Method for calculating leakage flux of disjointed river

Abstract

The invention discloses a method for calculating leakage flux of a disjointed river, which relates to the field of hydrogeology, and comprises the following steps of: constructing a coupling model integrating river water level, sediment seepage control equation and unsaturated zone seepage under sediment according to the characteristics of riverbed sediment of the disjointed river; according to the method, a suspended waterlogged zone is found to exist under a riverbed, a suspended waterlogged zone migration equation is analyzed by utilizing a coupling equation, the leakage flux of the disjoint river at different moments is invented according to the suspended waterlogged zone equation, and the leakage calculation problem of the disjoint river under the condition of different river water depths can be accurately calculated by the method. The method overcomes the problem of poor precision of leakage estimation by using the upstream and downstream section river flow difference at present, and enriches and develops the theory and method of river bed leakage dynamics.

Description

Technical Field

[0001] The present invention relates to the field of hydrogeology, and particularly to a method for calculating the leakage flux of a disconnected river. Background Art

[0002] River infiltration in arid regions is an important source of groundwater recharge. Affected by many factors such as the riverbed permeability coefficient, hydrodynamic conditions, meteorological changes, and human activities, the interaction between rivers and groundwater is a complex hydrological process. There are two hydraulic connection relationships between rivers and groundwater, namely river-aquifer disconnection and river-aquifer connection. In arid and semi-arid regions, due to the influence of natural and human factors, such as reduced precipitation and riverbank pumping, the groundwater level drops significantly, causing the connection relationship between rivers and groundwater to evolve from saturated connection, transitional disconnection to complete disconnection. Therefore, accurately estimating the exchange volume between rivers and groundwater has become a difficult problem to be explored and solved in the current technical field. The leakage flux is an important parameter reflecting the interaction and water volume exchange between rivers and groundwater.

[0003] In the prior art, when calculating the leakage volume of a disconnected river, it is usually assumed that the transformation from saturated flow to unsaturated flow under the riverbed only occurs at the riverbed-aquifer interface. However, some experimental and model studies have found that when the river is disconnected from the groundwater, regardless of the permeability of the underlying riverbed, a certain thickness of saturated water zone will form at the bottom of the riverbed, which is usually called the hanging saturated water zone. However, these previous studies usually ignored the dynamic process of the migration of the hanging saturated water zone within the riverbed, resulting in a serious underestimation or overestimation of the calculated seepage flux at the riverbed interface, and a large error is generated.

[0004] Therefore, there is an urgent need for a method to solve the problem of large calculation errors in the leakage flux of rivers in the river-groundwater disconnection system. Summary of the Invention

[0005] Based on this, it is necessary to provide a method for calculating the leakage flux of a disconnected river for the above technical problems. This method can solve the problem of large calculation errors in the leakage flux of rivers in the river-groundwater disconnection system.

[0006] The present invention adopts the following technical solutions:

[0007] The present invention provides a method for calculating the leakage flux of a disconnected river, including:

[0008] Generalize the hydrogeological model of the disconnected river to obtain the first definite solution system of equations and the second definite solution system of equations; the hydrogeological model of the disconnected river includes a river, a semi-pervious layer, a suspended saturated zone, an unsaturated zone, and groundwater; the first definite solution system of equations includes the control equation at the top plate of the semi-pervious layer, the initial condition at the top plate of the semi-pervious layer, the boundary condition at the top plate of the semi-pervious layer, and the boundary condition at the bottom plate of the semi-pervious layer; the second definite solution system of equations includes the control equation at the bottom plate of the semi-pervious layer, the initial condition at the bottom plate of the semi-pervious layer, the boundary condition at the bottom plate of the semi-pervious layer, the free surface boundary condition of the suspended saturated zone, and the free surface equation of the suspended saturated zone;

[0009] Perform Laplace transforms on the first definite solution system of equations and the second definite solution system of equations, and obtain the general solution of the control equation at the top plate of the semi-pervious layer in the first definite solution system of equations and the general solution of the control equation at the top plate of the semi-pervious layer in the second definite solution system of equations;

[0010] Determine the migration equation of the suspended saturated zone according to the general solution of the control equation at the top plate of the semi-pervious layer and the general solution of the control equation at the top plate of the semi-pervious layer; the migration equation of the suspended saturated zone is the change in the thickness of the suspended saturated zone over time;

[0011] Determine the calculation formula for the water head at the top plate of the semi-pervious layer according to the migration equation of the suspended saturated zone;

[0012] Substitute the calculation formula for the water head at the top plate of the semi-pervious layer into Darcy's law to obtain the leakage flux of the disconnected river at different times.

