A method for calculating seepage flux in disjointed rivers

Abstract

The present invention discloses a method for calculating the seepage flux of a disjointed river, which relates to the field of hydrogeology. According to the characteristics of riverbed sediments in the disjointed river, the method constructs a coupling model that integrates the river water level, sediment seepage control equations, and seepage in the unsaturated zone under the sediments. The method discovers the existence of a hanging saturated zone under the riverbed, and uses the coupling equation to solve the migration equation of the hanging saturated zone. Based on the hanging saturated zone equation, the seepage flux of the disjointed river at different times is invented. The method can accurately calculate the seepage amount of the disjointed river under different river water depths, overcomes the problem of poor accuracy in estimating the seepage amount by using the difference in river flow at upstream and downstream sections, and enriches and develops the theory and method of riverbed seepage dynamics.

Description

Technical Field

[0001] The present invention relates to the field of hydrogeology, and in particular to a method for calculating the seepage flux of a disjointed river. Background Art

[0002] River infiltration in arid regions is a significant source of groundwater recharge. Influenced by numerous factors, including riverbed permeability, hydrodynamic conditions, meteorological changes, and human activities, the interaction between rivers and groundwater is a complex hydrological process. Two types of hydraulic connections exist between rivers and groundwater: river-aquifer disconnection and river-aquifer connection. In arid and semi-arid regions, natural and human factors, such as reduced precipitation and riverside pumping, can significantly lower groundwater levels, causing the river-groundwater connection to evolve from saturated connection, transitional disconnection, to complete disconnection. Therefore, accurately estimating the exchange rate between rivers and groundwater has become a challenging issue that needs to be explored and addressed in current technology. Seepage flux is a key parameter reflecting the interaction and water exchange between rivers and groundwater.

[0003] Existing calculations of seepage in disconnected rivers typically assume that the transition from saturated to unsaturated flow beneath the riverbed occurs only at the riverbed-aquifer interface. However, some experimental and model studies have found that when a river is disconnected from the groundwater, a saturated zone of considerable thickness forms at the riverbed bottom, regardless of the underlying permeability. This zone is often referred to as the hanging saturated zone. However, these previous studies often overlooked the dynamics of the hanging saturated zone's migration within the riverbed, leading to significant underestimation or overestimation of seepage flux at the riverbed interface and significant errors.

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

[0005] Based on this, it is necessary to provide a method for calculating the seepage flux of disconnected rivers to address the above technical issues. This method can solve the problem of large errors in calculating the seepage flux of rivers in disconnected river-groundwater systems.

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

[0007] The present invention provides a method for calculating the seepage flux of a disjointed river, comprising:

[0008] 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 the governing equations at the top of the weak permeable layer, the initial conditions at the top of the weak permeable layer, the boundary conditions at the top of the weak permeable layer, and the boundary conditions at the bottom of the weak permeable layer; the second set of well-defined equations includes the governing equations at the bottom of the weak permeable layer, the initial conditions at the bottom of the weak permeable layer, the boundary conditions at the bottom of the weak permeable layer, the boundary conditions of the free surface of the suspended saturated zone, and the free surface equations of the suspended saturated zone;

[0009] Performing Laszlo transformation on the first set of well-defined equations and the second set of well-defined equations, and obtaining a general solution of the governing equation at the top of the aquitard in the first set of well-defined equations and a general solution of the governing equation at the top of the aquitard in the second set of well-defined equations;

[0010] Based on the general solution of the control equation at the top of the aquitard and the general solution of the control equation at the top of the aquitard, the migration equation of the hanging saturated zone is determined; the migration equation of the hanging saturated zone is the change of the thickness of the hanging saturated zone with time;

[0011] According to the suspended saturated zone migration equation, the calculation formula of the water head at the top of the aquitard is determined;

[0012] Substituting the calculation formula of the hydraulic head at the top of the aquitard into Darcy's law, the seepage flux of the disjointed river at different times is obtained.

