CN114357592A - Method for analyzing water inflow of suspended waterproof curtain of circular foundation pit of confined water layer - Google Patents
Method for analyzing water inflow of suspended waterproof curtain of circular foundation pit of confined water layer Download PDFInfo
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Abstract
The invention discloses a method for analyzing the water inflow of a suspended waterproof curtain of a circular foundation pit of a confined water layer, which solves the water inflow of the circular foundation pit of the suspended waterproof curtain of the confined water layer by applying the principle of groundwater dynamics, introduces the influence coefficient of the seepage diameter of the foundation pit and provides a determination method thereof, and the main implementation steps comprise S1 and the solution of the seepage flow of the foundation pit; s2, solving the seepage flow in the foundation pit; s3, determining the water inflow amount of the foundation pit; the method establishes a calculation model of the water inflow of the foundation pit with the suspended waterproof curtain in the confined water stratum, obtains a calculation formula of key parameters, namely the seepage diameter influence coefficient by adopting positive and negative analysis and fitting of numerical simulation, verifies the analytic solution of the method by supplementing numerical simulation of a large number of verification working conditions, has better coincidence of calculation results, and shows the correctness and the rationality of the analytic model of the method.
Description
Technical Field
The invention relates to a method for analyzing the water inflow of a suspended waterproof curtain, in particular to a method for analyzing the water inflow of a suspended waterproof curtain of a circular foundation pit of a confined water layer, and belongs to the technical field of analysis of the water inflow of the waterproof curtain at the bottom of a deep foundation pit.
Background
In recent years, with the increasing national economy and the increasing urbanization level, more and more super high-rise buildings and large-scale underground complexes appear in cities, and the number of deep foundation pits is increased sharply. The bottom of the deep foundation pit often has a confined water layer, and when the water head of the confined water layer is higher, the problems of sudden surge at the bottom of the pit, integral floating of the structure and the like need to be avoided by adopting a dewatering and pressure reducing measure. In the existing underground water pressure reduction measures, a wall-well intercepting and draining pressure reduction system formed by matching a pumping well with a suspended water stop curtain is widely adopted due to the advantages of good water control effect, simplicity and quickness in construction and the like. In the design process of a wall-well system, in order to reasonably design the total water pumping quantity or the total drainage quantity of a pressure reduction well group, the water inflow quantity in a suspended curtain foundation pit under different design values of a pit bottom water head needs to be accurately calculated. At present, scholars at home and abroad develop research on water inflow in a foundation pit of a suspended curtain by using research means such as theoretical derivation, numerical simulation, indoor model test and the like. The Wang military glow and the like modify a large well method formula and deduce a water inflow calculation formula for diving and confined water under the condition of considering the waterproof curtain by analyzing the seepage characteristics of a streaming area and a non-streaming area in a seepage field influenced by the suspended waterproof curtain. According to the distribution rule of the internal and external flow networks of the foundation pit, Zhang Zhihong and the like, a water inflow calculation formula of the circular foundation pit with the suspended waterproof curtain in the deep diving layer is deduced according to the underground water dynamics principle. Li Yu et al will hang the curtain foundation ditch and is equivalent to the major diameter pressure-bearing whole well that the wall of a well was intake according to the area, deduct the simplified formula that the foundation ditch was cut and is arranged the reduction of pressure and precipitation and gush water yield and calculate, and compare with numerical value calculation result and verify and draw the conclusion: the simplified formula has higher precision when the curtain insertion ratio is more than 0.6 and the ratio of the radius of the foundation pit to the thickness of the bearing water-containing layer is less than 2.0. The Xiaoming encourage and the like establish a three-dimensional seepage finite element model through analysis of the hydrogeological conditions of the Wuchang shield well foundation pit of the Wuhan Changjiang tunnel, and carry out numerical simulation calculation on the dewatering process of the deep foundation pit of the suspended waterproof curtain. Under the condition that the total water pumping amount of the foundation pit is fixed, the mutual relation between the insertion depth of the waterproof curtain and the water head values inside and outside the foundation pit is quantitatively analyzed. Liguanming and the like rely on the foundation pit dewatering project of a Tianjin subway station, the stratum parameters of a numerical model are inverted through field water pumping test data, and then the numerical simulation calculation is carried out on the water inflow amount in the pit in the dewatering process of the suspended curtain foundation pit by using a finite difference method. Zhangpei, Zhang Qinxian and the like explore the influence of the insertion depth of the waterproof curtain on the water inflow amount in the foundation pit through an indoor model box experiment, provide a reasonable value range of the insertion depth of the waterproof curtain and provide reference for design parameters of the waterproof curtain in the actual engineering.
