A method for calculating the steady-state seepage field in foundation pits with low permeability soil layers

Abstract

This invention discloses a method for calculating the steady-state seepage field of a foundation pit in a low-permeability soil layer, comprising: S1: simplifying the target foundation pit into a circular foundation pit using the principle of area equivalence; S2: establishing a three-dimensional seepage model of the foundation pit in a homogeneous soil layer based on the circular foundation pit; S3: determining the boundary conditions based on the three-dimensional seepage model of the foundation pit in the homogeneous soil layer; S4: obtaining the homogeneous differential equation of seepage continuity in spherical coordinates based on Hansberg's seepage law considering nonlinear seepage characteristics and the seepage continuity equation under the boundary conditions; S5: separating the variables of the homogeneous differential equation of seepage continuity to obtain the homogeneous differential equation after variable separation; S6: obtaining the pore water pressure and the water inflow at the bottom of the foundation pit at each point in the steady-state seepage field outside the foundation pit based on the homogeneous differential equation after variable separation and the boundary conditions. This invention can solve the problem of low permeability coefficient caused by the failure to consider nonlinear seepage factors in existing seepage field calculations.

Description

Technical Field

[0001] This invention relates to the field of civil engineering seepage field calculation technology, specifically to a method for calculating the steady-state seepage field of a foundation pit in a low-permeability soil layer. Background Technology

[0002] In recent years, with the continuous growth of the national economy and the increasing level of urbanization, more and more super high-rise buildings and large-scale underground complexes have appeared in cities, leading to a sharp increase in the number of deep foundation pits. Because there are often confined aquifers at the bottom of deep foundation pits, when the water head of the confined aquifer is high, dewatering and pressure-reducing measures are needed to avoid problems such as sudden water inrush at the bottom of the pit and overall structural uplift. Among existing groundwater pressure-reducing measures, the method of setting up a dense network of dewatering wells within the pit is widely used due to its advantages such as good water control effect and simple and rapid construction. In order to rationally design the total pumping volume or total drainage volume of the pressure-reducing well group, it is necessary to accurately calculate the inflow volume within the foundation pit under different design values ​​of the water head at the bottom of the pit.

[0003] For research on the seepage field distribution and water inflow around foundation pits, scholars both domestically and internationally mainly employ methods such as theoretical analysis, numerical simulation, and indoor and in-situ experiments. Theoretical analysis includes mathematical methods such as integral transform and conformal transformation; numerical methods include the finite element method and the finite difference method.

[0004] However, the above methods are all based on Darcy's seepage theory. Current research shows that fluids in low-permeability media exhibit significant nonlinear seepage characteristics, meaning they no longer conform to Darcy's law. Many urban strata exhibit distinct stratification, belonging to sand-clay mixed strata with low permeability coefficients. Extensive indoor experiments and field monitoring data demonstrate discrepancies between theoretical analysis results and measured data. Therefore, it is necessary to consider nonlinear seepage factors in the calculation formulas for the seepage field and inflow rate of foundation pits in low-permeability soil layers. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers, so as to solve the problem of low permeability coefficient caused by the failure of existing seepage field calculations to consider nonlinear seepage factors.

[0006] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for calculating the steady-state seepage field of a foundation pit in a low-permeability soil layer. The method includes:

[0008] S1: Simplify the target foundation pit into a circular foundation pit by using the principle of area equivalence;

[0009] S2: Based on the circular foundation pit, establish a three-dimensional model of the seepage in the homogeneous soil layer;

[0010] S3: Determine the boundary conditions based on the three-dimensional model of seepage in the foundation pit in the homogeneous soil layer;

[0011] S4: Based on Hansberg's seepage law considering nonlinear seepage characteristics and the seepage continuity equation under boundary conditions, the homogeneous differential equation of seepage continuity in spherical coordinates is obtained.

[0012] S5: Separate the variables of the homogeneous differential equation for the continuity of seepage to obtain the homogeneous differential equation after variable separation;

[0013] S6: Based on the homogeneous differential equation after separation of variables and the boundary conditions, the pore water pressure and the water inflow at the bottom of the foundation pit at each point in the steady-state seepage field outside the foundation pit are obtained.

[0014] Alternatively, S2 includes:

[0015] A three-dimensional coordinate system is established with the central axis of the circular foundation pit as the z-axis, the bottom plate of the foundation pit as the x-axis, and the intersection of the central axis and the bottom plate of the foundation pit as the origin o.

[0016] The circular foundation pit, including a three-dimensional coordinate system, is output as a three-dimensional model of the foundation pit seepage in the homogeneous soil layer.

[0017] Alternatively, in S3, the boundary conditions are:

[0018]

[0019] Among them, H r For total head and pr is the pore water pressure at each point in the seepage field, γ w The density of water, z Let R be the ordinate of the circular foundation pit, R be the radius of the seepage influence, r1 be the equivalent radius of the circular foundation pit, and H be the ordinate of the circular foundation pit. w For the far-field head.

