason is that the value of the seepage length in the pit is unreasonable. Most of the existing numerical methods for the research on the hanging curtain foundation pit are based on certain specific projects. The accuracy of the results depends on specific boundary conditions and hydrogeological parameters, and it is not universal for guiding the project. In this context, this method uses the principle of groundwater dynamics to solve the water inflow of the circular foundation pit with a suspended water-stopping curtain in the confined water layer, introduces the foundation pit seepage influence coefficient, and proposes its determination method. The analytical method of the present invention achieves good consistency with the numerical simulation.

[0004] Prior art CN110055989B Method for determining the pumping volume of a suspended curtain confined water foundation pit based on three-dimensional depth reduction: The present invention provides a method for determining the pumping volume of a suspended curtain confined water foundation pit based on three-dimensional depth reduction. First, the water level reduction control value outside the pit is calculated, and the total water inflow control value of the foundation pit is derived; after determining the safe depth reduction of the top of the confined water in the pit and arranging the dewatering scheme, the total water inflow of the foundation pit and the single well pumping volume of the dewatering scheme are determined by the safe depth reduction control value of the confined water in the pit, and the water inflow of the foundation pit can be further verified whether it is within the control value. Based on Darcy's law and flow balance theorem, the present invention fully considers the three-dimensional seepage field formed by the foundation pit dewatering under the suspended water-stop curtain and the safe water level reduction inside and outside the pit, and can accurately calculate the pumping volume of the foundation pit and the dewatering well under a specific dewatering scheme, and can ensure that the water level reduction of the confined water inside and outside the pit under this pumping volume is within a safe and controllable range. The dewatering scheme formulated based on the present invention not only reduces construction costs, but also ensures the safety of dewatering construction. According to the materials provided, a search was conducted and the prior art related to the present technical scheme was found (CN110055989B Method for Determining the Pumping Volume of a Suspended Curtain Confined Water Foundation Pit Based on Three-Dimensional Depth Reduction). The present technical scheme is compared with the prior art and has different technical features, so the present technical scheme is novel; the technical means adopted by the present technical scheme and the technical effects achieved have outstanding substantive characteristics and significant progress, so the present technical scheme is creative. Summary of the invention

[0005] The technical purpose of the present invention is to propose an analytical method for the water inflow of a suspended water-stop curtain in a circular foundation pit in a confined water layer. This method applies the principle of groundwater dynamics to solve the water inflow of a circular foundation pit with a suspended water-stop curtain in a confined water layer, introduces the influence coefficient of the foundation pit seepage path, and proposes a method for determining it. The analytical method of the present invention achieves good consistency with numerical simulation.

[0006] The technical solution adopted by the present invention is a method for analyzing the water inflow of a suspended water-stop curtain in a circular foundation pit in a confined water layer. The central axis of the circular foundation pit is taken as the z-axis, the radial direction of the foundation pit is taken as the r-axis, and the intersection of the central axis and the bottom plate of the aquifer is selected as the origin O to establish a cylindrical coordinate system. Thus, according to the principle of groundwater dynamics, a mathematical model of a suspended water-stop curtain foundation pit in a confined water layer is established, such as Figure 1 As shown. Where H is the pressure head height, r0 is the radius of the circular foundation pit, R is the radius of the foundation pit pumping, h0 is the head value of the head contour line at the center axis of the bottom of the water-stop curtain, D(z) is the head distribution function at the outer wall of the water-stop curtain (expression see formula 19), H d is the design value of water head in the pit, H w is the total head value at the maximum drawdown depth of the top plate of the confined aquifer outside the pit (see expression 27), L is the length of the water-stop curtain inserted into the confined aquifer, and M is the thickness of the aquifer.