[0013] Preferably, the control equation at the top plate of the semi-pervious layer is:

[0014]

[0015] where h 1 is the water head at the top plate of the semi-pervious layer, a represents the coefficient related to permeability, t is time, and x is the spatial coordinate;

[0016] The initial condition at the top plate of the semi-pervious layer is:

[0017] h 1 (x,0) = 0;

[0018] where h 1 (x,0) is the initial condition at the top plate of the semi-pervious layer;

[0019] The boundary condition at the top plate of the semi-pervious layer is:

[0020] h 1 (0,t) = d 0 ;

[0021] where h 1 (0,t) is the boundary condition at the top plate of the semi-pervious layer, d0 is the river water depth;

[0022] The boundary condition at the bottom of the semi-pervious layer is:

[0023] h 1 h(-M',t) = h 2 h(-M',t);

[0024] where M' is the thickness of the semi-pervious layer, h 1 h(-M',t) is the boundary condition at the top of the semi-pervious layer, and h 2 h(-M',t) is the boundary condition at the bottom of the semi-pervious layer.

[0025] Preferably, the governing equation at the bottom of the semi-pervious layer is:

[0026]

[0027] where h 2 is the hydraulic head at the bottom of the semi-pervious layer, and x is the spatial coordinate;

[0028] The initial condition at the bottom of the semi-pervious layer is:

[0029] h 2 h(x,0) = 0;

[0030] where h 2 h(x,0) is the initial condition at the bottom of the semi-pervious layer;

[0031] The boundary condition at the bottom of the semi-pervious layer is:

[0032] h 2 h(-M′,t) = h 1 h(-M′,t);

[0033] where h 2 h(-M',t) is the boundary condition at the bottom of the semi-pervious layer, h 1 h(-M',t) is the boundary condition at the top of the semi-pervious layer, M' is the thickness of the semi-pervious layer, and t is the time;

[0034] Free surface boundary condition of the suspended saturated zone:

[0035] h 2 h((-l(t),t) = -l(t) when x = -l(t) and |l(t)| > M';

[0036] where l(t) is the thickness of the suspended saturated zone at different times, and h 2 h((-l(t),t) is the hydraulic head of the free surface of the suspended saturated zone;

[0037] The equation of the free surface of the suspended saturated zone is:

[0038] x = -l(t) and |l(t)| > M';

[0039] where μ is the specific yield of the hanging saturated zone, k is the permeability coefficient of the hanging saturated zone, and h 2 is the water head at the bottom of the semi - permeable layer;

[0040] Preferably, the connection condition between the first definite - solution equations and the second definite - solution equations is the third set of equations.

[0041] Preferably, the third set of equations is:

[0042]

[0043] where h 1 is the water head at the top of the semi - permeable layer, h 2 is the water head at the bottom of the semi - permeable layer, x is the spatial coordinate, k is the permeability coefficient of the hanging saturated zone, and k' is the permeability coefficient of the riverbed.

[0044] Preferably, the migration equation of the hanging saturated zone is Based on the migration equation of the hanging saturated zone, the calculation formula for determining the water head at the top of the semi - permeable layer is specifically as follows:

[0045] The migration equation of the hanging saturated zone is:

[0046]

[0047] where l(t) is the thickness of the hanging saturated zone at different times, t is the time, P = iln2 / t, N is an even number, k is a positive integer, i = 1, 2... N, V i is the weight function, and l(P) is a quadratic equation of one variable about the thickness of the hanging saturated zone in the Laplace space;

[0048] The quadratic equation l(P) of the migration equation of the hanging saturated zone in the Laplace space is:

[0049]

[0050] where M' is the thickness of the semi - permeable layer, k is the permeability coefficient of the hanging saturated zone, k' is the permeability coefficient of the riverbed, μ is the specific yield of the hanging saturated zone, d 0 is the river depth, P represents the time - related term after Laplace transform, and a represents the coefficient related to permeability;

[0051] The calculation formula for the water head at the top of the semi - permeable layer is:

[0052] h 1 (-M′,t) = |l(t)| - 2M′;

[0053] where h 1 (-M', t) is the water head at the top plate of the semi-pervious layer, l(t) is the thickness of the suspended saturated zone at different times, and M' is the thickness of the semi-pervious layer.

[0054] Darcy's law is:

[0055]

[0056] where M' is the thickness of the semi-pervious layer, k' is the permeability coefficient of the riverbed, d 0 is the depth of the river water, t is the time, v(t) is the leakage flux of the disconnected river at different times, and h 1 (-M', t) is the water head at the top plate of the semi-pervious layer;

[0057] The leakage flux of the disconnected river at different times is:

[0058]

[0059] where v(t) is the leakage flux of the disconnected river at different times, d 0 is the depth of the river water, l(t) is the thickness of the suspended saturated zone at different times, M' is the thickness of the semi-pervious layer, and k' is the permeability coefficient of the riverbed.