[0020] Alternatively, in S4, the Hansberg seepage law considering nonlinear seepage characteristics is:

[0021]

[0022] Among them, v i K represents the radial seepage velocity. r Let be the soil permeability coefficient of the straight segment, i be the hydraulic gradient, m be the power, and k be the number of water molecules. rs Let i be the soil permeability coefficient of the curve segment, and when i approaches i1 i1 is the critical hydraulic gradient, representing the boundary between the curved segment and the straight segment, and i0 represents the intercept of the line segment with the coordinate axis, and as i approaches i1...

[0023] Alternatively, in S4, the homogeneous differential equation for seepage continuity in the spherical coordinate system is:

[0024]

[0025] Where m is the power, i is the hydraulic gradient, i1 is the critical hydraulic gradient, and H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, z Let r be the ordinate of the circular foundation pit, and r be the distance from any point in the seepage field to the origin.

[0026] Alternatively, in step S5, the homogeneous differential equation after separation of variables is:

[0027]

[0028] Among them, H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, z Let y be the ordinate of the circular foundation pit, r be the distance from any point in the seepage field to the origin, m be the power, i be the hydraulic gradient, i1 be the critical hydraulic gradient, and c1 ~ c 10 The coefficients are undetermined and R is the radius of the seepage influence, r1 is the equivalent radius of the circular foundation pit, and H w For the far-field head.

[0029] Alternatively, in S6, the pore water pressure p at each point in the steady-state seepage field outside the foundation pit... r for:

[0030]

[0031] Where, γ w Let be the unit weight of water, x, y, z be the coordinates of any point within the calculation region of the seepage field, r be the distance from any point in the seepage field to the origin, m be the power, i be the hydraulic gradient, i1 be the critical hydraulic gradient, and c1 ~ c 10 The coefficients are undetermined and R is the radius of influence of seepage, r1 is the equivalent radius of the circular foundation pit, and H w For the far-field head.

[0032] Alternatively, in step S6, the water inflow Q at the bottom of the foundation pit... r Calculated in the following way:

[0033]

[0034] Where π is the mathematical constant pi, r is the distance from any point in the seepage field to the origin, and k r Let be the soil permeability coefficient of the straight segment, i be the hydraulic gradient, m be the power, and k be the number of water molecules. rs Let i be the soil permeability coefficient of the curve segment, and when i approaches i1 i1 is the critical hydraulic gradient, representing the boundary between the curved segment and the straight segment, and i0 represents the intercept of the line segment with the coordinate axis, and as i approaches i1... H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, z Let c1 be the ordinate of the circular foundation pit, and c1 be the coordinate of the ordinate ... 10 The coefficients are undetermined and R is the radius of influence of seepage, r1 is the equivalent radius of the circular foundation pit, and H w For the far-field head.

[0035] The present invention has the following beneficial effects:

[0036] This invention fully considers the characteristics of nonlinear seepage, thereby obtaining seepage field data that matches the actual situation, and thus obtaining accurate water inflow, improving the efficiency and accuracy of urban pressure relief well group design. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the method for calculating the steady-state seepage field in a foundation pit using low-permeability soil layers, as described in this invention.

[0038] Figure 2 This is a schematic diagram of the three-dimensional seepage field in a circular foundation pit with homogeneous soil.

[0039] Figure 3 This is a schematic diagram of a three-dimensional seepage calculation model and water head boundary conditions for a circular foundation pit in homogeneous soil. Detailed Implementation

[0040] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0041] This invention provides a method for calculating the steady-state seepage field in a foundation pit with low permeability soil layers, with reference to... Figures 1 to 3 As shown, the method for calculating the steady-state seepage field of the foundation pit in the low-permeability soil layer includes:

[0042] S1: Simplify the target foundation pit into a circular foundation pit by using the principle of area equivalence;

[0043] S2: Based on the circular foundation pit, establish a three-dimensional model of the seepage in the homogeneous soil layer;

[0044] Different shaped foundation pits are simplified into circular foundation pits according to the principle of area equivalence. The central axis of the circular foundation pit is taken as the z-axis, the bottom plate of the foundation pit is taken as the x-axis, and the intersection of the central axis and the bottom plate of the foundation pit is selected as the origin to establish a coordinate system, thereby establishing a three-dimensional model of foundation pit seepage in homogeneous soil layer.

[0045] S3: Determine the boundary conditions based on the three-dimensional model of seepage in the foundation pit in the homogeneous soil layer;

[0046] The boundary conditions are as follows:

[0047]

[0048] Among them, H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, z Let R be the ordinate of the circular foundation pit, R be the radius of the seepage influence, r1 be the equivalent radius of the circular foundation pit, and H be the ordinate of the circular foundation pit. w For the far-field head.