[0007] This model ignores the thickness of the water-stop curtain and assumes that the seepage process in the pit is a three-dimensional stable flow, and the water head lines in the pit are all horizontal lines. The seepage area is divided into three parts: outside the pit (area 1), below the water-stop curtain in the pit (area 2), and the vertical seepage area in the pit (area 3). Due to the existence of the water-stop curtain, the water flow in area 1 flows around into area 2, and the flow direction of the water flow directly below the water-stop curtain is horizontal. The water flow turns in area 2 and flows into area 3 in the vertical direction. In general, if the dewatering wells in the foundation pit are dense and reasonably distributed, the foundation pit decompression dewatering process can be equivalent to the large-diameter pumping well dewatering process, and the pit can be simplified as vertical seepage. Therefore, this method assumes that area 3 is vertical seepage. According to the principle of seepage continuity, it can be seen that the flow rates in the three areas are the same, that is, Q1=Q2=Q3=Q, where Q1 is the flow rate in area 1, Q2 is the flow rate in area 2, Q3 is the flow rate in area 3, and Q is the total water inflow in the foundation pit.

[0008] The total water head h(r, θ, z) at any point (r, θ, z) in the seepage field of the calculation area is independent of the angle, that is, the total water head at each point can be expressed as h(r, z). The boundary conditions in the seepage area are:

[0009] h(r,z)=H; r=r0+R, z>0 (1)

[0010]

[0011]

[0012] h=h0; r=r0, 0≤z≤ML (4)

[0013] h=D(z); r=r0, ML≤z≤M (5)

[0014] h(r,z)=H d ; 0<r<r0, z=Hd (6)

[0015] According to the seepage continuity principle, the flow rates in the three regions are the same:

[0016] Q1=Q2=Q3 (7)

[0017] S1. Solution of foundation pit seepage flow;

[0018] First, the seepage volume in region 1 is calculated. According to Darcy’s law, the horizontal seepage velocity v at any point in the confined aquifer is r for:

[0019]

[0020] Where k r is the horizontal permeability coefficient in the confined aquifer:

[0021] In area 1, the flow rate passing through any section per unit time, that is, the flow rate Q1 in area 1 is:

[0022]

[0023] Substituting equation (8) into equation (9) yields the expression for flow rate Q1 in region 1:

[0024]

[0025] Transforming equation (11) yields:

[0026]

[0027] Integrate both sides of the equation with respect to r:

[0028]

[0029] Where C is the unknown coefficient. Substitute the boundary condition (1) into the formula to obtain the value of C:

[0030]

[0031] Substituting the C value into formula (13) we can obtain:

[0032]

[0033] When r=r0:

[0034]

[0035] Decompose the above integral:

[0036]

[0037] According to boundary conditions (3) and (4), we can obtain:

[0038]

[0039]

[0040] According to existing research results, the water head distribution function D(z) outside the water-stop curtain in the range of ML<z<M is expressed as:

[0041]

[0042] By combining equations (15) to (20), we can get the expression of seepage flow in region 1:

[0043]

[0044] S2. Solution of seepage flow in foundation pit

[0045] The water flow in area 1 flows around and enters area 2, and the water flow in area 2 turns and enters area 3. Only vertical seepage occurs in area 3, so the shortest seepage path of water flow in areas 2 and 3 is:

[0046] L min =H d -M+L (21)

[0047] The longest seepage path is:

[0048] L max =r0+H d (twenty two)

[0049] It should be noted that if the water head line at the bottom of the pit is above the bottom plate of the upper impermeable layer, that is, H d >M, then H in (21) and (22) d When using Darcy's law to solve the water inflow in the foundation pit, most of the existing theoretical analyses define the equivalent seepage length in the foundation pit as the average of the maximum seepage length and the minimum seepage length, or directly assume that 2L min In these two cases, the water inflow in the pit calculated is only reasonable in certain specific ranges of r0 / M and L / M. In fact, the value of the equivalent seepage path length in the foundation pit should vary with r0 / M and L / M. It is directly used as half of the sum of the maximum seepage path and the minimum seepage path or 2L. min Substitution is unreasonable. In order to accurately calculate the value of water inflow in the foundation pit under various working conditions, the seepage path influence coefficient α is introduced to reflect the change of the equivalent seepage path length with r0 / M and L / M, and the change law is explored through numerical experiments. The length of the equivalent seepage path in the foundation pit can be expressed as:

[0050]

[0051] Where α is the r0 / M, L / M function:

[0052]

[0053] The water inflow in areas 2 and 3 is:

[0054]

[0055] S3. Determine the water inflow from the foundation pit;

