A method for predicting the wetting line of loess bank slope under reservoir water level fluctuation

Abstract

The application discloses a kind of loess bank slope saturation line prediction methods under the action of reservoir water level, belong to water conservancy and hydropower engineering and geotechnical engineering technical field, can solve the problem that cannot accurately predict saturation line distribution under the coupling effect of "seepage-collapse". The method comprises: according to loess bank slope position information and dead water level, loess bank slope calculation model is constructed;According to the loess bank slope calculation model, the slope saturation relationship between the surface of the loess bank slope and the height of the saturation line is determined;The seepage collapse time relationship between the permeability coefficient of loess, porosity, collapse strain and effective stress is determined;According to the change rate of pore water volume of loess, seepage velocity and the seepage collapse time relationship, a collapse seepage control equation is constructed;The initial saturation relationship is used to solve the collapse seepage control equation to obtain the loess bank slope saturation line.This method constructs the saturation line evolution theory system of "seepage-collapse" coupling, and accurately predicts the distribution of loess bank slope saturation line.

Description

Technical Field

[0001] This invention relates to a method for predicting the phreatic line of loess bank slopes under the influence of reservoir water level fluctuations, belonging to the fields of water conservancy and hydropower engineering and geotechnical engineering. Background Technology

[0002] In recent years, the construction of water conservancy and hydropower projects in the Loess Plateau region has been increasing, and the thick loess layer is the main stratum constituting the reservoir bank slope. The superimposed characteristics of "periodic rise and fall of reservoir water level" and "loess collapse when wetted" make loess bank slopes a high-incidence area for geological disasters. As the core element in the study of seepage field of loess bank slopes, the dynamic distribution of the seepage line directly determines the spatial range of the saturated zone of the slope and the gradient characteristics of pore water pressure.

[0003] Current research on the phreatic line of loess slopes mostly revolves around the evolution of the seepage field under the influence of reservoir water level fluctuations, with numerical simulation and theoretical analysis being the most commonly used methods. Numerical simulation involves establishing a geometric model, meshing, setting parameters and conditions, and then using a computer to calculate element by element, finally outputting the complete phreatic line distribution. Theoretical analysis uses mathematical formulas to directly calculate the phreatic line. Generally, simplifying assumptions are made first, then mathematical equations are established, and finally the formula is directly derived. Substituting the numerical values ​​yields the calculation results.

[0004] However, the "seepage-collapse" coupling effect affects physical parameters of loess such as porosity and permeability coefficient. Yet, there is currently no research on the prediction of the seepage line that comprehensively considers the "seepage-collapse" coupling effect. Summary of the Invention

[0005] This invention provides a method for predicting the phreatic line of loess bank slopes under the influence of reservoir water level fluctuations, including:

[0006] A calculation model for loess slopes was constructed based on the location information and dead water level of the loess slopes.

[0007] The initial saturation relationship between the surface of the loess slope and the height of the saturation line is determined based on the loess slope calculation model.

[0008] Determine the infiltration-collapse time relationship between the permeability coefficient, porosity, collapsible strain, and effective stress of loess;

[0009] Based on the relationship between the pore water volume change rate, seepage velocity, and the seepage collapse time of loess, a seepage control equation for collapse is constructed.

[0010] The theoretical analytical solution of the phreatic line of the loess slope is obtained by solving the control equation of the collapsible seepage based on the initial phreatic relationship.

[0011] The loess slope calculation model is represented by a plane rectangular coordinate system, with the horizontal axis representing the waterproof base plate and the positive direction of the horizontal axis representing the interior of the loess slope; the vertical axis representing the vertical direction where the dead water level intersects with the slope surface; and the origin representing the projection of the intersection of the dead water level and the slope surface onto the waterproof base plate.

[0012] Furthermore, based on the loess slope calculation model, the initial phreatic relationship between the surface of the loess slope and the height of the phreatic line is determined, specifically as follows:

[0013] Determine the slope of the initial wetting line in the aforementioned Cartesian coordinate system;

[0014] The initial wetting relationship is determined based on the linear change of reservoir water level over time, the positive abscissa value, and the slope of the wetting line.

[0015] This also includes determining the infiltration-collapse time relationship between the permeability coefficient, porosity, collapsible strain, and effective stress of loess, including:

[0016] Determine the relationship between collapsible strain and effective stress in loess;

[0017] Determine the relationship between the porosity of loess and the porosity collapse strain;

[0018] Determine the relationship between the permeability coefficient and the porosity of loess;

[0019] The permeation-sinking time relationship is constructed based on the described sinking stress relationship, the described pore sinking relationship, and the described permeation-pore relationship.