[0013] The migration equation of the hanging saturated zone is:

[0014] ;

[0015] in, is the thickness of the saturated belt at different times, t For the moment, , N is an even number, k is a positive integer, , is the weight function, is a quadratic equation in Laplace space about the thickness of the suspended saturated zone;

[0016] The quadratic equation of the suspended saturated zone migration equation in Laplace space for:

[0017] ;

[0018] in, , , is the thickness of the aquitard, k is the permeability coefficient of the hanging saturated zone, is the riverbed permeability coefficient, is the water supply degree of the hanging saturated belt, is the river depth, P represents the time-dependent term after Laplace transform, represents the coefficient related to permeability;

[0019] The calculation formula for the water head at the top of the aquitard is:

[0020] ;

[0021] in, is the water head at the top of the aquitard, is the thickness of the saturated belt at different times, is the thickness of the aquitard;

[0022] Darcy's law is:

[0023] ;

[0024] in, is the thickness of the aquitard, is the riverbed permeability coefficient, is the river depth, t For the moment, is the leakage flux of the disjointed river at different times, is the water head at the top of the aquitard;

[0025] The leakage flux of the disjointed river at different times is:

[0026] ;

[0027] in, is the leakage flux of the disjointed river at different times, is the river depth, is the thickness of the saturated belt at different times, is the thickness of the aquitard, is the riverbed permeability coefficient.

[0028] Preferably, the governing equation at the top plate of the aquitard is:

[0029] ;

[0030] in, is the water head at the top of the aquitard, represents the coefficient related to permeability, t For time, x is the spatial coordinate;

[0031] The initial conditions at the top of the aquitard are:

[0032] ;

[0033] in, is the initial condition at the top of the aquitard;

[0034] The boundary conditions at the top of the aquitard are:

[0035] ;

[0036] in, is the boundary condition at the top of the aquitard, is the depth of the river;

[0037] The boundary conditions at the bottom of the aquitard are:

[0038] ;

[0039] in, is the thickness of the aquitard, is the boundary condition at the top of the aquitard, is the boundary condition at the bottom of the aquitard.

[0040] Preferably, the governing equation at the bottom plate of the aquitard is:

[0041] ;

[0042] in, is the water head at the bottom of the aquitard, x is the spatial coordinate;

[0043] The initial conditions at the bottom of the aquitard are:

[0044] ;

[0045] in, is the initial condition at the bottom of the aquitard;

[0046] The boundary conditions at the bottom of the aquitard are:

[0047] ;

[0048] in, is the boundary condition at the bottom of the aquitard, is the boundary condition at the top of the aquitard, is the thickness of the aquitard, t For time;

[0049] Free surface boundary conditions of the suspended saturated zone:

[0050] ;

[0051] in, is the thickness of the saturated belt at different times, The water head of the free surface of the hanging saturated zone;

[0052] The free surface equation of the suspension saturated zone is:

[0053] ;

[0054] in, is the water supply degree of the hanging saturated belt, k is the permeability coefficient of the hanging saturated zone, is the water head at the bottom of the aquitard;

[0055] Preferably, 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.

[0056] Preferably, the third program group is:

[0057] ;

[0058] in, is the water head at the top of the aquitard, is the water head at the bottom of the aquitard, x is the spatial coordinate, k is the permeability coefficient of the hanging saturated zone, is the riverbed permeability coefficient.

[0059] The present invention provides a device for calculating the seepage flux of a disjointed river, comprising:

[0060] A construction module is used to generalize the hydrogeological model of the disjointed river 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, a free surface boundary condition of the suspended saturated zone, and a free surface equation of the suspended saturated zone;

[0061] A solution module, configured to perform a Laszlo transformation on the first set of well-defined equations and the second set of well-defined equations, and obtain a general solution of the control equation at the top of the aquitard in the first set of well-defined equations and a general solution of the control equation at the top of the aquitard in the second set of well-defined equations;

[0062] A first determining module is configured to determine a hanging saturated zone migration equation based on a general solution of a control equation at a top plate of the aquitard and a general solution of a control equation at a top plate of the aquitard; the hanging saturated zone migration equation is a variation of the thickness of the hanging saturated zone with time;

[0063] The second determination module is used to determine the calculation formula of the water head at the top plate of the weak permeable layer according to the migration equation of the hanging saturated zone;

[0064] The third determination module is used to substitute the calculation formula of the water head at the top of the weak permeable layer into Darcy's law to obtain the leakage flux of the disjointed river at different times; the migration equation of the hanging saturated zone is:

[0065] ;