[0060] The present invention provides a calculation device for the leakage flux of a disconnected river, including:

[0061] A construction module for generalizing the hydrogeological model of the disconnected river to obtain a first definite solution system of equations and a second definite solution system of equations; the hydrogeological model of the disconnected river includes a river, a semi-pervious layer, a suspended saturated zone, an unsaturated zone, and groundwater; the first definite solution system of equations includes a control equation at the top plate of the semi-pervious layer, an initial condition at the top plate of the semi-pervious layer, a boundary condition at the top plate of the semi-pervious layer, and a boundary condition at the bottom plate of the semi-pervious layer; the second definite solution system of equations includes a control equation at the bottom plate of the semi-pervious layer, an initial condition at the bottom plate of the semi-pervious layer, a boundary condition at the bottom plate of the semi-pervious layer, a free surface boundary condition of the suspended saturated zone, and a free surface equation of the suspended saturated zone;

[0062] A solution module for performing Laplace transform on the first definite solution system of equations and the second definite solution system of equations, and obtaining the general solution of the control equation at the top plate of the semi-pervious layer in the first definite solution system of equations and the general solution of the control equation at the top plate of the semi-pervious layer in the second definite solution system of equations;

[0063] A first determination module for determining the migration equation of the suspended saturated zone according to the general solution of the control equation at the top plate of the semi-pervious layer and the general solution of the control equation at the top plate of the semi-pervious layer; the migration equation of the suspended saturated zone is the change of the thickness of the suspended saturated zone with time;

[0064] A second determination module, configured to determine a calculation formula for the water head at the top plate of the semi-pervious layer according to the migration equation of the suspended saturated zone.

[0065] A third determination module, configured to substitute the calculation formula for the water head at the top plate of the semi-pervious layer into Darcy's law to obtain the leakage flux of the disconnected river at different times.

[0066] The present invention provides a computer-readable storage medium storing a computer program, which when executed by a processor implements the above-mentioned calculation method for the leakage flux of a disconnected river.

[0067] The present invention provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, it implements the above-mentioned calculation method for the leakage flux of a disconnected river.

[0068] The above at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0069] A calculation method for the leakage flux of a disconnected river. By constructing a coupling model integrating river water level, sediment seepage control equation, and subsurface unsaturated zone seepage below the sediment, it can more accurately simulate the water flow dynamics of the disconnected river; solving the definite solution equations for the migration of the suspended saturated zone over time according to the initial conditions and boundary conditions of the semi-pervious layer to obtain the migration equation of the suspended saturated zone, and substituting the migration equation of the suspended saturated zone into Darcy's law to obtain the leakage flux of the disconnected river at different times. This method considers the migration process of the suspended saturated zone when calculating the leakage flux, and can solve the problem of large calculation errors in the leakage flux of the river-groundwater disconnection system. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The drawings described herein are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0071] Figure 1 It is a schematic diagram of the transformation between a river and groundwater at the basin scale provided by the present invention;

[0072] Figure 2 It is a schematic flow chart of the calculation method for the leakage flux of a disconnected river provided by the present invention;

[0073] Figure 3 It is a schematic diagram of the river-semi-pervious layer-suspended saturated zone-unsaturated zone-groundwater conceptual model provided by the present invention;

[0074] Figure 4Schematic diagram of the change in the thickness of the hanging saturated zone under different permeability coefficients of the weak aquitard provided by the present invention;

[0075] Figure 5 Schematic diagram of the change in the river leakage volume with the permeability coefficient of the riverbed weak aquitard at different times provided by the present invention;

[0076] Figure 6 Schematic diagram of the change in the river leakage volume with the river water depth at different times provided by the present invention;

[0077] Figure 7 Schematic diagram of the calculation device for the leakage flux of a disjointed river provided by the present invention;

[0078] Figure 8 Schematic diagram of a computer device for implementing the calculation method of the leakage flux of a disjointed river provided by the present invention. Detailed implementation manners

[0079] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0080] The transformation between rivers and groundwater at the basin scale is as Figure 1 shown. In arid regions, the interaction between rivers and groundwater is an upstream-downstream unity linked by the river-aquifer. There are two transformation relationships. One is the disjointed relationship without a unified phreatic curve, and the other is the interactive relationship with a unified phreatic curve, and the hydraulic connection is close. Among them, the disjointed section of the river-aquifer is usually located at the basin outlet, and the leakage volume of the disjointed river constitutes the main source of groundwater recharge in the basin. However, due to the formation of a blocking layer on the riverbed under the action of river scouring, the temporal and spatial changes in the migration of the hanging saturated zone under the riverbed make it difficult to calculate the river leakage volume.

[0081] In arid regions, the interaction between rivers and groundwater is an upstream-downstream unity linked by the river-aquifer. There are two transformation relationships. One is the disjointed relationship without a unified phreatic curve, and the other is the interactive relationship with a unified phreatic curve, and the hydraulic connection is close. Among them, the disjointed section of the river-aquifer is usually located at the basin outlet, and the leakage volume of the disjointed river constitutes the main source of groundwater recharge in the basin. However, due to the formation of a blocking layer on the riverbed under the action of river scouring, the temporal and spatial changes in the migration of the hanging saturated zone under the riverbed make it difficult to calculate the river leakage volume.

[0082] In view of the problem of large calculation errors in the leakage flux of disconnected rivers in the prior art, the present invention provides a method for calculating the leakage flux of disconnected rivers with a saturated water zone suspended under the riverbed.

[0083] For devices such as desktops, laptops, servers, etc. that execute the solution of the present invention, for the convenience of description, only the server will be used as the execution entity for description below.

[0084] The following will detail the technical solutions provided by each embodiment of the present invention in conjunction with the accompanying drawings.