However, the existing theoretical analysis for solving the water inflow of the foundation pit with the suspended curtain has larger error compared with the actual situation and the numerical simulation result, and only in certain specific r0With better accuracy in the/M, L/M range (where r0Radius of the circular foundation pit, L is the insertion depth of the water curtain, and M is the thickness of the pressure-bearing water-containing layer), because the seepage length in the pit is unreasonable. The existing numerical method is mainly used for researching the suspended curtain foundation pit based on certain specific engineering, the accuracy of the result depends on specific boundary conditions and hydrogeological parameters, and the method has no universality on the guidance of the engineering. Under the background, the method uses the groundwater dynamics principle to solve the water inflow of the circular foundation pit with the confined water layer suspended waterproof curtain, introduces the influence coefficient of the seepage diameter of the foundation pit, and provides a determination method thereof.
In the prior art, a method for determining the water pumping amount of a suspended curtain confined water foundation pit based on three-dimensional depth reduction is disclosed in the specification: the invention provides a method for determining the pumping capacity of a foundation pit with suspended curtain confined water based on three-dimensional depth reduction, which comprises the steps of firstly calculating a water level depth reduction control value outside the pit and deducing a total water inflow control value of the foundation pit; after the safe depth reduction of the top of the confined water in the pit is determined and the precipitation scheme is arranged, the total water inflow of the foundation pit and the water pumping amount of a single well of the precipitation scheme are determined through the safe depth reduction control value of the confined water in the pit, and whether the water inflow of the foundation pit is within the control value can be further checked. Based on Darcy's law and flow balance theorem, the invention fully considers the three-dimensional seepage field formed by the foundation pit dewatering under the suspension type waterproof curtain and the safe water level depth reduction inside and outside the pit, can accurately calculate the water pumping amount of the foundation pit and the dewatering well under a specific dewatering scheme, and can ensure that the water level depth reduction of the confined water inside and outside the pit under the water pumping amount is in a safe and controllable range. The precipitation scheme formulated based on the invention not only reduces the construction cost, but also ensures the safety of precipitation construction. According to the provided materials, the prior art related to the technical scheme is searched (CN110055989B is a method for determining the pumping quantity of a foundation pit of confined water of a suspended curtain based on three-dimensional depth reduction), and compared with the prior art, the technical scheme has the distinguishing technical characteristics, so the technical scheme has novelty; aiming at the technical means adopted by the technical scheme and the achieved technical effect, the technical scheme has outstanding substantive features and obvious progress, so the technical scheme has creativity.
Disclosure of Invention
The invention aims to provide an analysis method for the water inflow of a suspended waterproof curtain of a circular foundation pit of a confined water layer.
The technical scheme adopted by the invention is a method for analyzing the water inflow of the suspended waterproof curtain of the circular foundation pit of the confined water layer, the central axis of the circular foundation pit is taken as a z axis, the radial direction of the foundation pit is taken as an r axis, and the intersection point of the central axis and the bottom plate of the confined water layer is selected as an origin O to establish a cylindrical coordinate system, so that a mathematical model of the suspended waterproof curtain of the confined water layer is established according to the underground water dynamics principle, as shown in figure 1. Wherein H is the height of the confined water head, r0Is the radius of a round foundation pit, and R is a basePit pumping affects radius h0A water head value of a water head contour line at a central axis of the bottom of the water curtain, D (z) a water head distribution function (expression formula 19) at an outer side wall of the water curtain, HdDesigned value for water head in pit, HwThe total water head value (the expression is shown in 27) of the maximum depth of the top plate of the confined aquifer outside the pit, L is the length of the water curtain inserted into the confined aquifer, and M is the thickness of the aquifer.