[0066] in, is the thickness of the saturated belt at different times, t For the moment, , N is an even number, k is a positive integer, , is the weight function, is a quadratic equation in Laplace space about the thickness of the suspended saturated zone;

[0067] The quadratic equation of the suspended saturated zone migration equation in Laplace space for:

[0068] ;

[0069] in, , , is the thickness of the aquitard, k is the permeability coefficient of the hanging saturated zone, is the riverbed permeability coefficient, is the water supply degree of the hanging saturated belt, is the river depth, P represents the time-dependent term after Laplace transform, represents the coefficient related to permeability;

[0070] The calculation formula for the water head at the top of the aquitard is:

[0071] ;

[0072] in, is the water head at the top of the aquitard, is the thickness of the saturated belt at different times, is the thickness of the aquitard;

[0073] Darcy's law is:

[0074] ;

[0075] in, is the thickness of the aquitard, is the riverbed permeability coefficient, is the river depth, t For the moment, is the leakage flux of the disjointed river at different times, is the water head at the top of the aquitard;

[0076] The leakage flux of the disjointed river at different times is:

[0077] ;

[0078] in, is the leakage flux of the disjointed river at different times, is the river depth, is the thickness of the saturated belt at different times, is the thickness of the aquitard, is the riverbed permeability coefficient.

[0079] The present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the computer program implements the above-mentioned method for calculating the seepage flux of a disjointed river.

[0080] The present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for calculating the seepage flux of a disjointed river is implemented.

[0081] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects:

[0082] A method for calculating seepage flux in disjointed rivers is proposed. This method constructs a coupled model that integrates the river water level, the governing equations for sediment seepage, and the seepage in the unsaturated zone beneath the sediment. This model can more accurately simulate the flow dynamics of disjointed rivers. Based on the initial and boundary conditions of the aquitard, the system of well-defined equations for the temporal migration of the suspended saturated zone is solved to obtain the migration equation for the suspended saturated zone. Substituting this equation into Darcy's law yields the seepage flux for disjointed rivers at different times. This method considers the migration of the suspended saturated zone when calculating the seepage flux, addressing the problem of large errors in calculating river seepage flux in disconnected river-groundwater systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0084] Figure 1 A schematic diagram of river and groundwater conversion at a basin scale provided by the present invention;

[0085] Figure 2 A schematic flow chart of a method for calculating seepage flux in a disjointed river provided by the present invention;

[0086] Figure 3 Schematic diagram of the river-aquitard-saturated zone-unsaturated zone-groundwater conceptual model provided by the present invention;

[0087] Figure 4 A schematic diagram of the thickness change of the hanging saturated zone under different permeability coefficients of a weakly permeable layer provided by the present invention;

[0088] Figure 5 A schematic diagram of the change of river leakage at different times with the permeability coefficient of the riverbed aquitard provided by the present invention;

[0089] Figure 6 A schematic diagram of river leakage at different times as the depth of the river water changes, provided by the present invention;

[0090] Figure 7 A schematic diagram of a device for calculating seepage flux of a disjointed river provided by the present invention;

[0091] Figure 8 A schematic diagram of a computer device for implementing a method for calculating seepage flux of a disjointed river provided by the present invention. DETAILED DESCRIPTION

[0092] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0093] The transformation of river and groundwater at the basin scale Figure 1As shown, in arid regions, the interaction between rivers and groundwater is a unified upstream and downstream entity, with the river-aquifer link serving as the link. Two transformation relationships exist: a disconnected relationship without a unified infiltration curve, and an interactive relationship with a unified infiltration curve, demonstrating a close hydraulic connection. Disconnected sections between rivers and aquifers are typically located at the outlets of mountain streams, and seepage from disconnected rivers constitutes the primary source of groundwater recharge in the basin. However, the formation of a blocking layer in the riverbed due to river erosion and the spatiotemporal variations in the migration of the suspended saturated zone beneath the riverbed make calculation of river seepage difficult.

