A method for calculating critical hydraulic gradient based on particle size distribution curves

Abstract

This invention discloses a method for calculating critical hydraulic gradient based on particle size distribution curves. It includes the following steps: determining all soil particle size groups that may be activated when soil seepage failure occurs; plotting a particle size-to-weight ratio curve; converting the ordinate of the particle size-to-weight ratio curve into the cumulative volume percentage of soil particle size; calculating the distinguishing particle size d0 between coarse and fine particles, and determining the initiating particle size d that causes soil failure when seepage failure occurs, where d ≤ d0; deriving the critical hydraulic gradient calculation formula when particle size groups smaller than or equal to the initiating particle size d are simultaneously subjected to seepage force; treating particle size groups smaller than the initiating particle size d as a loss state, and considering coarse particles and particle size groups equal to the initiating particle size d as jointly bearing the seepage force, and calculating the critical hydraulic gradient value. This invention can more accurately calculate the critical hydraulic gradient value closest to the actual value, obtaining a critical hydraulic gradient value for soil that conforms to engineering practice.

Description

Technical Field

[0001] This invention relates to the field of dike seepage technology, specifically to a method for calculating critical hydraulic gradient based on particle size distribution curves. Background Technology

[0002] In the design of seepage control for dikes, the critical hydraulic gradient of the soil is a key design factor. Currently, for the two common seepage deformations, piping and erosion, relevant specifications and reference books provide semi-theoretical and semi-empirical formulas for calculating the critical hydraulic gradient of soil for piping or erosion.

[0003] However, these formulas have the following problems in their theoretical derivation:

[0004] First, it only considers the balance between the seepage force and buoyancy of a single soil particle under the vertical upward seepage action. However, in reality, seepage deformation is not initiated by a single particle, but more commonly by a group of particles. Therefore, the derivation formula that starts with a single particle may underestimate the critical hydraulic gradient of the soil.

[0005] Second, in the derivation of the formula, the soil particles that have already been lost are still included in the scope of the permeability bearing capacity. However, in reality, soil particles are gradually lost from fine to coarse. Once the soil is close to the point of seepage failure, the soil particles that bear the permeability bearing capacity should not include the soil particles that have already been lost. Therefore, the derivation formula that includes the soil particles that have already been lost in the scope of the permeability bearing capacity may overestimate the critical hydraulic gradient of the soil.

[0006] Whether the former underestimates the critical hydraulic gradient of the soil or the latter overestimates it, both will bring safety hazards to the design of seepage control for dikes. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes a critical hydraulic gradient calculation method based on particle size distribution curves. In deriving the critical hydraulic gradient of soil, this method not only avoids underestimating the critical hydraulic gradient due to considering only a single soil particle as the initiator, but also excludes soil particles that have already migrated and been lost during the analysis of the permeability and buoyancy balance of the particle group. This avoids overestimating the critical hydraulic gradient, thus obtaining a critical hydraulic gradient that conforms to engineering realities. This method can effectively guide the seepage control design of dikes, ensuring the stability and safety of dikes during seepage.

[0008] To achieve the above objectives, the present invention provides a critical hydraulic gradient calculation method based on particle size distribution curves, which is characterized by including the following steps:

[0009] S1) Determine all soil particle size groups that may be activated when soil seepage failure occurs. All soil particle size groups include the finest soil particle size to the coarsest soil particle size that may be activated.

[0010] S2) Plot the soil particle size-soil weight content curve, where the horizontal axis represents the soil particle size and the vertical axis represents the cumulative soil weight percentage of particles with a particle size less than or equal to a certain size.

[0011] S3) Transform the soil particle size-soil weight content curve into a particle size-volume content curve, where the vertical axis represents the cumulative volume percentage of soil particles that are less than or equal to the corresponding particle size.

[0012] S4) For continuously graded soil, calculate the distinguishing particle size d0 between coarse and fine particles, where the coarse particles are in a stable skeleton state and the fine particles are in a free-stacking state; and determine the initiating particle size d that causes soil failure when seepage failure occurs, where d≤d0.

[0013] S5) For non-uniformly graded continuous soil, all particle size groups less than or equal to the starting particle size d are considered to start simultaneously. The critical condition is that the seepage force on the particle group is balanced with the corresponding buoyancy weight. The critical hydraulic gradient calculation formula when particle size groups less than or equal to the starting particle size d are simultaneously subjected to seepage force is derived.

[0014] S6) The critical hydraulic gradient calculation formula for particle size groups that are smaller than or equal to the starting particle size d and are simultaneously subjected to seepage force is adjusted. Particle size groups smaller than the starting particle size d are regarded as loss state, and coarse particles and particle size groups equal to the starting particle size d are considered to jointly bear the seepage force. When the starting particle size d is infinitely close to the distinguishing particle size d0, the critical hydraulic gradient calculation formula (1) for piping occurs in the non-uniform soil is obtained. The calculated critical hydraulic gradient value is taken as the closest to the true critical hydraulic gradient value.

[0015] Formula (1) is shown below.

[0016]

[0017] In the formula,

[0018] J c 'Indicates the critical hydraulic gradient at which piping occurs in heterogeneous soil.'