The thickness of the waterproof curtain is ignored by the model, the seepage process in the pit is assumed to be three-dimensional stable flow, and the water head lines in the pit are all horizontal lines. The seepage area is divided into three parts, namely an area 1 outside the pit, an area 2 below a waterproof curtain in the pit and a vertical seepage area 3 in the pit. The water flow in the area 1 enters the area 2 in a circumfluence way due to the existence of the waterproof curtain, the flow direction of the water flow right below the waterproof curtain is horizontal, the water flow turns in the area 2 and flows into the area 3 along the vertical direction. In general, if the dewatering well points in the foundation pit are dense and reasonably distributed, the pressure reduction and dewatering process of the foundation pit can be equivalent to a large-diameter pumping well dewatering process, and the interior of the pit can be simplified into vertical seepage, so that the method assumes that the interior of the area 3 is vertical seepage. According to the seepage continuity principle, the flow in 3 areas is the same, namely Q1＝Q2＝Q3Q, wherein Q1Is the flow rate in the region 1, Q2Is the flow rate in zone 2, Q3The flow in the area 3 and Q is the total water inflow in the foundation pit.
The total head h (r, theta, z) of any point (r, theta, z) in the seepage field of the area is calculated independent of the angle, namely the total head of each point can be expressed as h (r, z). The boundary conditions in the percolation region are:
h(r,z)＝H；r＝r0+R，z＞0 (1)
h＝h0；r＝r0，0≤z≤M-L (4)
h＝D(z)；r＝r0，M-L≤z≤M (5)
h(r,z)＝Hd；0＜r＜r0，z＝Hd (6)
according to the seepage continuity principle, the flow in the three areas is the same:
Q1＝Q2＝Q3 (7)
s1, solving the foundation pit extravasation flow;
firstly, calculating the seepage flow in the region 1, and according to Darcy's law, calculating the horizontal seepage velocity v of any point in the pressure-bearing water-containing layerrComprises the following steps:
in the formula krThe horizontal permeability coefficient in the confined water-containing layer is as follows:
in zone 1, the flow rate per unit time through any cross section, i.e., the flow rate Q in zone 11Comprises the following steps:
bringing formula (8) into formula (9) to obtain a flow rate Q in area 11Expression:
by modifying the formula (11), the following can be obtained:
r is integrated simultaneously on both the left and right sides of the equation:
and C is a coefficient to be determined, a boundary condition (1) is substituted, and a value of C is obtained:
the C value is substituted for formula (13) to obtain:
when r is r0The method comprises the following steps:
the above equation is integrated:
from the boundary conditions (3) and (4):
according to the prior research result, the distribution function D (z) of the water stopping curtain outer side water head in the range of M-L < z < M is expressed as:
(15) expression of the seepage rate in the region 1 can be obtained by combining the expressions (20):
s2 solving seepage flow in foundation pit
The water flow in the area 1 flows into the area 2 in a circumambulated mode, the water flow in the area 2 turns to flow into the area 3, and only vertical seepage occurs in the area 3, so that the shortest seepage path of the water flow in the area 2 and the area 3 is as follows:
Lmin＝Hd-M+L (21)
the longest percolation path is:
Lmax＝r0+Hd (22)
it should be noted that: if the water head line at the bottom of the pit is positioned above the bottom plate of the upper impervious layer, namely Hd>M, then H in (21) and (22)dAnd is replaced by M. When the Darcy's law is utilized to solve the water inflow rate in the foundation pit, most of the existing theoretical analysis is to determine the equivalent seepage path length in the foundation pit as the average value of the maximum seepage path and the minimum seepage path, or directly assume 2LminThe water inflow quantity in the pit calculated in the two conditions is only r0It is reasonable to have some specific interval of/M, L/M. In fact, the value of the equivalent seepage length in the foundation pit should follow r0The ratio/M, L/M varies depending on the difference, and is directly determined by half the sum of the maximum and minimum diameters or 2LminThe replacement is not reasonable. In order to accurately calculate the value of the water inflow in the foundation pit under each working condition, the introduction of the equivalent seepage length along with r0The seepage diameter influence coefficient alpha of/M, L/M change is determined, and the change rule is explored through numerical experiments. The length of the equivalent seepage path in the foundation pit can be expressed as:
wherein α is r0the/M, L/M function:
the water gushes in zone 2 and zone 3 were:
s3, determining the water inflow amount of the foundation pit;
when the water flow flows around the waterproof curtain under the condition of neglecting the thickness of the waterproof curtain, the head loss passing through the inner side of the curtain is larger than the head loss passing through the outer side of the curtain. According to the existing experimental data and theoretical research results, the following results are shown: the head loss of the water flow passing through the inner side of the curtain in each working condition of the diving aquifer is about 2/3 of the total loss of the bypass flow. The direction and the characteristics of the water flow when the water flow flows around the waterproof curtain are consistent no matter in the confined water layer or the diving layer, so the conclusion is applied to the water head value h of the equal head line at the bottom end of the waterproof curtain in the confined water stratum0Denoted as (26). According to the seepage continuity principle, the maximum falling water head Hw distribution function (27) at the top plate of the confined aquifer outside the pit is obtained by combining (20), (25) and (26):
and (25) and (26) are substituted into (27) to obtain the water inflow of the circular foundation pit.