[0094] In arid regions, the interaction between rivers and groundwater forms an upstream-downstream unity, with the river-aquifer link serving as the link. Two transformation relationships exist: a disconnected relationship without a unified infiltration curve, and an interactive relationship with a unified infiltration curve, demonstrating a close hydraulic connection. Disconnected sections between rivers and aquifers are typically located at the outlets of mountain streams, and seepage from disconnected rivers constitutes the primary source of groundwater recharge in the basin. However, the formation of a blocking layer in the riverbed due to river erosion and the spatiotemporal variations in the migration of the suspended saturated zone beneath the riverbed make calculation of river seepage difficult.

[0095] Based on the problem of large errors in the calculation of seepage flux of disjointed rivers in the prior art, the present invention provides a method for calculating the seepage flux of disjointed rivers with a saturated zone suspended under the riverbed.

[0096] For the convenience of description, the following description only takes the server as the execution subject as the device that executes the solution of the present invention, such as a desktop computer, a laptop computer, a server, etc.

[0097] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0098] Figure 2 The figure is a flow chart of the method for calculating the seepage flux of a disjointed river in the present invention, which specifically includes the following steps:

[0099] S201: 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 the control equations at the top plate of the weak permeable layer, the initial conditions at the top plate of the weak permeable layer, the boundary conditions at the top plate of the weak permeable layer and the boundary conditions at the bottom plate of the weak permeable layer; the second set of well-defined equations includes the control equations at the bottom plate of the weak permeable layer, the initial conditions at the bottom plate of the weak permeable layer, the boundary conditions at the bottom plate of the weak permeable layer and the free surface boundary conditions of the suspended saturated zone and the free surface equations of the suspended saturated zone.

[0100] The river-aquitard-suspended saturated zone-unsaturated zone-groundwater model was generalized to determine the hydrogeological conditions and riverbed lithology of the disjointed river-aquifer system. The suspended saturated zone is a saturated medium formed under the riverbed of the river-groundwater disjointed section. Its water content reaches the maximum and it is a relatively stable aquifer. The water in the suspended saturated 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 zone. Figure 3 As shown, on the lower interface of the suspended saturated zone, the water pressure state reaches a state equal to the atmospheric pressure, or a certain pressure gradient is formed due to the gravity of the water. This change in pressure state makes this interface a free surface.

[0101] like Figure 3 As shown in the figure, the generalized hydrogeological model is converted into a mathematical model. The river depth of the mathematical model is The thickness of the aquitard is , the riverbed permeability coefficient is , the riverbed water storage coefficient is The permeability coefficient of the hanging saturated zone and the water content of the hanging saturated zone are 、 .

[0102] The initial conditions of the mathematical model are: the water head of the aquitard under the riverbed and the hanging saturated zone is 0 at the initial moment, the coordinate origin is located at the center of the top plate of the aquitard under the riverbed as point A, and the water head at the top plate is The center of the bottom plate of the riverbed aquitard is point B, and the water head at the bottom plate is The distance that the saturated zone at the bottom of the aquitard on the center line of the riverbed moves over time is , in order to facilitate calculation, assume Calculated from the coordinate origin, the distance of the saturated zone below point B is -( )。

[0103] Specifically, according to the setting of the above mathematical model, the first set of well-defined equations is constructed based on the control equations at the top plate of the aquitard, the initial conditions at the top plate of the aquitard, the boundary conditions at the top plate of the aquitard, and the boundary conditions at the bottom plate of the aquitard. The control equations at the top plate of the aquitard are derived based on the conservation of mass and energy. The first set of well-defined equations is shown in formula (1):

[0104] (1);

[0105] in, is the water head at the top of the aquitard, is the water head at the bottom of the aquitard, t For the moment, is the river depth, is the thickness of the aquitard, x is the spatial coordinate, is the boundary condition at the top of the aquitard, is the boundary condition at the bottom of the aquitard.

[0106] Specifically, according to the setting of the above mathematical model, the second set of well-defined equations is constructed based on the control equations at the bottom of the weak permeable layer, the initial conditions at the bottom of the weak permeable layer, the boundary conditions at the bottom of the weak permeable layer, the boundary conditions of the free surface of the hanging saturated zone, and the free surface equations of the hanging saturated zone. The control equations at the bottom of the weak permeable layer are derived according to the conservation of mass and energy. The second set of well-defined equations is shown in formula (2):

[0107] (2);

[0108] in, is the water head at the top of the aquitard, is the water head at the bottom of the aquitard, x is the spatial coordinate, is the thickness of the aquitard, is the thickness of the saturated belt at different times, t For time, k is the permeability coefficient of the hanging saturated zone, is the water supply degree of the hanging saturated belt, is the boundary condition at the bottom of the aquitard, is the boundary condition at the top of the aquitard, It is the water head of the free surface of the suspended saturated zone.