[0056] When the thickness of the water-stop curtain is ignored, when water flows around the water-stop curtain, the head loss through the inner side of the curtain is greater than the head loss through the outer side of the curtain. According to the existing experimental data and theoretical research results, the head loss of water flowing through the inner side of the curtain under various working conditions of the phreatic aquifer accounts for about 2 / 3 of the total loss of the flow. Regardless of whether in the confined water layer or the phreatic layer, the direction and characteristics of water flowing around the water-stop curtain are consistent. Therefore, this conclusion is applied to the confined water formation, and the head value h0 of the equal head line at the bottom of the curtain is expressed as (26). According to the principle of seepage continuity, (20), (25), and (26) are combined to obtain the maximum drawdown head Hw distribution function at the top plate of the confined aquifer outside the pit (27):

[0057]

[0058]

[0059] Substituting (25)(26) into (27) can calculate the water inflow of the circular foundation pit.

[0060] Compared with the existing technology, this method establishes a calculation model for the water inflow of a suspended water-stop curtain foundation pit in a confined water formation, and uses numerical simulation forward and reverse analysis to fit the key parameter: the calculation formula of the seepage influence coefficient. The analytical solution of this method is verified by a large number of supplementary numerical simulations of verification conditions. The calculation results are in good agreement, indicating the correctness and rationality of the analytical model of this method. The main conclusions obtained are as follows:

[0061] (1) For the analytical model of water inflow from a foundation pit with a suspended water-stop curtain in a confined water stratum, the value of the seepage influence coefficient has a great influence on the calculation result and should be determined comprehensively based on factors such as the foundation pit radius, the thickness of the confined water stratum, and the thickness of the suspended water-stop curtain inserted into the confined water stratum.

[0062] (2) The ratio of the foundation pit radius to the thickness of the confined water layer (r0 / M) and the ratio of the thickness of the suspended water-stop curtain inserted into the confined water layer (L / M) have the most direct and significant impact on the seepage influence coefficient α, and r0 / M=3 and L / M=0.7 are the critical values ​​of their influence. This method uses numerical simulation and positive and negative analysis to give the calculation formulas for α in four cases: (0<r0 / M≤3, 0<L / M<0.7), (0<r0 / M≤3, 0.7≤L / M<1), (r0 / M>3, 0<L / M<0.7), and (r0 / M>3, 0.7≤L / M<1).

[0063] (3) When a suspended water-stop curtain is selected as a groundwater control measure, the water control effect will decrease as r0 / M increases. When the size of the foundation pit is large, it is recommended to select a bottom-drop water-stop curtain to achieve the purpose of cutting off the hydraulic connection between the inside and outside of the foundation pit. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Calculation model of foundation pit with suspended water-stop curtain in confined water strata.

[0065] Figure 2 Numerical model of circular foundation pit with suspended water-stop curtain.

[0066] Figure 3 The relationship between water inflow and insertion ratio.

[0067] Figure 4 The relationship between water inflow and r0 / M.

[0068] Figure 5 The coefficient α varies with the insertion ratio.

[0069] Figure 6 The relationship between coefficient α and r0 / M.

[0070] Figure 7 Coefficient α fitting function when r0 / M>3; (a) linear function and numerical experimental fitting results when 0<L / M<0.7; (b) quadratic polynomial and numerical experimental fitting results when 0.7≤L / M<1.

[0071] Figure 8 The linear variation law of parameters A, K, I, B1, and B2 with r0 / M; (a) The linear variation fitting results of A and K with r0 / M; (b) The linear variation fitting results of I, B1, and B2 with r0 / M.

[0072] Fig. 9 Coefficient α fitting function when 0<r0 / M≤3; (a) linear function and numerical experimental fitting results when 0<L / M<0.7; (b) quadratic polynomial and numerical experimental fitting results when 0.7≤L / M<1. DETAILED DESCRIPTION

[0073] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0074] Method for determining seepage influence coefficient based on numerical simulation:

[0075] Building a numerical model

[0076] According to the symmetry, a numerical model for seepage calculation of circular foundation pit is established, such as Figure 2 The soil layer of the numerical model is a mixed sand-clay stratum, and the aquifer is mainly fine sand. The permeability coefficient k is calculated as r =k v =5×10 -6 m / s, water head height of pressure layer H = 30m, water head design value in the pit H d The thickness M of the aquifer is 10 m.