Compared with the prior art, the method establishes a calculation model of the water inflow of the foundation pit with the suspended waterproof curtain in the confined water stratum, obtains a calculation formula of key parameters, namely the seepage diameter influence coefficient by adopting positive and negative analysis fitting of numerical simulation, verifies the analytic solution of the method through supplementary numerical simulation of a large number of verification working conditions, has better coincidence of calculation results, and shows the correctness and the rationality of the analytic model of the method. The main conclusions obtained are as follows:
(1) for an analytic model of the water inflow of a foundation pit of a suspension type water-stop curtain in a confined water stratum, the influence coefficient value of the seepage has great influence on a calculation result, and the influence is comprehensively determined according to the factors such as the radius of the foundation pit, the thickness of the confined water layer in which the suspension type water-stop curtain is inserted, and the like.
(2) The method comprises the steps of obtaining a ratio (r0/M) of the radius of a foundation pit to the thickness of the confined water layer and a ratio (L/M) of the thickness of the confined water layer when a suspended waterproof curtain is inserted into the confined water layer, wherein the two parameters have the most direct and obvious influence on a seepage diameter influence coefficient alpha, and r0/M is 3 and L/M is 0.7, which are both influence critical values, and the method respectively provides calculation formulas of alpha under 4 conditions (r0/M is more than 0 and less than 3, L/M is more than 0 and less than 0.7), (r0/M is more than 0 and less than 3, L/M is more than 0.7 and less than 1), (r0/M is more than 3, L/M is more than 0 and less than 0.7), (r0/M is more than 3, L/M is more than 0.7 and less than 1) through numerical simulation positive and negative analysis.
(3) When the suspended waterproof curtain is selected as a groundwater control measure, the water control effect is reduced along with the increase of r0/M, and when the size of the foundation pit is larger, the falling bottom type waterproof curtain is recommended to be selected, so that the purpose of cutting off the hydraulic connection between the inside and the outside of the foundation pit is achieved.
Drawings
FIG. 1 shows a calculation model of a confined water stratum suspended waterproof curtain foundation pit.
FIG. 2 is a numerical model of a circular foundation pit with a suspended waterproof curtain.
FIG. 3 shows the water inflow as a function of the insertion ratio.
FIG. 4 shows the water inflow as a function of r 0/M.
Fig. 5 coefficient α varies with insertion ratio.
FIG. 6 shows the variation of the coefficient α with r 0/M.
FIG. 7 r0/M >3 coefficient α fit function; (a) fitting results of linear functions and numerical experiments when L/M is more than 0 and less than 0.7; (b) fitting results of quadratic polynomial and numerical experiments when L/M is more than or equal to 0.7 and less than 1.
FIG. 8 illustrates the linear variation rule of the parameters A, K, I, B1 and B2 with r 0/M; (a) a, K fitting results linearly changing with r 0/M; (b) i, B1, B2 linearly varied the fitting results with r 0/M.
The coefficient α fit function for a plot 90 < r0/M ≦ 3; (a) fitting results of linear functions and numerical experiments when L/M is more than 0 and less than 0.7; (b) fitting results of quadratic polynomial and numerical experiments when L/M is more than or equal to 0.7 and less than 1.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
The method for determining the seepage influence coefficient based on numerical simulation comprises the following steps:
establishing a numerical model
And establishing a numerical model for calculating the seepage of the circular foundation pit according to the symmetry, as shown in figure 2. The supporting engineering soil layer of the numerical model is characterized in that sand is sticky and mixed with the stratum, and the aquifer is mainly fine sand. Calculating and taking permeability coefficient kr＝kv＝5×10-6m/s, the height H of the water head of the confined layer is 30m, and the design value H of the water head in the pitdAnd the thickness M of the aqueous layer were each 10M.