[0109] Formula (1) and formula (2) constitute a coupled model that integrates the river water level, sediment seepage control equations, and seepage in the unsaturated zone under the sediment.

[0110] In an exemplary embodiment, 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.

[0111] Specifically, the connection condition between the first set of well-defined equations and the second set of well-defined equations is that when When , the third equation group is as shown in formula (3):

[0112] (3);

[0113] in, is the water head at the top of the aquitard, is the water head at the bottom of the aquitard, xis the spatial coordinate, k is the permeability coefficient of the hanging saturated zone, is the riverbed permeability coefficient.

[0114] S202: 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 governing equations at the top of the aquitard in the first set of well-defined equations and a general solution of the governing equations at the top of the aquitard in the second set of well-defined equations.

[0115] Specifically, the first group of well-defined equations, the second group of well-defined equations and the third group of well-defined equations are subjected to Laplace transformation to obtain the first group of well-defined equations, the second group of well-defined equations and the third group of well-defined equations; the first group of well-defined equations is solved according to the initial conditions and boundary conditions of the aquitard to obtain the general solution of the first group of well-defined equations; the second group of well-defined equations is solved according to the initial conditions and boundary conditions of the aquitard to obtain the general solution of the second group of well-defined equations.

[0116] Specifically, the first set of well-defined equations, the second set of well-defined equations and the third set of well-defined equations are subjected to Laplace transformation respectively to obtain a first set of well-defined equations, a second set of well-defined equations and a third set of well-defined equations.

[0117] The first Lassen transformation solves the equations, as shown in formulas (4), (5), and (6):

[0118] ;

[0119] The second Lassen transformation solves the equations, as shown in formulas (7), (8), (9), and (10):

[0120] ;

[0121] The third Lassen transformation equations are shown in formulas (11) and (12):

[0122] ;

[0123] The general solution of formula (4) is shown in formula (13):

[0124] (13);

[0125] The general solution of formula (7) is shown in formula (14):

[0126] (14);

[0127] Determine the coefficients C, D, E, and F in the general solution equation.

[0128] Substituting boundary condition (5) into formula (13), we obtain formula (15), which is as follows:

[0129] (15);

[0130] Substituting boundary condition (8) into formula (13), we obtain formula (16), which is as follows:

[0131] (16);

[0132] Substitute formula (12) into formula (13) to determine C , C The calculation method of is shown in formula (17):

[0133] (17);

[0134] Coefficient of determination and .

[0135] Derivative formula (11) and combined with boundary condition (9) yield formula (18), which is as follows:

[0136] (18);

[0137] Right now: (19);

[0138] Taking the derivative of formula (13), we get formula (20), which is as follows:

[0139] (20);

[0140] Substituting formula (20) into formula (19), we obtain formula (21), which is as follows:

[0141] (twenty one);

[0142] Determine the coefficient F and substitute the boundary condition (9) into formula (14) to obtain formula (22), which is as follows:

[0143] (twenty two);

[0144] By solving the above set of equations, we can obtain the expressions of coefficients C, D, E, and F respectively.

[0145] S203: Determine a hanging saturated zone migration equation based on the general solution of the control equation at the top of the aquitard and the general solution of the control equation at the top of the aquitard; the hanging saturated zone migration equation is the change of the thickness of the hanging saturated zone with time.