[0077] Five working conditions r0 / M = 1, 3, 5, 7, and 9 were selected for numerical experiments, and the variation law of coefficient α was explored based on this. The remaining five working conditions r0 / M = 2, 4, 6, 8, and 10 were used as verification conditions in the following text. By changing the foundation pit radius r0 and the length L of the water-stop curtain inserted into the confined aquifer, the variation law of the foundation pit water inflow with r0 / M and L / M was calculated, as shown in Figure 3 As shown. It can be seen that the insertion ratio L / M has a great influence on the amount of water inflow from the foundation pit. As L / M increases, the amount of water inflow from the foundation pit decreases continuously, and when the diameter of the foundation pit is small (r0 / M=1), Q and L / M are linearly related; in other cases, Q decreases linearly with the increase of L / M, and then decreases exponentially. Under the same L / M, as r0 / M increases, the amount of water inflow from the foundation pit increases continuously, but the rate of increase decreases continuously. Figure 4 It can be seen that when the foundation pit size is large, at a larger insertion ratio (L / M=0.9), the water inflow in the foundation pit is still large. To effectively control the water inflow, it is necessary to increase the insertion ratio to form a bottom-drop water-stop curtain. The specific relationship will be analyzed later.

[0078] Substituting the water inflow obtained by numerical calculation into the analytical formula for calculating water inflow in this method, the variation law of the seepage influence coefficient α with r0 / M and L / M can be obtained, as follows: Figure 5 As shown. It can be seen that r0 / M and L / M have different degrees of influence on α, and L / M has a greater influence relatively speaking. If the influence of the curtain insertion ratio on the equivalent seepage diameter is not considered, α is taken as 1, and each working condition roughly corresponds to the condition when L / M = 0.7-0.8 in the figure, that is, at this time, the theoretical calculation results of water inflow are consistent with the numerical results.

[0079] The seepage coefficient α is obtained by inverse analysis of the water inflow from the numerical simulation results and its function expression is fitted.

[0080] For r0 / M>3:

[0081] (1) First establish the functional relationship between α and L / M

[0082] When r0 / M>3, Figure 5 The curves of coefficient α changing with L / M when r0 / M=5, 7, and 9 obtained from numerical experiments are fitted with functions, and the fitting function is used as the value function of coefficient α when r0 / M>3. Observing the curve, it is found that when 0<L / M<0.7, the relationship between coefficient α and L / M changes is close to linear change, that is, it conforms to a linear function:

[0083]

[0084] For the nonlinear segment of the curve when 0.7≤L / M<1, a quadratic polynomial is used to fit the relationship between the coefficient α and the L / M change:

[0085]

[0086] Where A is the intercept of the linear function, K is the slope of the linear function, I is the intercept of the quadratic polynomial, B1 is the coefficient of the linear term, and B2 is the coefficient of the quadratic term.

[0087] Therefore, L / M = 0.7 is used as the dividing point between the linear segment and the nonlinear segment, and the coefficient α is used as the piecewise function. The piecewise fitting results and the values ​​of the parameters of the fitting function are as follows: Figure 7 , as shown in Table 1:

[0088] Table 1 Parameters of the fitting function when r0 / M=5,7,9

[0089]

[0090] (2) Establish the functional relationship between coefficient α and r0 / M

[0091] Using the data in Table 1, the variation of A, K, I, B1, and B2 with r0 / M is assumed to be linear and fitted, that is, formula (30). The fitting results and parameter values ​​in formula (30) are shown in Tables 2, 3, Figure 8 Shown

[0092]

[0093] Table 2 The linear function parameter values ​​of A and K as r0 / M changes

[0094]

[0095] Table 3 The linear function parameter values ​​of I, B1, B2 as r0 / M changes

[0096]

[0097] (3) Finally, when \(r_0 / M>3\), the expression of coefficient \(\alpha\) with respect to \(L / M\) and \(r_0 / M\) is obtained, that is, (32)

[0098]

[0099] Substituting (30) into (28) and (29), the piecewise function of coefficient \(\alpha\) when \(r_0 / M>3\) can be obtained