Selecting r0The method is characterized in that numerical experiments are carried out on five working conditions of 1,3, 5,7 and 9, and based on the research of the change rule of the coefficient alpha, the residual r0Five conditions of 2, 4, 6, 8 and 10 are used as the verification conditions. Changing the radius r of the pit0And the length L of the waterproof curtain inserted into the confined aquifer is calculated to obtain the water inflow of the foundation pit along with r0The variation rule of/M, L/M is shown in FIG. 3. It can be seen that the insertion ratio L/M has a large influence on the water inflow of the foundation pit. Along with the increase of L/M, the water inflow of the foundation pit is continuously reduced, and when the diameter of the foundation pit is smaller (r)01) Q is in linear relation with L/M; in other cases, Q decreases linearly first and then exponentially as L/M increases. In the case of the same L/M, with r0And the water inflow of the foundation pit is increased continuously by increasing the/M, but the increasing rate is reduced continuously. As can be seen from fig. 4, when the size of the foundation pit is large, the water inflow in the foundation pit is still large under a large insertion ratio (L/M is 0.9), and to effectively control the water inflow, the insertion ratio needs to be increased to form a bottom-falling waterproof curtain, and the specific relationship will be analyzed later.
Substituting the water inflow obtained by numerical calculation into the analytic formula of the water inflow calculation to obtain the seepage diameter influence coefficient alpha along with r0The variation rule of/M, L/M is shown in FIG. 5. It can be seen that r0Each of the/M, L/M has a different degree of influence on α, and the L/M effect is relatively greater. If the influence of the curtain insertion ratio on the equivalent seepage diameter is not considered, alpha is constantly equal to 1, and each working condition approximately corresponds to the condition that L/M is 0.7-0.8 in the graph, namely the water inflow at the momentThe theoretical calculation result is matched with the numerical result.
Obtaining the seepage diameter influence coefficient alpha value according to the inverse solution of the water inflow of the numerical simulation result and fitting a function expression thereof
For r0/M>Case 3:
(1) firstly, establishing a functional relation between alpha and L/M
r0/M>At 3, r in FIG. 5 obtained by numerical experiments0Fitting the function of the curve with the coefficient alpha varying with L/M when the/M is 5,7 and 9, wherein the fitting function is taken as r0The value function of the coefficient alpha when/M is more than 3. Observation of the curve shows that: when the L/M is more than 0 and less than 0.7, the coefficient alpha changes approximately linearly along with the change relation of the L/M, namely, the coefficient alpha conforms to a linear function:
and for the nonlinear section of the curve when L/M is more than or equal to 0.7 and less than 1, performing function fitting on the change relation between the coefficient alpha and L/M by using a quadratic polynomial:
where A is the intercept of the linear function and K is the slope of the linear function. I is the quadratic polynomial intercept, B1Is a coefficient of a first order term, B2Is a quadratic coefficient.
Therefore, L/M is 0.7 as the boundary point between the linear segment and the nonlinear segment, the coefficient α is used as the piecewise function, and the piecewise fitting result and the values of the parameters of the fitting function are shown in fig. 7 and table 1:
TABLE 1 r0Parameter value of fitting function when/M is 5,7 and 9
(2) And then the functional relation between the coefficient alpha and r0/M is established
Using the data in Table 1, A,K、I、B1、B2With r0The change rule of the/M is assumed to be linear change and fitting is carried out, namely, the formula (30), and the fitting result and the parameter values in the formula (30) are shown in tables 2, 3 and 8
TABLE 2A, K with r0Linear function parameter value of/M variation
TABLE 3I, B1、B2With r0Linear function parameter value of/M variation
(3) Finally obtaining r0Coefficient alpha with respect to L/M and r when/M >30The expression of/M, i.e. (32)
R is obtained by substituting (30) into (28) or (29)0A coefficient alpha piecewise function when/M >3
In the formula a1、a2、k1、k2、i1、i2、b1、b2、b3、b4The values are constant and shown in tables 2 and 3.
Here, the formula of the coefficient α piecewise function (31) is discontinuous at a point L/M of 0.7, and if a curve that the water inflow continuously changes with L/M is desired, the water inflow in the interval 0.6 < L/M < 0.7 can be calculated by interpolation, and the later analysis of the water inflow is also based on this method. Through calculation verification, in the interval of 0.6 < L/M < 0.7, the numerical value of the water inrush quantity calculated by the formula (31) and an interpolation method is very close, and the accuracy requirement can be met.