[0085] Figure 2 It is a schematic flow diagram of the method for calculating the leakage flux of disconnected rivers in the present invention, which specifically includes the following steps:

[0086] S201: Generalize the hydrogeological model of the disconnected river to obtain the first definite solution equations and the second definite solution equations; the hydrogeological model of the disconnected river includes a river, a semi-pervious layer, a suspended saturated water zone, an unsaturated zone, and groundwater; the first definite solution equations include the control equation at the top of the semi-pervious layer, the initial condition at the top of the semi-pervious layer, the boundary condition at the top of the semi-pervious layer, and the boundary condition at the bottom of the semi-pervious layer; the second definite solution equations include the control equation at the bottom of the semi-pervious layer, the initial condition at the bottom of the semi-pervious layer, the boundary condition at the bottom of the semi-pervious layer, the free surface boundary condition of the suspended saturated water zone, and the free surface equation of the suspended saturated water zone.

[0087] Generalize the river - semi-pervious layer - suspended saturated water zone - unsaturated zone - groundwater model to determine the hydrogeological conditions and riverbed lithology of the disconnected river - aquifer system. The suspended saturated water zone is a saturated medium formed under the riverbed in the disconnected section between the river and the groundwater. Its water content reaches the maximum and it is a relatively stable aquifer. The water in the suspended saturated water zone seeps downward under the action of gravity, but due to the resistance or poor permeability of the underlying medium, the water cannot continue to seep, resulting in the formation of a free surface at the lower interface of the suspended saturated water zone as Figure 3 shown. On the lower interface of the suspended saturated water zone, since the pressure state of the water reaches a state equal to the atmospheric pressure, or due to the action of gravity of the water, a certain pressure gradient is formed. This change in the pressure state makes this interface a free surface.

[0088] As Figure 3 shown, convert the generalized hydrogeological model into a mathematical model. The depth of the river water in the mathematical model is d 0 , the thickness of the semi-pervious layer is M', the permeability coefficient of the riverbed is k', the storage coefficient of the riverbed is S', and the permeability coefficient and specific yield of the suspended saturated water zone are k and μ respectively.

[0089] The initial conditions of the mathematical model are as follows: at the initial moment, the water heads of the weak pervious layer under the riverbed and the hanging saturated zone are 0. Take the origin of the coordinate system at the center of the roof of the weak pervious layer of the riverbed as point A, and assume the water head at the roof is h 1 , the center of the bottom plate of the weak pervious layer of the riverbed is point B, and assume the water head at the bottom plate is h 2 . The upward direction is positive. The distance that the hanging saturated zone at the bottom of the weak pervious layer on the center line of the riverbed moves with time is l(t). For the convenience of calculation, assume that l(t) starts from the origin of the coordinate system. For the distance of the hanging saturated zone below point B, it is -(|l(t)| - M').

[0090] Specifically, according to the settings of the above mathematical model, a first definite solution system of equations is constructed based on the control equation at the roof of the weak pervious layer, the initial conditions at the roof of the weak pervious layer, the boundary conditions at the roof of the weak pervious layer, and the boundary conditions at the bottom plate of the weak pervious layer. Among them, the control equation at the roof of the weak pervious layer is derived based on mass conservation and energy conservation. The first definite solution system of equations is shown in formula (1):

[0091]

[0092] Among them, h 1 is the water head at the roof of the weak pervious layer, h 2 is the water head at the bottom plate of the weak pervious layer, t is the time, d 0 is the depth of the river water, M' is the thickness of the weak pervious layer, x is the spatial coordinate, h 1 (-M', t) is the boundary condition at the roof of the weak pervious layer, h 2 (-M', t) is the boundary condition at the bottom plate of the weak pervious layer.

[0093] Specifically, according to the settings of the above mathematical model, a second definite solution system of equations is constructed based on the control equation at the bottom plate of the weak pervious layer, the initial conditions at the bottom plate of the weak pervious layer, the boundary conditions at the bottom plate of the weak pervious layer, the free surface boundary condition of the hanging saturated zone, and the free surface equation of the hanging saturated zone. Among them, the control equation at the bottom plate of the weak pervious layer is derived based on mass conservation and energy conservation. The second definite solution system of equations is shown in formula (2):

[0094]

[0095] Among them, h 1 is the water head at the roof of the weak pervious layer, h 2 is the water head at the bottom plate of the weak pervious layer, x is the spatial coordinate, M' is the thickness of the weak pervious layer, l(t) is the thickness of the hanging saturated zone at different times, t is the time, k is the permeability coefficient of the hanging saturated zone, μ is the specific yield of the hanging saturated zone, h 2 (-M', t) is the boundary condition at the bottom plate of the weak pervious layer, h 1 (-M', t) is the boundary condition at the roof of the weak pervious layer, h2 (-l(t), t) is the water head of the free surface of the hanging saturated zone.

[0096] Equations (1) and (2) constitute a coupled model that integrates the river water level, sediment seepage control equations, and the seepage in the unsaturated zone below the sediment.

[0097] In an exemplary embodiment, the connection condition between the first set of definite solution equations and the second set of definite solution equations is the third set of equations.