[0049] S4: Based on Hansberg's seepage law considering nonlinear seepage characteristics and the seepage continuity equation under boundary conditions, the homogeneous differential equation of seepage continuity in spherical coordinates is obtained.

[0050] Assuming the soil layer is single, homogeneous, and isotropic, the seepage of water in the soil conforms to the principle of seepage continuity, the equipotential surfaces in the seepage field are hemispherical, and only radial seepage is considered.

[0051] The continuity equation for seepage is:

[0052]

[0053] Where u, v, and w are the seepage velocities in the three directions, and x, y, and z are the coordinates of any point within the calculation area of ​​the seepage field.

[0054] Hansberg's seepage law, considering nonlinear seepage characteristics, is as follows:

[0055]

[0056] Among them, v i K represents the radial seepage velocity. r Let be the soil permeability coefficient of the straight segment, i be the hydraulic gradient, m be the power, and k be the number of water molecules. rs Let be the soil permeability coefficient of the curved segment, and i1 be the critical hydraulic gradient, representing the boundary between the curved and straight segments. i0 represents the intercept of the straight line segment with the coordinate axis. Since the Hansberg seepage model is a smooth curve, when i approaches i1, the slope of the curve segment equals the slope of the straight line segment, therefore k... rs i0 can be represented as:

[0057]

[0058] The Hansberg seepage law, which considers nonlinear seepage characteristics, is substituted into the seepage continuity equation (i.e.,...) and (Simultaneous equations), and then express the system of equations in spherical coordinates to obtain homogeneous differential equations.

[0059] In a spherical coordinate system with the center of the bottom of the excavation pit as the origin, v i i can be represented as:

[0060]

[0061]

[0062] Where θ represents v i The angle between the projection of the object onto the xoy plane and the x-axis. Indicates v i The angle with the z-axis.

[0063] Therefore, the homogeneous differential equation for seepage continuity in the spherical coordinate system is:

[0064]

[0065] After simplification, it becomes:

[0066]

[0067] Where m is the power, i is the hydraulic gradient, i1 is the critical hydraulic gradient, and H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, z Let r be the ordinate of the circular foundation pit, and r be the distance from any point in the seepage field to the origin.

[0068] S5: Separate the variables of the homogeneous differential equation for the continuity of seepage to obtain the homogeneous differential equation after variable separation;

[0069] The homogeneous differential equation after separation of variables is:

[0070]

[0071] Among them, H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, z Let y be the ordinate of the circular foundation pit, r be the distance from any point in the seepage field to the origin, m be the power, i be the hydraulic gradient, i1 be the critical hydraulic gradient, and c1 ~ c 10 The coefficients are undetermined and R is the radius of influence of seepage, r1 is the equivalent radius of the circular foundation pit, and H w For the far-field head.

[0072] S6: Based on the homogeneous differential equation after separation of variables and the boundary conditions, the pore water pressure and the water inflow at the bottom of the foundation pit at each point in the steady-state seepage field outside the foundation pit are obtained.

[0073] Because the total head is: Based on this, the pore water pressure p at each point in the steady-state seepage field outside the foundation pit r for:

[0074]

[0075] Where, γ w Let x, y, z be the coordinates of any point within the calculation region of the seepage field, r be the distance from any point in the seepage field to the origin, m be the power, i be the hydraulic gradient, i1 be the critical hydraulic gradient, and c1 ~ c 10 The coefficients are undetermined and R is the radius of influence of seepage, r1 is the equivalent radius of the circular foundation pit, and H w For the far-field head.

[0076] Optionally, the water inflow Q at the bottom of the foundation pit r Calculated in the following way:

[0077]

[0078] Where π is the mathematical constant pi, r is the distance from any point in the seepage field to the origin, and k r Let be the soil permeability coefficient of the straight segment, i be the hydraulic gradient, m be the power, and k be the number of water molecules. rs Let i be the soil permeability coefficient of the curve segment, and when i approaches i1 i1 is the critical hydraulic gradient, representing the boundary between the curved segment and the straight segment, and i0 represents the intercept of the line segment with the coordinate axis, and as i approaches i1... H r For total head and p r γ is the pore water pressure at each point in the seepage field. w The density of water, zLet c1 be the ordinate of the circular foundation pit, and c1 be the coordinate of the ordinate ... 10 The coefficients are undetermined and R is the radius of influence of seepage, r1 is the equivalent radius of the circular foundation pit, and H w For the far-field head.

[0079] The water inflow of the foundation pit calculated under different values ​​of m and i1 according to the present invention is shown in Table 1.

[0080] Table 1 shows the calculated pit water inflow under different values ​​of m and i1.