[0020] Based on the relationship between the pore water volume change rate, seepage velocity, and the seepage collapse time of loess, a seepage control equation for collapse is constructed, including:

[0021] Based on the aforementioned Cartesian coordinate system, the loess micro-element is constructed, and the pore water volume change rate of the loess micro-element is calculated.

[0022] The relationship between pore seepage rate and the pore water volume change rate is determined;

[0023] Based on the pore flow rate relationship and the infiltration-collapse time relationship, a collapse flow control equation is constructed.

[0024] It also includes solving the collapsible seepage control equation based on the initial phreatic relationship to obtain the theoretical analytical solution of the phreatic line of the loess slope, including:

[0025] Substituting the initial wetting relationship into the collapsible seepage control equation and solving it using the method of separation of variables, the first solution is obtained;

[0026] By combining the boundary conditions, the first solution is solved to obtain the expression for the bank slope distance, which is the relationship between the horizontal coordinate value, porosity and the farthest distance affected by the reservoir water level.

[0027] Integrating the first solution yields the exponential function.

[0028] Based on the initial saturation relationship, the expression for the bank slope distance, and the exponential function, the theoretical analytical solution for the saturation line of the loess bank slope is obtained.

[0029] The boundary conditions are as follows: when the horizontal coordinate value is 0, the height of the seepage line is level with the reservoir water level; when the horizontal coordinate value is the farthest distance affected by the reservoir water level, the height of the seepage line is constant.

[0030] The beneficial effects of this invention include: establishing a quantitative correlation between collapsibility strain, porosity, and permeability coefficient, clarifying the feedback effect of loess collapsibility upon contact with water on seepage parameters, and constructing a theoretical system for the evolution of the phreatic line coupled with seepage, thus solving the problem that conventional methods are unable to accurately characterize the influence of collapsibility on the phreatic line; the derived analytical solution has a clear physical meaning and parameter correspondence, and can be directly substituted into actual engineering parameters (such as collapsibility coefficient, reservoir water level rise and fall rate, permeability coefficient, etc.) to calculate the phreatic line height at any cross section and at any time. Compared with pure numerical simulation methods, it is easier to reveal the influence law of key parameters on the phreatic line and can also provide a theoretical verification benchmark for numerical simulation results; it can also quickly predict the dynamic distribution range of saturated collapsible areas on slopes during reservoir water level rise and fall, and accurately delineate risk areas that need reinforcement; at the same time, it can quantitatively analyze the sensitivity of parameters such as collapsibility coefficient and permeability coefficient to the evolution of the phreatic line, providing a scientific basis for optimizing the layout of the bank slope drainage system and setting the threshold for reservoir water level rise and fall rate, thereby reducing the risk of geological disasters such as loess bank landslides and collapsibility deformation. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of a method for predicting the phreatic line of loess bank slope under the influence of reservoir water level fluctuations, provided by an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram of the loess slope calculation model provided in an embodiment of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0034] This invention provides a method for predicting the phreatic line of loess slopes under the influence of reservoir water level fluctuations, such as... Figure 1 As shown, the method includes:

[0035] S1. Construct a calculation model for the loess slope based on the location information and dead water level of the loess slope;

[0036] Specifically, the loess slope calculation model is represented by a plane rectangular coordinate system, with the horizontal axis being the waterproof base plate and the positive direction of the horizontal axis being the interior of the loess slope; the vertical axis being the vertical direction where the dead water level intersects with the slope surface; and the origin being the projection of the intersection of the dead water level and the slope surface onto the waterproof base plate.

[0037] In this embodiment of the invention, see Figure 2 , Figure 2 The initial wetting line refers to the boundary between the saturated and unsaturated zones in the soil under the initial state. Figure 2 The mid-to-final state wetting line refers to the line that passes through At any given moment, under the coupling effect of "seepage-collapse", the boundary between the saturated seepage zone and the unsaturated zone in the soil; Figure 2 The mid-surface refers to the upper natural boundary of the soil mass. The origin is denoted as... The horizontal axis is The axis represents the vertical axis. Axis representation, The axis is the horizontal direction of the waterproof base plate. The positive direction of the axis is inside the loess slope; The axis is the vertical direction where the dead water level intersects with the slope surface; the seepage is steady-plane seepage, along... A plane with no seepage in the direction perpendicular to this plane; the height (m) from the dead water level to the impermeable base plate is denoted as... The height (m) from the highest water level to the waterproof base plate is denoted as The furthest distance affected by the reservoir water level is recorded as follows: And when the reservoir water level actually affects the distance At that time, the actual wetting line height at that location Unaffected by rises and falls in reservoir water level, i.e. .