[0100]

[0101] In the formula, \(a_1\), \(a_2\), \(k_1\), \(k_2\), \(i_1\), \(i_2\), \(b_1\), \(b_2\), \(b_3\), \(b_4\) are fixed values, and their values are shown in Tables 2 and 3

[0102] It should be noted here that the piecewise function of coefficient \(\alpha\) in formula (31) is discontinuous at the point \(L / M = 0.7\). If you want to obtain the curve of the water inflow varying continuously with \(L / M\), then the water inflow in the interval \(0.6<L / M<0.7\) can be calculated by the interpolation method. The analytical solution of the water inflow in the following text is also based on this method. After calculation and verification, in the interval \(0.6<L / M<0.7\), the water inflow values calculated by formula (31) and the interpolation method are very close and can meet the accuracy requirements

[0103] For the case of \(0 < r_0 / M\leq3\)

[0104] (1) First, establish the functional relationship between \(\alpha\) and \(L / M\)

[0105] When \(0 < r_0 / M\leq3\), according to the above method, for the coefficient \(\alpha\) varying with \(L / M\) in the intervals \(0 < L / M < 0.7\) and \(0.7\leq L / M < 1\), a linear function and a quadratic polynomial fitting are carried out for the change curves respectively. The fitting results and the parameter values of the fitting functions are as Fig. 9 shown in Table 4

[0106] Table 4 Parameter values of the fitting function when \(r_0 / M = 1, 3\):

[0107]

[0108] 2) Then, establish the functional relationship between coefficient \(\alpha\) and \(r_0 / M\)

[0109] Similarly, as shown in formula (30), assume that the values of \(A\), \(K\), \(I\), \(B_1\), \(B_2\) vary linearly with \(r_0 / M\) and carry out fitting. The parameter values are shown in Tables 5 and 6

[0110] Table 5 Parameter values of the linear fitting function of \(A\), \(K\) varying with \(r_0 / M\)

[0111]

[0112] Table 6 The linear fitting function parameter values ​​of I, B1, B2 as r0 / M changes

[0113]

[0114] When 0<r0 / M≤3, the coefficient α variation function form is the same as (31), where a1, a2, k1, k2, i1, i2, b1, b2, b3, and b4 are constants, and their values ​​are shown in Tables 5 and 6.

[0115] (3) Finally, we get the expression of coefficient α with respect to L / M and r0 / M when r0 / M>3, that is, (32)

[0116]

[0117] In summary, the value of coefficient α in different cases can be calculated according to (32):

[0118]