[0019] n represents the porosity of soil per unit volume.

[0020] G s This represents the average relative density of coarse and fine particles.

[0021] dp represents the volume percentage of the starting particle size d.

[0022] d(p) represents the starting particle size d corresponding to a volume percentage content of p.

[0023] p(d0) represents the cumulative volume percentage of the particle size group that distinguishes particle size d0.

[0024] Furthermore, in S2), the abscissa of the particle size-soil weight content curve is divided according to the soil particle size group.

[0025] Furthermore, in S3), the cumulative soil weight percentage on the ordinate of the curve is converted into the cumulative volume percentage using the following formula.

[0026]

[0027] In the formula,

[0028] V s This indicates the cumulative volume percentage of soil particles.

[0029] m s Indicates the cumulative mass of soil particles.

[0030] G s This represents the average relative density of coarse and fine particles.

[0031] ρ w This indicates the density of water.

[0032] Furthermore, in S4), the particle size d0 is distinguished by calculating the particle size-soil weight content curve in step S2).

[0033] Furthermore, in S4), the distinguishing particle size d0 between coarse and fine particles is calculated using the following formula.

[0034]

[0035] In the formula,

[0036] d0 represents the particle size that distinguishes between coarse and fine particles.

[0037] d 10 This indicates the particle size that represents 10% or more of the total soil weight by weight.

[0038] d 70 This indicates the particle size that accounts for 70% or more of the total soil weight by weight.

[0039] Furthermore, in S5), when the critical condition is that the permeation force on the particle group is in equilibrium with the corresponding buoyancy weight, the following formula (2) is obtained.

[0040]

[0041] From the above formula (2), the critical hydraulic gradient calculation formula (3) is derived when a group of particle sizes less than or equal to the starting particle size d is simultaneously subjected to seepage force. Formula (3) is shown below.

[0042]

[0043] In the formula,

[0044] J c This represents the critical hydraulic gradient when a group of particles with a diameter less than or equal to the starting particle size d are simultaneously subjected to osmotic forces.

[0045] n represents the porosity of soil per unit volume.

[0046] γ w Indicates the specific gravity of water.

[0047] γ s This indicates the unit weight of soil particles.

[0048] dp represents the volume percentage of the starting particle size d.

[0049] d(p) represents the starting particle size d corresponding to a volume percentage content of p.

[0050] p(d) represents the cumulative volume percentage of the particle size group that is less than or equal to the starting particle size d, G s This indicates the average relative density of coarse and fine particles.

[0051] Furthermore, in S6), when the critical condition is that the seepage force borne by the particle group equal to the starting particle size d is equal to the sum of the resistance and constraint caused by its own weight, the following formula (4) is obtained. From formula (4), the critical hydraulic gradient calculation formula (1) for piping in uneven soil is derived.

[0052] The formula (4) is as follows:

[0053]

[0054] In the formula,

[0055] J c 'Indicates the critical hydraulic gradient at which piping occurs in heterogeneous soil.'

[0056] n represents the porosity of soil per unit volume.

[0057] G s This represents the average relative density of coarse and fine particles.

[0058] dp represents the cumulative volume percentage of the starting particle size d.

[0059] d(p) represents the starting particle size d corresponding to a volume percentage content of p.

[0060] p(d0) represents the cumulative volume percentage of the particle size group that distinguishes particle size d0.

[0061] The advantages of this invention are:

[0062] 1. Based on the definition of critical hydraulic gradient of soil, this invention considers the coarsest particle size that may be activated when seepage failure occurs when deriving the formula for critical hydraulic gradient of soil. It regards the finest particle size to the coarsest particle size that may be activated as the entire particle size group for soil seepage failure, thus avoiding the defect of the current semi-theoretical and semi-empirical formula that only considers the activation of a single soil particle, which leads to an underestimation of the critical hydraulic gradient of soil.

[0063] 2. When performing the equilibrium analysis of permeability and buoyancy on the particle group, this invention only considers the remaining soil particles that participate in the permeation movement according to the actual engineering situation, and does not include soil particles that have already migrated and been lost in the early stage. This can avoid the defect of overestimating the critical hydraulic gradient of the soil.

[0064] 3. This invention utilizes common particle size distribution curves (particle size-soil weight content curves) for appropriate coordinate transformation to derive the calculation formula for the most accurate critical hydraulic gradient. Compared with the current traditional calculation formula for the critical hydraulic gradient of piping, this invention considers both the actual situation of particle group initiation in engineering practice and the situation of particle groups that actually participate in the seepage force balance when seepage failure occurs. This makes the calculated hydraulic gradient value closest to the actual critical hydraulic gradient value, resulting in a critical hydraulic gradient value for soil that conforms to engineering practice. This can effectively guide the seepage control design of dikes and ensure the seepage stability and safety of dikes.