[0146] Specifically, based on the general solution obtained from the first and second well-defined equations, the equation for the transport of the suspended saturated zone under the riverbed is further derived. According to boundary conditions (9) and (10), formula (23) is obtained, which is as follows:

[0147] (twenty three);

[0148] Derivative of formula (14) yields , substituting into formula (23), we get formula (24), which is as follows:

[0149] (twenty four);

[0150] Substituting the expressions of C, D, E, and F into formula (14), we obtain formula (25), which is as follows:

[0151] (25);

[0152] Formula (25) is simplified to formula (26), which is as follows:

[0153] (26);

[0154] Substituting the expressions of coefficients E and F into formula (14), we obtain The expression of is formula (27), which is as follows:

[0155] (27);

[0156] Substituting formula (27) into formula (26), we obtain formula (28), which is as follows:

[0157] (28);

[0158] Substituting formula (24) into formula (28), we obtain formula (29), which is as follows:

[0159] (29);

[0160] Let the above formula

[0161] Therefore, formula (29) can be expressed as shown in formula (30): (30);

[0162] Simplifying the above formula, we can obtain formula (31) and formula (32), which are as follows:

[0163] (31);

[0164] (32);

[0165] Through the above steps, the thickness of the hanging saturated zone is derived. The quadratic equation of one variable, according to the selected reference surface is a negative number, so remove the inappropriate solution. In Laplace space, The solution is shown in formula (33):

[0166] (33);

[0167] in: (34);

[0168] (35);

[0169] The Stehfest numerical inversion formula is used to solve formula (33) and the suspended saturated zone migration equation is obtained, as shown in formula (36):

[0170] (36);

[0171] in, , ，N An even number, generally N is 6-10 to get satisfactory calculation accuracy ，k is a positive integer ， , is the weight function ， For a given N, the following holds: 。

[0172] In an exemplary embodiment, the river depth remain unchanged, that is , thickness of the aquitard , analyze the different permeability coefficients of weak permeable layers The variation law of the thickness of the suspended saturated zone under the riverbed under the conditions, such as Figure 4 As shown, regardless How does it change? The migration equation of the hanging saturated zone is the thickness of the hanging saturated zone. The change over time is -( ), and finally reaches stability. After stabilization, the thickness of the suspended saturated zone is close to the river water depth. Moreover, the greater the permeability coefficient of the weak permeable layer, Therefore, for a disjointed river with a blocking layer, if the permeability coefficient of the weak permeable layer under the riverbed is very small, there will be a significant lag in the recharge of groundwater by river leakage.

[0173] S204: Determine the calculation formula for the water head at the top plate of the weak permeable layer based on the suspended saturated zone migration equation.

[0174] In an exemplary embodiment, the calculation formula for the water head at the top plate of the weak permeable layer is shown in formula (37):

[0175] (37);

[0176] in, is the water head at the top of the aquitard, is the thickness of the saturated belt at different times, is the thickness of the aquitard.

[0177] S205: Substitute the calculation formula of the water head at the top of the weak permeable layer into Darcy's law to obtain the leakage flux of the disjointed river at different times

[0178] The calculation formula of Darcy's law is shown in formula (38):

[0179] (38);

[0180] in, is the leakage flux of the disjointed river at different times, is the riverbed permeability coefficient, The water head at the top of the aquitard, The depth of the river.

[0181] When a hanging saturated zone is formed at the bottom of the aquitard, the calculation formula of the water head at the top of the aquitard is substituted into Darcy's law to obtain the seepage flux of the disjointed river at different times.

[0182] Substituting formula (37) into formula (38), we can obtain the leakage flux of the disjointed river through the aquitard at different times. The calculation method of the leakage flux of the disjointed river at different times is shown in formula (39):

[0183] (39);

[0184] in, is the leakage flux of the disjointed river at different times,t For the moment, is the river depth, is the thickness of the saturated belt at different times, is the riverbed permeability coefficient, is the thickness of the aquitard.

[0185] Specifically, since the thickness of the saturated zone under the aquitard changes with time, the seepage flux of the river also changes with time.

[0186] is the water head at the lowest point of the hanging saturated zone, and there is another case of its change with time, as shown in formula (40):

[0187] (40);

[0188] in, is the negative pressure head at the bottom of the riverbed aquitard. When, and , , At this time, the bottom plate of the weak permeable layer and the saturated zone below the bottom plate have not yet formed. At this time, the pressure at the bottom plate A of the weak permeable layer is negative. This situation rarely occurs in nature and is an extremely special case.