Claims

1. The method for analyzing the water inflow of a suspended water-stop curtain in a circular foundation pit of a confined water layer is characterized by: The central axis of the circular foundation pit is taken as the z-axis, the radial direction of the foundation pit is taken as the r-axis, and the intersection of the central axis and the bottom plate of the aquifer is selected as the origin O to establish a cylindrical coordinate system. According to the principle of groundwater dynamics, a mathematical model of a suspended water-stop curtain foundation pit in a confined water stratum is established; where H is the height of the confined water head, r0 is the radius of the circular foundation pit, R is the influence radius of the foundation pit pumping, h0 is the head value of the water head contour line at the central axis of the bottom of the water-stop curtain, D(z) is the water head distribution function at the outer wall of the water-stop curtain, and H d is the design value of water head in the pit, H w is the total water head value at the maximum depth of the top plate of the confined aquifer outside the pit, L is the length of the water-stop curtain inserted into the confined aquifer, and M is the thickness of the aquifer; This model ignores the thickness of the water-stop curtain, assumes that the seepage process in the pit is a three-dimensional stable flow, and the water head lines in the pit are all horizontal lines; the seepage area is divided into three parts: the area outside the pit, that is, area 1; the area below the water-stop curtain in the pit, that is, area 2; and the vertical seepage area in the pit, that is, area 3; due to the existence of the water-stop curtain, the water flow in area 1 flows around into area 2, and the flow direction of the water flow directly below the water-stop curtain is horizontal. The water flow turns in area 2 and flows into area 3 in the vertical direction; the foundation pit decompression and dewatering process is equivalent to the large-diameter pumping well dewatering process, and the pit is simplified to vertical seepage, so it is assumed that area 3 is vertical seepage; according to the seepage continuity principle, it can be seen that the flow rates in the three areas are the same, that is, Q1=Q2=Q3=Q, where Q1 is the flow rate in area 1, Q2 is the flow rate in area 2, Q3 is the flow rate in area 3, and Q is the total water inflow in the foundation pit; The total water head h(r, θ, z) at any point (r, θ, z) in the seepage field of the calculation area is independent of the angle, that is, the total water head at each point is expressed as h(r, z); the boundary conditions in the seepage area are: h(r,z)=H; r=r0+R, z>0 (1) h=h0; r=r0, 0≤z≤ML (4) h=D(z); r=r0, ML≤z≤M (5) h(r,z)=H d ;0<r<r0,z=H d (6) According to the seepage continuity principle, the flow rates in the three regions are the same: Q1=Q2=Q3 (7) S1. Solution of foundation pit seepage flow; First, the seepage volume in region 1 is calculated. According to Darcy’s law, the horizontal seepage velocity v at any point in the confined aquifer is r for: Where k r is the horizontal permeability coefficient in the confined aquifer: In area 1, the flow rate passing through any section per unit time, that is, the flow rate Q1 in area 1 is: Substituting equation (8) into equation (9) yields the expression for flow rate Q1 in region 1: Transforming formula (10) we can get: Integrate both sides of the equation with respect to r: Where C is the unknown coefficient. Substitute the boundary condition (1) into the formula to obtain the value of C: Substituting the C value into formula (12) we can obtain: When r=r0: Decompose the above integral: According to boundary conditions (3) and (4), we can obtain: According to existing research results, the water head distribution function D(z) outside the water-stop curtain in the range of ML<z<M is expressed as: By combining equations (15) to (20), we can get the expression of seepage flow in region 1: S2. Solution of seepage flow in foundation pit The water flow in area 1 flows around and enters area 2, and the water flow in area 2 turns and enters area 3. Only vertical seepage occurs in area 3, so the shortest seepage path of water flow in areas 2 and 3 is: L min =H d -M+L (21) The longest seepage path is: L max =r0+H d (22) It should be noted that if the water head line at the bottom of the pit is above the bottom plate of the upper impermeable layer, that is, H d >M, then H in (21) and (22) d When using Darcy's law to solve the water inflow in the foundation pit, most of the existing theoretical analyses define the equivalent seepage length in the foundation pit as the average of the maximum seepage length and the minimum seepage length, or directly assume that 2L min The water inflow in the pit calculated in these two cases is only reasonable in certain specific intervals of r0 / M and L / M. In fact, the value of the equivalent seepage length in the foundation pit should vary with r0 / M and L / M. It is directly used as half of the sum of the maximum seepage length and the minimum seepage length or 2L. min The substitution is unreasonable. In order to accurately calculate the value of water inflow in the foundation pit under various working conditions, the seepage path influence coefficient α, which reflects the change of the equivalent seepage path length with r0 / M and L / M, is introduced, and the change law is explored through numerical experiments. The length of the equivalent seepage path in the foundation pit can be expressed as: Where α is the r0 / M, L / M function: The water inflow in areas 2 and 3 is: S3. Determine the water inflow from the foundation pit; When the thickness of the water-stop curtain is ignored, when water flows around the water-stop curtain, the head loss through the inner side of the curtain is greater than the head loss through the outer side of the curtain. According to the existing experimental data and theoretical research results, the head loss of water flowing through the inner side of the curtain under various working conditions in the phreatic aquifer accounts for 2 / 3 of the total loss. Regardless of whether in the confined water layer or the phreatic layer, the direction and characteristics of water flowing around the water-stop curtain are consistent. Therefore, this conclusion is applied to the confined water formation, and the head value h0 of the equal head line at the bottom of the curtain is expressed as (26). According to the principle of seepage continuity, (20), (25), and (26) are combined to obtain the maximum drawdown head H at the top plate of the confined aquifer outside the pit. w Distribution function (27): Substituting (25) (26) into (27) can obtain the water inflow of the circular foundation pit, and the permeability coefficient k is calculated as r =k v =5×10 -6 m / s.

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