[0098] Specifically, the connection condition between the first set of definite solution equations and the second set of definite solution equations is that when x = -M, the third set of equations is as shown in Equation (3):

[0099]

[0100] where h 1 is the water head at the top plate of the semi-pervious layer, h 2 is the water head at the bottom plate of the semi-pervious layer, x is the spatial coordinate, k is the permeability coefficient of the hanging saturated zone, and k' is the permeability coefficient of the riverbed.

[0101] S202: Perform Laplace transform on the first set of definite solution equations and the second set of definite solution equations, and obtain the general solutions of the control equations at the top plate of the semi-pervious layer in the first set of definite solution equations and the general solutions of the control equations at the top plate of the semi-pervious layer in the second set of definite solution equations.

[0102] Specifically, perform Laplace transform on the first set of definite solution equations, the second set of definite solution equations, and the third set of equations to obtain the first Laplace-transformed set of definite solution equations, the second Laplace-transformed set of definite solution equations, and the third Laplace-transformed set of equations; solve the first Laplace-transformed set of definite solution equations according to the initial conditions and boundary conditions of the semi-pervious layer to obtain the general solution of the first Laplace-transformed set of definite solution equations; solve the second Laplace-transformed set of definite solution equations according to the initial conditions and boundary conditions of the semi-pervious layer to obtain the general solution of the second Laplace-transformed set of definite solution equations.

[0103] Specifically, perform Laplace transform on the first set of definite solution equations, the second set of definite solution equations, and the third set of equations respectively to obtain the first Laplace-transformed set of definite solution equations, the second Laplace-transformed set of definite solution equations, and the third Laplace-transformed set of equations.

[0104] The first Laplace-transformed set of definite solution equations is as shown in Equations (4)(5)(6):

[0105]

[0106] The second Laplace-transformed set of definite solution equations is as shown in Equations (7)(8)(9)(10):

[0107]

[0108] The third Lassen transformation equation group is shown in formula (11) (12):

[0109]

[0110] The general solution of formula (4) is shown in formula (13):

[0111]

[0112] The general solution of formula (7) is shown in formula (14):

[0113]

[0114] Determine the coefficients C, D, E, and F in the general solution equation.

[0115] Substituting boundary condition (5) into formula (13), we obtain formula (15), which is as follows:

[0116]

[0117] Substituting boundary condition (8) into formula (13), we obtain formula (16), which is as follows:

[0118]

[0119] Substitute formula (12) into formula (13) to determine C. The calculation method of C is shown in formula (17):

[0120]

[0121] Determination coefficients E and F.

[0122] By taking the derivative of formula (11) and combining it with boundary condition (9), we get formula (18), which is as follows:

[0123]

[0124] Right now:

[0125] By taking the derivative of formula (13), we get formula (20), which is as follows:

[0126]

[0127] Substituting formula (20) into formula (19), we obtain formula (21), which is as follows:

[0128]

[0129] Determine the coefficient F. Substitute the boundary condition (9) into Equation (14) to obtain Equation (22), which is shown as follows:

[0130] F = l(p)(E - 1) (22);

[0131] Solve the above system of equations to obtain the expressions for the coefficients C, D, E, and F respectively.

[0132] S203: Determine the migration equation of the hanging saturated zone based on the general solution of the governing equation at the top plate of the semi-pervious layer and the general solution of the governing equation at the top plate of the semi-pervious layer; the migration equation of the hanging saturated zone is the change in the thickness of the hanging saturated zone over time.

[0133] Specifically, based on the general solutions obtained from the first and second definite solution systems of equations, further derive the migration equation of the hanging saturated zone under the riverbed. According to the boundary conditions (9) and (10), obtain Equation (23), which is shown as follows:

[0134]

[0135] Take the derivative of Equation (14) to obtain Substitute it into Equation (23) to obtain Equation (24), which is shown as follows:

[0136]

[0137] Substitute the expressions of C, D, E, and F into Equation (14) to obtain Equation (25), which is shown as follows:

[0138]

[0139] Simplify Equation (25) to Equation (26), which is shown as follows:

[0140]

[0141] Substitute the expressions of the coefficients E and F into Equation (14) to obtain The expression of is Equation (27), which is shown as follows:

[0142]

[0143] Substitute Equation (27) into Equation (26) to obtain Equation (28), which is shown as follows:

[0144]

[0145] Substitute Equation (24) into Equation (28) to obtain Equation (29), which is shown as follows:

[0146]

[0147] Let in the above formula

[0148] Therefore, formula (29) can be expressed as shown in formula (30):

[0149]

[0150] Simplifying the above formula gives formula (31) and formula (32), which are as follows:

[0151]

[0152] Through the above steps, a quadratic equation in one variable about the thickness l(P) of the hanging saturated zone is derived. Since l(P) is negative according to the selected reference plane, the inappropriate solutions are removed. In the Laplace space, the solution of l(P) is as shown in formula (33):

[0153]

[0154] Where:

[0155]

[0156] Using the Stehfest numerical inversion formula to solve formula (33), the migration equation of the hanging saturated zone is obtained, as shown in formula (36):