[0189] In an exemplary embodiment, when the thickness of the suspended saturated zone stabilizes over time, the amount of river leakage per unit area per unit time is approximately equal to twice the permeability coefficient of the aquitard, that is, This conclusion shows that the amount of river leakage is mainly affected by the permeability of the weak permeable layer of the riverbed. When the permeability coefficient of the weak permeable layer is larger, the leakage flux of the river is larger. When the thickness of the hanging saturated zone stabilizes over time, the leakage flux of the river per unit time and per unit area is approximately equal to twice the permeability coefficient of the weak permeable layer, that is, This conclusion shows that the magnitude of river leakage flux is mainly affected by the permeability of the weak permeable layer of the riverbed. When the permeability coefficient of the weak permeable layer is larger, the leakage flux of the river is larger.

[0190] The depth of the river in the river-aquifer disconnection section of a certain basin , thickness of riverbed aquitard , suspension saturated zone permeability coefficient , water supply , the changes in river seepage flux when the permeability coefficient of the aquitard changes at different times can be obtained through the above formulas (37) and (38). Figure 5As shown in the figure, compared with the variation in the thickness of the hanging saturated zone, the river seepage flux shows a trend of initially being stable, then rapidly increasing, and then decreasing to a stable state as the thickness of the saturated zone gradually increases over time. During the initial period, the river seepage flux exhibits a horizontal section, indicating that the hanging saturated zone has not yet formed under the riverbed. As the thickness of the hanging saturated zone increases, the river seepage flux decreases and then stabilizes.

[0191] Based on the above example, assuming that the riverbed permeability coefficient remains unchanged, we further analyze the variation of the seepage flux of the disjointed river with the river depth. Figure 6 It can be seen that as the river depth increases, the river leakage also tends to increase, but the increase is limited. The reason for this phenomenon is that, restricted by the weak permeable layer of the riverbed, when the river depth increases to a certain extent, the river leakage flux undergoes nonlinear changes. Therefore, it is difficult to significantly increase the river leakage flux by simply increasing the river depth.

[0192] In the above embodiment, based on the principle of conservation of mass and energy equations, a formula for calculating the seepage flux of a disjointed river at the riverbed interface is theoretically derived, and this formula is applied to the calculation of the seepage flux of an actual disjointed river. This takes into account the migration of the thickness of the suspended saturated zone over time when there is a blocking layer in the riverbed, thereby avoiding the difficulty in obtaining the hydraulic gradient of the riverbed in field experiments, which increases the calculation error of the seepage flux of the disjointed river.

[0193] When applying the calculation method of the seepage flux of a disjointed river provided by the present invention, it is not necessary to Figure 2 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0194] The above is a method for calculating the seepage flux of a disjointed river provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding device for calculating the seepage flux of a disjointed river, such as Figure 7 shown.

[0195] Figure 7 A schematic diagram of a device for calculating seepage flux of a disjointed river provided by the present invention, comprising:

[0196] Construction module 701 is used to generalize the hydrogeological model of the disjointed river 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 the control equations at the top plate of the weak permeable layer, the initial conditions at the top plate of the weak permeable layer, the boundary conditions at the top plate of the weak permeable layer and the boundary conditions at the bottom plate of the weak permeable layer; the second set of well-defined equations includes the control equations at the bottom plate of the weak permeable layer, the initial conditions at the bottom plate of the weak permeable layer, the boundary conditions at the bottom plate of the weak permeable layer and the free surface boundary conditions of the suspended saturated zone and the free surface equations of the suspended saturated zone.

[0197] The solution module 702 is used to perform a Las Vegas transformation on the first set of well-defined equations and the second set of well-defined equations, and obtain 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.

[0198] The first determination module 703 is used to determine the hanging saturated zone migration equation based on 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 hanging saturated zone migration equation is the change of the thickness of the hanging saturated zone with time.

[0199] The second determining module 704 is used to determine a calculation formula for the water head at the top plate of the aquitard according to the suspended saturated zone migration equation.

[0200] The third determining module 705 is used to substitute the calculation formula of the water head at the top plate of the weak permeable layer into Darcy's law to obtain the leakage flux of the disjointed river at different times.

[0201] The specific definitions of a device for calculating the seepage flux of a disjointed river can be found in the definitions of the method for calculating the seepage flux of a disjointed river described above and will not be repeated here. Each module in the disjointed river seepage flux device described above can be implemented in whole or in part via software, hardware, or a combination thereof. Each of these modules can be embedded in or independent of a processor in a computer device in hardware form, or stored in a computer device memory in software form, so that the processor can call and execute the corresponding operations of each module.