[0038] In this embodiment of the invention, the initial wetting line is set as a straight line, and the hydraulic gradient is along... The axial direction is constant; the reservoir water level changes linearly with time, that is: ,in The rate of rise and fall of the reservoir water level, and when the reservoir water level rises... When the reservoir water level drops .

[0039] In practical applications, along the inside of the slope Wetting line monitoring wells are deployed along the direction of the reservoir water level. By monitoring the head changes at each well during the rise and fall of the reservoir water level, the stable wetting line height at the farthest point of influence of the reservoir water level can be obtained based on the head changes at each well. If the water head at a certain monitoring well remains at its initial stable height... Then the monitoring hole corresponds to The coordinates are .

[0040] S2. Determine the initial saturation relationship between the surface of the loess slope and the height of the saturation line based on the loess slope calculation model;

[0041] Specifically:

[0042] Determine the slope of the initial wetting line in the aforementioned Cartesian coordinate system;

[0043] The initial wetting relationship is determined based on the linear change of reservoir water level over time, the positive abscissa value, and the slope of the wetting line.

[0044] In this embodiment of the invention, based on the Dubuis assumption, for stable planar seepage of a horizontal impermeable base, the initial wetting line is a straight line, and it is near the reservoir bank boundary ( When the seepage line is level with the reservoir water level, that is... ; Stable boundary within the slope ( ), the height of the immersion line is ,Right now Therefore, the slope of the initial wetting line is:

[0045] (1)

[0046] Based on the slope of the initial wetting line described above, the equation of the initial wetting line can be determined as follows:

[0047] (2)

[0048] S3. Determine the infiltration-collapse time relationship between the permeability coefficient, porosity, collapsible strain and effective stress of loess;

[0049] Specifically:

[0050] Determine the relationship between collapsible strain and effective stress in loess;

[0051] In this embodiment of the invention, the collapse of loess is caused by a decrease in effective stress, and its effective stress The expression is:

[0052] (3)

[0053] In the formula: For the total stress, Pore ​​water pressure, Loess saturated with high density, The density of water, The height of the wetting line (m). The reservoir water level (m) is at any given time.

[0054] exist At that moment, the reservoir water level was... The initial effective stress at this time is:

[0055] (4)

[0056] The relationship between collapsibility strain and collapsibility coefficient is as follows:

[0057] (5)

[0058] in, For wet collapse strain, This is the collapsibility coefficient;

[0059] Combining equations (3), (4), and (5), the relationship between the collapsible strain and the effective stress of the loess is as follows:

[0060] (6)

[0061] Determine the relationship between the porosity of loess and the porosity collapse strain;

[0062] In this embodiment of the invention, it is set The porosity of loess. If we consider the collapsible strain, then the porosity of loess is related to the collapsible strain:

[0063] (7)

[0064] Substituting equation (6) into equation (7), we obtain the relationship between the porosity of the loess and the pore collapse strain:

[0065] (8)

[0066] in: This represents the initial porosity of the loess.

[0067] Determine the relationship between the permeability coefficient and the porosity of loess;

[0068] In this embodiment of the invention, it should be noted that the permeability coefficient of loess is... Determined by the pore structure, and for the same soil medium, the permeability coefficient of the loess and the permeability-porosity relationship conform to the Kozeny-Carman formula:

[0069] (9)

[0070] in, The initial permeability coefficient, The porosity influence index (an empirical parameter of the Kozeny-Carman formula) is an existing formula, which will not be elaborated upon in this invention.

[0071] The permeation-sinking time relationship is constructed based on the described sinking stress relationship, the described pore sinking relationship, and the described permeation-pore relationship.

[0072] In this embodiment of the invention, the small slippage strain approximation is used, i.e. , Based on the described stress relationship, pore collapse relationship, and permeability-pore relationship, the permeability-collapse time relationship is constructed as follows:

[0073] (10)

[0074] in, is the permeability coefficient.

[0075] In practical applications, the physical and mechanical parameters of loess, such as the collapsibility coefficient, can be obtained through field exploration, in-situ testing, and laboratory testing. Initial porosity Initial permeability coefficient Porosity Influence Index .

[0076] S4. Construct the seepage control equation for collapse based on the pore water volume change rate, seepage velocity, and the relationship between seepage collapse time in loess.