[0157]

[0158] Wherein, P = iln2 / t, N is an even number. Generally, satisfactory calculation accuracy can be obtained when N takes 6 - 10. k is a positive integer, i = 1, 2... N, V i is the weight function, and the following formula holds for a given N:

[0159] In an exemplary embodiment, let the river depth d 0 remain unchanged, that is, d 0 = 1m, the thickness of the semi-pervious layer M' = 0.5m, and analyze the variation law of the thickness of the hanging saturated zone under the riverbed under different permeability coefficients of the semi-pervious layer, as Figure 4 shown. No matter No matter how it changes, the migration equation of the perched water table shows that the change of the thickness l(t) of the perched water table with time is -(|l(t)| - M'), and it finally reaches stability. After stability, the thickness of the perched water table approaches the river depth. Moreover, the greater the permeability coefficient of the semi-pervious layer, the shorter the time for l(t) to reach stability, and vice versa. Therefore, for the disjunctive rivers in the basin with a blocking layer, if the permeability coefficient of the semi-pervious layer under the riverbed is very small, there is an obvious lag phenomenon in the recharge of river leakage to groundwater.

[0160] S204: According to the migration equation of the perched water table, determine the calculation formula for the water head at the top of the semi-pervious layer.

[0161] In an exemplary embodiment, the calculation formula for the water head at the top of the semi-pervious layer is shown in Formula (37):

[0162] h 1 h(-M', t) = |l(t)| - 2M' (37);

[0163] Wherein, h 1 h(-M', t) is the water head at the top of the semi-pervious layer, l(t) is the thickness of the perched water table at different times, and M' is the thickness of the semi-pervious layer.

[0164] S205: Substitute the calculation formula for the water head at the top of the semi-pervious layer into Darcy's law to obtain the leakage flux of the disjunctive river at different times

[0165] The calculation formula of Darcy's law is shown in Formula (38):

[0166]

[0167] Wherein, v(t) is the leakage flux of the disjunctive river at different times, k' is the riverbed permeability coefficient, h 1 h(-M', t) is the water head at the top of the semi-pervious layer, and d 0 is the river depth.

[0168] When a perched water table is formed at the bottom of the semi-pervious layer, substitute the calculation formula for the water head at the top of the semi-pervious layer into Darcy's law to obtain the leakage flux of the disjunctive river at different times.

[0169] Substitute Formula (37) into Formula (38) to obtain the leakage flux of the disjunctive river through the semi-pervious layer at different times. The calculation method of the leakage flux of the disjunctive river at different times is shown in Formula (39):

[0170]

[0171] Wherein, v(t) is the leakage flux of the disjunctive river at different times, t is the time, and d 0h is the river water depth, l(t) is the thickness of the hanging saturated zone at different times, k' is the permeability coefficient of the riverbed, and M' is the thickness of the semi-pervious layer.

[0172] Specifically, since the thickness of the hanging saturated zone under the semi-pervious layer changes with time, the leakage flux of the river also changes with time.

[0173] h 1 h(-M',t) is the water head at the lowest point of the hanging saturated zone, and its change with time has another situation, as shown in formula (40):

[0174] h 1 h(-M',t) = h c -M' |l(t)| < M' (40);

[0175] where h c is the negative water head at the bottom plate of the semi-pervious layer of the riverbed. When |l(t)| < M', and k' ≠ 0, M' ≠ 0, k = c, a saturated zone has not yet formed under the bottom plate of the semi-pervious layer and below. At this time, the pressure at the bottom plate A of the semi-pervious layer is negative. This situation rarely occurs in nature and is an extremely special case.

[0176] In an exemplary embodiment, when the thickness of the hanging saturated zone stabilizes with time, the leakage amount of the river per unit time and per unit area is approximately equal to twice the permeability coefficient of the semi-pervious layer, that is, v(t) = 2k'. This conclusion shows that the magnitude of the river leakage amount is mainly affected by the permeability of the semi-pervious layer of the riverbed. When the permeability coefficient of the semi-pervious layer is larger, the leakage flux of the river is larger. When the thickness of the hanging saturated zone stabilizes with time, the leakage flux of the river per unit time and per unit area is approximately equal to twice the permeability coefficient of the semi-pervious layer, that is, v(t) = 2k'. This conclusion shows that the magnitude of the river leakage flux is mainly affected by the permeability of the semi-pervious layer of the riverbed. When the permeability coefficient of the semi-pervious layer is larger, the leakage flux of the river is larger.

[0177] Taking the river water depth d 0 = 1m, the thickness M' of the semi-pervious layer of the riverbed = 0.5m, the permeability coefficient k of the hanging saturated zone = 20m / d, and the specific yield μ = 0.15 of a certain river-aquifer disconnection section in a basin as an example, the changes in the river leakage flux with the change of the permeability coefficient of the semi-pervious layer at different times are obtained through the above formulas (37) and (38). As Figure 5 shown, by comparing with the change law of the thickness of the saturated zone, it can be seen that as time goes by, the thickness of the saturated zone gradually increases, and the river leakage flux shows a change process of first being stable, then increasing rapidly, and then decreasing to being stable. In the initial time period, the river leakage flux shows a horizontal section, indicating that a hanging saturated zone has not yet formed under the riverbed. As the thickness of the hanging saturated zone increases, the river leakage flux shows a decreasing and then stable change trend.