[0202] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 2 A method for calculating the seepage flux of disjointed rivers is provided.

[0203] The present invention also provides Figure 8 The structural diagram of the computer equipment shown in FIG. Figure 8As shown in the figure, 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, it may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 2 A method for calculating the seepage flux of disjointed rivers is provided.

[0204] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware using a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes in the above-described method embodiments. Any reference to memory, storage, database, or other media used in the various embodiments provided herein may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0205] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, 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, they should be considered to be within the scope of 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, a free surface boundary condition of the suspended saturated zone, and a free surface equation of the suspended saturated zone; Performing a Laszlo transformation on the first set of well-defined equations and the second set of well-defined equations, and obtaining a general solution of the governing equations at the top of the aquitard in the first set of well-defined equations and a general solution of the governing equations at the top of the aquitard in the second set of well-defined equations; Determine a hanging saturated zone migration equation based on the general solution of the control equation at the top of the aquitard and the general solution of the control equation at the top of the aquitard; the hanging saturated zone migration equation is the change of the thickness of the hanging saturated zone with time; Determine the calculation formula of the water head at the top plate of the weak permeable layer according to the suspended saturated zone migration equation; Substituting the calculation formula of the water head at the top plate of the weak permeable layer into Darcy's law, the leakage flux of the disjointed river at different times is obtained; The migration equation of the suspended saturated zone is: ； in, is the thickness of the saturated belt at different times, t For the moment, , N is an even number, k is a positive integer, , is the weight function, is a quadratic equation in Laplace space about the thickness of the suspended saturated zone; The suspended saturated zone migration equation is a quadratic equation in Laplace space. for: ； in, , , is the thickness of the aquitard, k is the permeability coefficient of the hanging saturated zone, is the riverbed permeability coefficient, is the water supply degree of the hanging saturated belt, is the river depth, P represents the time-dependent term after Laplace transform, represents the coefficient related to permeability; The calculation formula for the water head at the top plate of the aquitard is: ； in, is the water head at the top of the aquitard, is the thickness of the saturated belt at different times, is the thickness of the aquitard; The Darcy's law is: ； in, is the thickness of the aquitard, is the riverbed permeability coefficient, is the river depth, t For the moment, is the leakage flux of the disjointed river at different times, is the water head at the top of the aquitard; The leakage flux of the disjointed river at different times is: ； in, is the leakage flux of the disjointed river at different times, is the river depth, is the thickness of the saturated belt at different times, is the thickness of the aquitard, is the riverbed permeability coefficient.

2. The method according to claim 1, wherein The governing equation at the top plate of the aquitard is: ； in, is the water head at the top of the aquitard, represents the coefficient related to permeability, t For time, x is the spatial coordinate; The initial conditions at the top of the aquitard are: ； in, is the initial condition at the top of the aquitard; The boundary conditions at the top of the aquitard are: ； in, is the boundary condition at the top of the aquitard, is the depth of the river; The boundary conditions at the bottom of the aquitard are: ； in, is the thickness of the aquitard, is the boundary condition at the top of the aquitard, is the boundary condition at the bottom of the aquitard.

3. The method according to claim 1, wherein The governing equation at the bottom plate of the aquitard is: ； in, is the water head at the bottom of the aquitard, x is the spatial coordinate; The initial conditions at the bottom of the aquitard are: ； in, is the initial condition at the bottom of the aquitard; The boundary conditions at the bottom of the aquitard are: ； in, is the boundary condition at the bottom of the aquitard, is the boundary condition at the top of the aquitard, is the thickness of the aquitard, t For time; The free surface boundary conditions of the suspended saturated zone are: ； in, is the thickness of the saturated belt at different times, The water head of the free surface of the hanging saturated zone; The free surface equation of the suspension saturated zone is: ； in, is the water supply degree of the hanging saturated belt, k is the permeability coefficient of the hanging saturated zone, It is the water head at the bottom of the aquitard.

4. The method according to claim 1, wherein 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, wherein The third program group is: ； in, is the water head at the top of the aquitard, is the water head at the bottom of the aquitard, x is the spatial coordinate, k is the permeability coefficient of the hanging saturated zone, is the riverbed permeability coefficient.

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