[0081] Nonlinear coefficients <![CDATA[m=1,i1=10]]> <![CDATA[m=2,i1=10]]> <![CDATA[m=3,i1=10]]> <![CDATA[Water inflow Q / (m 3 / d)]]> 678.58 419.15 200.96

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the steady-state seepage field in a foundation pit with low permeability soil layers, characterized in that, The calculation method for the steady-state seepage field of the foundation pit in the low-permeability soil layer includes: S1: Simplify the target foundation pit into a circular foundation pit by using the principle of area equivalence; S2: Based on the circular foundation pit, establish a three-dimensional model of the seepage in the homogeneous soil layer; S3: Determine the boundary conditions based on the three-dimensional model of seepage in the foundation pit in the homogeneous soil layer; S4: Assuming the soil layer is homogeneous and isotropic, the equipotential surfaces in the seepage field are hemispherical, and only radial seepage is considered, based on Hansberg's seepage law considering nonlinear seepage characteristics and the seepage continuity equation under boundary conditions, the homogeneous differential equation for seepage continuity in spherical coordinates is obtained, where the seepage continuity equation is: Where u, v, and w are the seepage velocities in the three directions, and x, y, and z are the coordinates of any point within the calculation area of ​​the seepage field; S5: Separate the variables of the homogeneous differential equation for the continuity of seepage to obtain the homogeneous differential equation after variable separation; S6: Based on the homogeneous differential equation after separation of variables and the boundary conditions, the pore water pressure and the water inflow at the bottom of the foundation pit at each point in the steady-state seepage field outside the foundation pit are obtained.

2. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 1, characterized in that, S2 includes: With the central axis of the circular foundation pit as z The shaft and the bottom slab of the foundation pit are x The origin is the intersection of the axis, the central axis, and the bottom slab of the foundation pit. o Establish a three-dimensional coordinate system; The circular foundation pit, including a three-dimensional coordinate system, is output as a three-dimensional model of the foundation pit seepage in the homogeneous soil layer.

3. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 1, characterized in that, In S3, the boundary conditions are: in, For total head and , p r The pore water pressure at each point in the seepage field is... The density of water, Let be the ordinate of the circular foundation pit. Let be the distance from any point in the seepage field to the origin. Radius affected by seepage This is the radius of the equivalent circular foundation pit. For the far-field head.

4. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 3, characterized in that, In S4, the Hansberg seepage law considering nonlinear seepage characteristics is: in, Radial seepage velocity, Let be the soil permeability coefficient for the straight segment. For hydraulic gradient, For powers, Let be the soil permeability coefficient of the curve segment and when tending to hour , The critical hydraulic gradient represents the boundary between the curved segment and the straight segment. , Represents the intercepts of a line segment with the coordinate axes, and when tending to hour .

5. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 4, characterized in that, In S4, the homogeneous differential equation for seepage continuity in the spherical coordinate system is: in, For powers, For hydraulic gradient, The critical hydraulic gradient, For total head and , The pore water pressure at each point in the seepage field is... The density of water, Let be the ordinate of the circular foundation pit. Let be the distance from any point in the seepage field to the origin.

6. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 5, characterized in that, In S5, the homogeneous differential equation after separation of variables is: in, For total head and , The pore water pressure at each point in the seepage field is... The density of water, Let be the ordinate of the circular foundation pit. Let be the distance from any point in the seepage field to the origin. For powers, For hydraulic gradient, The critical hydraulic gradient, ~ The coefficients are undetermined and , Radius affected by seepage This is the radius of the equivalent circular foundation pit. For the far-field head.

7. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 6, characterized in that, In S6, the pore water pressure at each point in the steady-state seepage field outside the foundation pit. for: in, The density of water, 、 、 Given the coordinates of any point within the seepage field calculation area, Let be the distance from any point in the seepage field to the origin. For powers, For hydraulic gradient, The critical hydraulic gradient, ~ The coefficients are undetermined and , Radius affected by seepage This is the radius of the equivalent circular foundation pit. For the far-field head.

8. The method for calculating the steady-state seepage field of a foundation pit in low-permeability soil layers according to claim 7, characterized in that, In S6, the water inflow at the bottom of the foundation pit Calculated in the following way: in, Pi Let be the distance from any point in the seepage field to the origin. Let be the soil permeability coefficient for the straight segment. For hydraulic gradient, For powers, Let be the soil permeability coefficient of the curve segment and when tending to hour , The critical hydraulic gradient represents the boundary between the curved segment and the straight segment. , Represents the intercepts of a line segment with the coordinate axes, and when tending to hour , For total head and , The pore water pressure at each point in the seepage field is... The density of water, Let be the ordinate of the circular foundation pit. ~ The coefficients are undetermined and , Radius affected by seepage This is the radius of the equivalent circular foundation pit. For the far-field head.

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