[0178] Based on the above example, assuming that the permeability coefficient of the riverbed remains unchanged, the variation law of the leakage flux of the discontinuous river with the river water depth is further analyzed. From Figure 6 it can be seen that as the river water depth increases, the river leakage also shows an increasing trend, but the increase amplitude is limited. The reason for this phenomenon is that restricted by the weak pervious layer of the riverbed, when the river water depth increases to a certain extent, the leakage flux of the river shows non-linear variation. Therefore, simply increasing the river water depth is difficult to significantly increase the leakage flux of the river.

[0179] In the above embodiment, based on the principles of the mass and energy conservation equations, the formula for calculating the leakage flux of the discontinuous river at the riverbed interface is calculated through theoretical derivation. Applying this formula to the actual calculation of the leakage flux of the discontinuous river takes into account the migration process of the thickness of the hanging saturated zone with time when there is a blocking layer in the riverbed, avoiding the calculation error of the leakage flux of the discontinuous river caused by the difficulty of obtaining the hydraulic gradient of the riverbed in on-site tests.

[0180] When applying the calculation method for the leakage flux of a discontinuous river provided by the present invention, it is not necessary to execute according to Figure 2 the order of the steps shown. The specific execution order of each step can be determined as needed, and the present invention does not limit this.

[0181] The above is a calculation method for the leakage flux of a discontinuous river provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding calculation device for the leakage flux of a discontinuous river, as Figure 7 shown.

[0182] Figure 7 It is a schematic diagram of a calculation device for the leakage flux of a discontinuous river provided by the present invention, including:

[0183] A construction module 701, configured to generalize the hydrogeological model of the discontinuous river to obtain a first definite solution system of equations and a second definite solution system of equations; the hydrogeological model of the discontinuous river includes a river, a weak pervious layer, a hanging saturated zone, an unsaturated zone, and groundwater; the first definite solution system of equations includes a control equation at the top plate of the weak pervious layer, an initial condition at the top plate of the weak pervious layer, a boundary condition at the top plate of the weak pervious layer, and a boundary condition at the bottom plate of the weak pervious layer; the second definite solution system of equations includes a control equation at the bottom plate of the weak pervious layer, an initial condition at the bottom plate of the weak pervious layer, a boundary condition at the bottom plate of the weak pervious layer, a free surface boundary condition of the hanging saturated zone, and a free surface equation of the hanging saturated zone.

[0184] A solution module 702, configured to perform Laplace transform on the first definite solution system of equations and the second definite solution system of equations, and obtain the general solution of the control equation at the top plate of the weak pervious layer in the first definite solution system of equations and the general solution of the control equation at the top plate of the weak pervious layer in the second definite solution system of equations.

[0185] The first determination module 703 is configured to determine the migration equation of the suspended saturated zone according to the general solution of the control equation at the roof of the semi-pervious layer and the general solution of the control equation at the roof of the semi-pervious layer; the migration equation of the suspended saturated zone is the change of the thickness of the suspended saturated zone with time.

[0186] The second determination module 704 is configured to determine the calculation formula of the water head at the roof of the semi-pervious layer according to the migration equation of the suspended saturated zone.

[0187] The third determination module 705 is configured to substitute the calculation formula of the water head at the roof of the semi-pervious layer into Darcy's law to obtain the leakage flux of the disconnected river at different times.

[0188] For the specific limitations of a calculation device for the leakage flux of a disconnected river, reference may be made to the limitations of the method for the leakage flux of a disconnected river in the above text, which will not be elaborated here. Each module in the above-mentioned leakage flux device of the disconnected river can be implemented in whole or in part by software, hardware, and their combination. The above-mentioned modules can be embedded in the processor of the computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0189] The present invention also provides a computer-readable storage medium, which stores a computer program, and the computer program can be used to execute the above Figure 2 A calculation method for the leakage flux of a disconnected river provided.

[0190] The present invention also provides Figure 8 The structural schematic diagram of the computer device shown, as Figure 8 shown, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, other hardware required for other services may also be included. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the above Figure 2 A calculation method for the leakage flux of a disconnected river provided.

[0191] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided by the present invention can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0192] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope recorded by the present invention.