[0077] Specifically, it includes:

[0078] Based on the aforementioned Cartesian coordinate system, the loess micro-element is constructed, and the pore water volume change rate of the loess micro-element is calculated.

[0079] In this embodiment of the invention, the following are selected Figure 2 middle arrive , arrive If a micro-element has a width of 1 in the vertical cross-section (planar seepage), then the volume of the micro-element is:

[0080] (11)

[0081] exist The pore water volume of the micro-element at time [time] for:

[0082] (12)

[0083] Differentiating the above equation, the rate of change of pore water volume in the loess micro-element per unit time is:

[0084] (13)

[0085] The relationship between pore seepage rate and the pore water volume change rate is determined;

[0086] In this embodiment of the invention, according to Darcy's law, the seepage velocity is:

[0087] (14)

[0088] in, The value represents the seepage velocity; the negative sign indicates that the seepage direction is opposite to the hydraulic gradient.

[0089] exist Inflow for:

[0090] (15)

[0091] exist Outflow for:

[0092] (16)

[0093] According to the above formula, net outflow for:

[0094] (17)

[0095] Since the reduction in pore water in the micro-element is equal to the net outflow from seepage, that is:

[0096] (18)

[0097] The above net outflow Substituting the expression into equation (18), the pore seepage flow relationship is obtained as follows:

[0098] (19)

[0099] Based on the pore flow rate relationship and the infiltration-collapse time relationship, a collapse flow control equation is constructed.

[0100] In this embodiment of the invention, based on the pore sinking relationship, the infiltration sinking time relationship, and the pore seepage flow relationship, that is, substituting equations (8) and (10) into equation (19), and ignoring higher-order minor terms (small deformation of sinking), the sinking seepage control equation is constructed as follows:

[0101] (20)

[0102] S5. Based on the initial saturation relationship, the collapsible seepage control equation is solved to obtain the theoretical analytical solution of the saturation line of the loess slope.

[0103] Specifically, this includes: substituting the initial wetting relationship into the collapsible seepage control equation and solving it using the method of separation of variables to obtain the first solution formula;

[0104] Based on the initial infiltration relationship, when At that time, the seepage line is level with the reservoir water level, that is:

[0105] (twenty one)

[0106] when At that time, the immersion line remains Unchanged, that is:

[0107] (twenty two)

[0108] And set initial conditions: In At that moment, the slope initially stabilizes for seepage, i.e.:

[0109] (twenty three)

[0110] In this embodiment of the invention, the wetting line equation can be decomposed into:

[0111] (twenty four)

[0112] In the formula, This represents the change in the phreatic line caused by the rise and fall of the reservoir water level.

[0113] Substituting equation (24) into equation (20) and ignoring higher-order terms, we get:

[0114] (25)

[0115] The above equation is solved using the method of separation of variables, and assumptions are made. Substituting into equation (25), we obtain the first solution equation as follows:

[0116] (26)

[0117] By combining the boundary conditions, the first solution is solved to obtain the expression for the bank slope distance, which is the relationship between the horizontal coordinate value, porosity and the farthest distance affected by the reservoir water level.

[0118] In this embodiment of the invention, the first solution formula (26) is solved. Since the left side of the first solution formula (26) only contains The right side contains only Therefore, let both sides of the first solution (26) be equal to a . , Irrelevant constants Then the left side of equation (26) simplifies to:

[0119] (27)

[0120] Combining boundary conditions, when hour, ,when hour, The expression for the bank slope distance is obtained as follows:

[0121] (28)

[0122] Integrating the first solution yields the exponential function.

[0123] In this embodiment of the invention, the right side of equation (26) is simplified to obtain:

[0124] (29)

[0125] Integrating the simplified equation (26), we obtain the exponential function:

[0126] (30)

[0127] Where: eigenvalues .

[0128] Based on the initial saturation relationship, the expression for the bank slope distance, and the exponential function, the theoretical analytical solution for the saturation line of the loess bank slope is obtained.

[0129] In this embodiment of the invention, based on the phreatic line equation (24), the bank slope distance expression (28), and the exponential function (30), the theoretical analytical solution of the phreatic line of the loess bank slope is obtained as follows:

[0130] (31)

[0131] in, The constant of integration is given by the initial conditions. The fit was determined.

[0132] In practical applications, the theoretically calculated value can be compared with the measured wetting line height of the field monitoring well, and the collapsibility coefficient can be adjusted accordingly. Porosity Influence Index Parameters such as these are optimized to improve calculation accuracy and ensure that the results closely match the actual engineering situation.