For 0<r0Case of/M.ltoreq.3
(1) Firstly, establishing a functional relation between alpha and L/M
0<r0When the/M is less than or equal to 3, according to the method, the linear function and the quadratic polynomial fitting are carried out on the change curve of the coefficient alpha along with the L/M when the L/M is more than 0 and less than 0.7 and the L/M is more than or equal to 0.7 and less than 1 in a segmented mode. The fitting result and the values of the parameters of the fitting function are shown in fig. 9 and table 4:
TABLE 4 r0The parameter of the fitting function takes the value when/M is 1 and 3:
2) and then the functional relation between the coefficient alpha and r0/M is established
Similarly, as shown in equation (30), assume A, K, I, B1、B2Is taken as r0the/M is linearly changed and fitted, and the parameter values are shown in tables 5 and 6:
TABLE 5A, K with r0Parameter evaluation of linear fitting function for/M variation
TABLE 6I, B1、B2With r0Parameter evaluation of linear fitting function for/M variation
Find 0 < r0The form of the function of the change of the coefficient alpha when/M is less than or equal to 3 is the same as that of (31), wherein a1、a2、k1、k2、i1、i2、b1、b2、b3、b4The values are shown in tables 5 and 6.
(3) Finally obtaining r0Coefficient alpha with respect to L/M and r when/M >30The expression of/M, i.e. (32)
In summary, the value of the coefficient α can be calculated according to (32) in different cases:
Claims (2)
1. the method for analyzing the water inflow of the suspended waterproof curtain of the circular foundation pit of the confined water layer is characterized by comprising the following steps of: a central axis of a circular foundation pit is taken as a z axis, the radial direction of the foundation pit is taken as an r axis, and an intersection point of the central axis and a bottom plate of an aquifer is selected as an origin O to establish a cylindrical coordinate system, so that a mathematical model of a confined water stratum suspended waterproof curtain foundation pit is established according to the underground water dynamics principle, as shown in figure 1; wherein H is the height of the confined water head, r0Is the radius of a circular foundation pit, R is the pumping influence radius of the foundation pit, h0Head value of contour line of head at central axis of bottom of curtain until water curtain, D (z) distribution function of head at outer side wall of curtain until water curtain, HdDesigned value for water head in pit, HwThe total head value of the maximum depth of the top plate of the confined aquifer outside the pit is L, the length of the water curtain inserted into the confined aquifer is L, and M is the thickness of the aquifer;
the thickness of a waterproof curtain is ignored by the model, the seepage process in the pit is assumed to be three-dimensional stable flow, and the water head lines in the pit are all horizontal lines; dividing a seepage area into three parts, namely an area 1 outside a pit, an area 2 below a waterproof curtain in the pit, and a vertical seepage area in the pit, namely an area 3; the water flow in the area 1 enters the area 2 in a winding manner due to the existence of the waterproof curtain, the flow directions of the water flow right below the waterproof curtain are all horizontal, the water flow turns in the area 2 and flows into the area 3 along the vertical direction; the pressure reduction and precipitation process of the foundation pit is equivalent to the precipitation process of a large-diameter water pumping well, and the interior of the pit is simplifiedVertical seepage is assumed, so vertical seepage is assumed in zone 3; according to the seepage continuity principle, the flow in 3 areas is the same, namely Q1＝Q2＝Q3Q, wherein Q1Is the flow rate in the region 1, Q2Is the flow rate in zone 2, Q3The flow in the area 3, and Q is the total water inflow in the foundation pit;
calculating the total water head h (r, theta, z) of any point (r, theta, z) in the regional seepage field, wherein the total water head h (r, theta, z) is independent of the angle, namely the total water head of each point can be expressed as h (r, z); the boundary conditions in the percolation region are:
h(r,z)＝H；r＝r0+R，z＞0 (1)
h＝h0；r＝r0，0≤z≤M-L (4)
h＝D(z)；r＝r0，M-L≤z≤M (5)
h(r,z)＝Hd；0＜r＜r0，z＝Hd (6)
according to the seepage continuity principle, the flow in the three areas is the same:
Q1＝Q2＝Q3 (7)。
2. the method for analyzing the water inflow of the suspended waterproof curtain of the circular foundation pit of the confined water layer according to claim 1, characterized in that:
s1, solving the foundation pit extravasation flow;
firstly, calculating the seepage flow in the region 1, and according to Darcy's law, calculating the horizontal seepage velocity v of any point in the pressure-bearing water-containing layerrComprises the following steps:
in the formula krThe horizontal permeability coefficient in the confined water-containing layer is as follows:
in zone 1, the flow rate per unit time through any cross section, i.e., the flow rate Q in zone 11Comprises the following steps:
bringing formula (8) into formula (9) to obtain a flow rate Q in area 11Expression:
by modifying the formula (11), the following can be obtained:
r is integrated simultaneously on both the left and right sides of the equation:
and C is a coefficient to be determined, a boundary condition (1) is substituted, and a value of C is obtained:
the C value is substituted for formula (13) to obtain:
when r is r0The method comprises the following steps:
the above equation is integrated:
from the boundary conditions (3) and (4):
according to the prior research result, the distribution function D (z) of the water stopping curtain outer side water head in the range of M-L < z < M is expressed as:
(15) expression of the seepage rate in the region 1 can be obtained by combining the expressions (20):
s2 solving seepage flow in foundation pit
The water flow in the area 1 flows into the area 2 in a circumambulated mode, the water flow in the area 2 turns to flow into the area 3, and only vertical seepage occurs in the area 3, so that the shortest seepage path of the water flow in the area 2 and the area 3 is as follows:
Lmin＝Hd-M+L (21)
the longest percolation path is:
Lmax＝r0+Hd (22)
it should be noted that: if the water head line at the bottom of the pit is positioned above the bottom plate of the upper impervious layer, namely Hd>M, then H in (21) and (22)dReplacing with M; when the Darcy's law is utilized to solve the water inflow rate in the foundation pit, most of the existing theoretical analysis is to determine the equivalent seepage path length in the foundation pit as the average value of the maximum seepage path and the minimum seepage path, or directly assume 2LminThe water inflow quantity in the pit calculated in the two conditions is only r0Certain specific intervals of/M, L/M are reasonable; in fact, the value of the equivalent seepage length in the foundation pit should follow r0The ratio/M, L/M varies depending on the difference, and is directly determined by half the sum of the maximum and minimum diameters or 2LminReplacement is not reasonable; in order to accurately calculate the value of the water inflow in the foundation pit under each working condition, the introduction of the equivalent seepage length along with r0The seepage diameter influence coefficient alpha of/M, L/M change is determined, and a change rule is explored through a numerical experiment; the length of the equivalent seepage path in the foundation pit can be expressed as:
wherein α is r0the/M, L/M function:
the water gushes in zone 2 and zone 3 were:
s3, determining the water inflow amount of the foundation pit;
under the condition of neglecting the thickness of the waterproof curtain, when water flows around the waterproof curtain, the head loss passing through the inner side of the curtain is larger than the head loss passing through the outer side of the curtain; according to the existing experimental data and theoretical research results, the following results are shown:the head loss of water flow passing through the inner side of the curtain in each working condition of the diving aquifer is about 2/3 of the total loss of the bypass flow; the direction and the characteristics of the water flow when the water flow flows around the waterproof curtain are consistent no matter in the confined water layer or the diving layer, so the conclusion is applied to the water head value h of the equal head line at the bottom end of the waterproof curtain in the confined water stratum0Denoted as (26); according to the seepage continuity principle, the maximum falling water head Hw distribution function (27) at the top plate of the confined aquifer outside the pit is obtained by combining (20), (25) and (26):
and (25) and (26) are substituted into (27) to obtain the water inflow of the circular foundation pit.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114528786A (en) * | 2022-04-24 | 2022-05-24 | 中铁城建集团有限公司 | Method and system for calculating two-dimensional steady-state seepage field of foundation pit under suspension type retaining wall support |
| CN117390344A (en) * | 2023-10-25 | 2024-01-12 | 中国华水水电开发有限公司 | Method for calculating linear leakage of side wall of underground diaphragm wall |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114528786A (en) * | 2022-04-24 | 2022-05-24 | 中铁城建集团有限公司 | Method and system for calculating two-dimensional steady-state seepage field of foundation pit under suspension type retaining wall support |
| CN117390344A (en) * | 2023-10-25 | 2024-01-12 | 中国华水水电开发有限公司 | Method for calculating linear leakage of side wall of underground diaphragm wall |
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