Claims

1. A method for calculating the seepage flux of a disjointed river, characterized in that: include: The hydrogeological model of the disjointed river is generalized to obtain a first set of well-defined equations and a second set of well-defined equations; the hydrogeological model of the disjointed river includes a river, a weak permeable layer, a suspended saturated zone, an unsaturated zone and groundwater; the first set of well-defined equations includes a control equation at the top plate of the weak permeable layer, an initial condition at the top plate of the weak permeable layer, a boundary condition at the top plate of the weak permeable layer and a boundary condition at the bottom plate of the weak permeable layer; the second set of well-defined equations includes a control equation at the bottom plate of the weak permeable layer, an initial condition at the bottom plate of the weak permeable layer, a boundary condition at the bottom plate of the weak permeable layer and a free surface boundary condition of the suspended saturated zone and a free surface equation of the suspended saturated zone; Performing a Lassen transformation on the first set of well-defined equations and the second set of well-defined equations, and obtaining a general solution of the control equation at the top plate of the weak permeable layer in the first set of well-defined equations and a general solution of the control equation at the top plate of the weak permeable layer in the second set of well-defined equations; According to the general solution of the control equation at the top plate of the weak permeable layer and the general solution of the control equation at the top plate of the weak permeable layer, the suspension saturated zone migration equation is determined; the suspension saturated zone migration equation is the change of the thickness of the suspension saturated zone with time; According to the suspended saturated zone migration equation, a calculation formula for the water head at the top plate of the weak permeable layer is determined; The calculation formula of the water head at the top plate of the aquitard is substituted into Darcy's law to obtain the seepage flux of the disjointed river at different times.

2. The method according to claim 1, characterized in that The control equation at the top plate of the aquitard is: Where h1 is the water head at the top of the aquitard, a represents the coefficient related to permeability, t is time, and x is the spatial coordinate; The initial condition at the top of the aquitard is: h1(x,0)=0; Among them, h1(x,0) is the initial condition at the top of the aquitard; The boundary condition at the top plate of the aquitard is: h1(0,t)=d0; Among them, h1(0,t) is the boundary condition at the top of the aquitard, and d0 is the depth of the river; The boundary condition at the bottom of the aquitard is: h1(-M',t)=h2(-M',t); Wherein, M' is the thickness of the aquitard, h1(-M',t) is the boundary condition at the top plate of the aquitard, and h2(-M',t) is the boundary condition at the bottom plate of the aquitard.

3. The method according to claim 1, characterized in that The control equation at the bottom plate of the aquitard is: Among them, h2 is the water head at the bottom of the aquitard, and x is the spatial coordinate; The initial condition at the bottom of the aquitard is: h2(x,0)=0; Among them, h2(x,0) is the initial condition at the bottom of the aquitard; The boundary condition at the bottom of the aquitard is: h2(-M',t)=h1(-M',t); Wherein, h2(-M',t) is the boundary condition at the bottom of the aquitard, h1(-M',t) is the boundary condition at the top of the aquitard, M' is the thickness of the aquitard, and t is the time; The free surface boundary conditions of the suspension saturated zone are: h2((-l(t),t)=-l(t) x=-l(t) and |l(t)|>M'; Among them, l(t) is the thickness of the suspended saturated zone at different times, and h2((-l(t),t) is the water head on the free surface of the suspended saturated zone; The free surface equation of the suspension saturated zone is: x=-l(t) and |l(t)|>M'; Among them, μ is the water supply degree of the hanging saturated zone, k is the permeability coefficient of the hanging saturated zone, and h2 is the water head at the bottom of the weak permeable layer.

4. The method according to claim 1, characterized in that The connection condition between the first set of well-defined equations and the second set of well-defined equations is a third set of equations.

5. The method according to claim 4, characterized in that The third program group is: Among them, h1 is the water head at the top of the weak permeable layer, h2 is the water head at the bottom of the weak permeable layer, x is the spatial coordinate, k is the permeability coefficient of the hanging saturated zone, and k' is the permeability coefficient of the riverbed.

6. The method according to claim 1, characterized in that The suspended saturated zone migration equation is a calculation formula for determining the water head at the top plate of the weak permeable layer according to the suspended saturated zone migration equation, which specifically includes: The suspended saturated zone migration equation is: Where l(t) is the thickness of the saturated zone at different times, t is the time, P = iln2 / t, N is an even number, k is a positive integer, i = 1, 2…N, V i is a weight function, l(P) is a quadratic equation in Laplace space about the thickness of the suspension saturated zone; The suspended saturated zone migration equation is a quadratic equation l(P) in Laplace space: in, M' is the thickness of the aquitard, k is the permeability coefficient of the suspended saturated zone, k' is the permeability coefficient of the riverbed, μ is the water supply degree of the suspended saturated zone, d0 is the depth of the river, P represents the time-related term after Laplace transformation, and a represents the coefficient related to permeability; The calculation formula for the water head at the top plate of the aquitard is: h1(-M′,t)=|l(t)|-2M′; Among them, h1(-M',t) is the water head at the top of the weak permeable layer, l(t) is the thickness of the suspended saturated zone at different times, and M' is the thickness of the weak permeable layer.

7. The method according to claim 1, characterized in that The Darcy's law is: Wherein, M' is the thickness of the aquitard, k' is the permeability coefficient of the riverbed, d0 is the depth of the river, t is the time, v(t) is the seepage flux of the disjointed river at different times, and h1(-M',t) is the water head at the top of the aquitard; The leakage flux of the disjointed river at different times is: Wherein, v(t) is the seepage flux of the disjointed river at different times, d0 is the river water depth, l(t) is the thickness of the suspended saturated zone at different times, M' is the thickness of the aquitard, and k' is the permeability coefficient of the riverbed.

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