[0133] This invention establishes a quantitative correlation between collapsibility strain, porosity, and permeability coefficient to clarify the feedback effect of loess collapsibility on seepage parameters. It constructs a theoretical system for the evolution of the phreatic line coupled with seepage, solving the problem that conventional methods struggle to accurately characterize the influence of collapsibility on the phreatic line. The obtained analytical solution for the phreatic line of loess slopes has clear physical meaning and parameter correspondence. Substituting actual engineering parameters (such as the collapsibility coefficient, reservoir water level rise / fall rate, and permeability coefficient) allows for direct calculation of the phreatic line height at any cross-section and any time. Compared to pure numerical simulation methods, this approach more easily reveals the influence of key parameters on the phreatic line and provides a theoretical verification benchmark for numerical simulation results. Furthermore, it can quickly predict the dynamic distribution range of saturated collapsible areas on the slope during reservoir water level rises and falls, accurately delineating risk areas requiring reinforcement. Simultaneously, it can quantitatively analyze the sensitivity of parameters such as the collapsibility coefficient and permeability coefficient to the evolution of the phreatic line, providing a scientific basis for optimizing the layout of the slope drainage system and setting thresholds for reservoir water level rise / fall rates, thereby reducing the risk of geological disasters such as landslides and collapsibility deformation on loess slopes.

[0134] The above description is merely a few embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for predicting the phreatic line of loess bank slopes under the influence of reservoir water level fluctuations, characterized in that, The method includes: A calculation model of the loess slope is constructed based on the location information and dead water level of the loess slope. The calculation model of the loess slope is represented by a plane rectangular coordinate system, with the horizontal axis being the water-resistant bottom plate and the positive direction of the horizontal axis being the interior of the loess slope. The vertical axis is the vertical direction where the intersection of the dead water level and the slope surface is located. The origin is the projection of the intersection of the dead water level and the slope surface onto the water-resistant bottom plate. The initial saturation relationship between the surface of the loess slope and the height of the saturation line is determined based on the loess slope calculation model. Determine the infiltration-collapse time relationship between the permeability coefficient, porosity, collapsible strain, and effective stress of loess; Based on the relationship between the pore water volume change rate, seepage velocity, and the seepage collapse time of loess, a seepage control equation for collapse is constructed. Based on the initial saturation relationship, the theoretical analytical solution of the collapsible seepage control equation is obtained by solving the equation. The determination of the infiltration-collapse time relationship between the permeability coefficient, porosity, collapsible strain, and effective stress of loess includes: The relationship between collapsible strain and effective stress in loess is determined; the relationship between porosity and collapsible strain in loess is determined; the relationship between permeability coefficient and porosity in loess is determined; and a permeability-collapse time relationship is constructed based on the collapsible stress relationship, the porosity-collapse relationship, and the permeability-collapse relationship. The process of constructing the collapsibility seepage control equation based on the relationship between the pore water volume change rate, seepage velocity, and the seepage collapse time of loess includes: Based on the plane rectangular coordinate system, a loess micro-element is constructed, and the pore water volume change rate of the loess micro-element is calculated; the pore seepage flow relationship is determined according to the seepage velocity and the pore water volume change rate; and the collapse seepage control equation is constructed according to the pore seepage flow relationship and the seepage collapse time relationship.

2. The method according to claim 1, characterized in that, The initial phreatic relationship between the surface of the loess slope and the height of the phreatic line is determined based on the loess slope calculation model, specifically as follows: Determine the slope of the initial wetting line in the aforementioned Cartesian coordinate system; The initial wetting relationship is determined based on the linear change of reservoir water level over time, the positive abscissa value, and the slope of the initial wetting line.

3. The method according to claim 1, characterized in that, Based on the initial phreatic relationship, the theoretical analytical solution of the collapsible seepage control equation is obtained by solving the equation, including: Substituting the initial wetting relationship into the collapsible seepage control equation and solving it using the method of separation of variables, the first solution is obtained; By combining the boundary conditions, the first solution is solved to obtain the expression for the bank slope distance, which is the relationship between the horizontal coordinate value, porosity and the farthest distance affected by the reservoir water level. Integrating the first solution yields the exponential function. Based on the initial saturation relationship, the expression for the bank slope distance, and the exponential function, the theoretical analytical solution for the saturation line of the loess bank slope is obtained.

4. The method according to claim 3, characterized in that, The boundary conditions are as follows: when the horizontal coordinate value is 0, the height of the seepage line is level with the reservoir water level; when the horizontal coordinate value is the farthest distance affected by the reservoir water level, the height of the seepage line is constant.

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