[0065] This invention provides a critical hydraulic gradient calculation method based on particle size distribution curves, which can more accurately calculate the critical hydraulic gradient value closest to the actual value, and obtain the critical hydraulic gradient value of soil that conforms to engineering practice. This provides theoretical and technical support for seepage control design of embankment foundations and has important theoretical and engineering practical significance. Attached Figure Description

[0066] Figure 1 This is a flowchart of the present invention;

[0067] Figure 2 This is a particle size-soil weight content curve in an embodiment of the present invention;

[0068] Figure 3 This is the particle size-volume content curve converted from the particle size-soil weight content curve in this embodiment of the invention. Detailed Implementation

[0069] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] In the description of this invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention.

[0071] like Figure 1 As shown, the present invention provides a method for calculating the critical hydraulic gradient based on particle size distribution curves, comprising the following steps:

[0072] S1) Determine all soil particle size groups that may be activated when soil seepage failure occurs. All soil particle size groups include the finest soil particle size to the coarsest soil particle size that may be activated.

[0073] In this embodiment, a certain dike project uses cohesive soil to fill the dike body, and the results of the sieve analysis test of the dike foundation soil are shown in Table 1.

[0074] Table 1 Results of sieve analysis test on embankment foundation soil

[0075] Particle size / mm 200 60 20 5 2 0.5 0.25 0.075 0.005 content / % 100 100 90 62.5 27 8 4 1 0

[0076] S2) Plot the soil particle size-soil weight content curve, where the horizontal axis represents the soil particle size and the vertical axis represents the cumulative soil weight percentage of particles with a particle size less than or equal to a certain size.

[0077] Specifically, the x-axis of the particle size-soil weight content curve is divided according to soil particle size groups. The particle size-soil weight content curve is plotted based on the results of sieve analysis tests. The x-axis represents the particle size group, which, according to the particle size group classification in the "Engineering Classification Standard for Soil" (GB / T50145-2007), is divided into 10 particle size groups from smallest to largest: <0.005, 0.005–0.075, 0.075–0.250, 0.250–0.500, 0.500–2, 2–5, 5–20, 20–60, 60–200, and >200 mm. These groups are represented using a logarithmic coordinate system. The y-axis represents the cumulative percentage of soil weight content smaller than a certain particle size, such as... Figure 2 As shown. By Figure 2 It can be determined that the soil is a graded continuous soil.

[0078] S3) Transform the soil particle size-soil weight content curve into a particle size-volume content curve, where the vertical axis represents the cumulative volume percentage of soil particles smaller than or equal to the corresponding particle size.

[0079] Specifically, the cumulative soil weight percentage of the curve ordinate is converted into the cumulative volume percentage through the following formula:

[0080]

[0081] In the formula:

[0082] V s represents the cumulative volume percentage of soil particles;

[0083] m s represents the cumulative mass of soil particles;

[0084] G s represents the average relative density of coarse and fine particles;

[0085] ρ w represents the density of water.

[0086] As shown in Figure 3 , it is the particle size-volume content curve converted from the above particle size-soil weight content curve, where the ordinate is represented by p, and 0 < p ≤ 1. In this embodiment, for simplicity of calculation, the average relative density of coarse and fine particles is approximately taken as G s = 2.65, and at this time, the particle size-soil weight content curve and the particle size-volume content curve are completely consistent in shape.

[0087] S4) For soils with continuous gradation, calculate the discrimination particle size d0 of coarse and fine particles. The coarse particles are in a stable skeleton state, and the fine particles are in a state of free packing; and determine the initiation particle size d that causes the soil to fail when seepage failure occurs, and d ≤ d0.

[0088] Specifically, calculate the discrimination particle size d0 through the particle size-soil weight content curve in step S2).

[0089] For non-uniform soils, the soil particles can be divided into two parts: coarse particles I and fine particles II according to particle size. Among them, coarse particles I form the skeleton of the soil, and fine particles II fill the voids between the skeletons. The discrimination particle size between coarse and fine particles is defined as d0. For the discrimination particle size d0, following Appendix G.0.4 of the Code for Geological Investigation of Water Conservancy and Hydropower Projects GB 50487-2008, soils with the particle content (weight) of at least one or more grain groups on the particle size distribution curve (the particle size-soil weight content curve in this invention) less than or equal to 3% are defined as soils with discontinuous gradation, and the average value or the minimum particle size of the maximum and minimum particle sizes of the gentle section formed by the above grain groups on the particle size distribution curve is used as the discrimination particle size d0 of coarse and fine particles.

[0090] For soils with continuous gradation, the discrimination particle size d0 of coarse and fine particles is calculated by the following formula

[0091]

[0092] In the formula,

[0093] d0 represents the particle size that distinguishes between coarse and fine particles.

[0094] d 10 This indicates the particle size that represents 10% or more of the total soil weight by weight.

[0095] d 70 This indicates the particle size that accounts for 70% or more of the total soil weight by weight.

[0096] according to Figure 2 The particle size-soil weight content curve can be used to obtain d5 = 0.3 mm, d 10 =0.6mm, d 20 =1.3mm, d 70 =6.6mm. The calculation formula yields d0 = 1.99mm, which is close to 2.0mm.

[0097] S5) For non-uniformly graded continuous soil, all particle size groups less than or equal to the starting particle size d are considered to start simultaneously. The critical condition is that the seepage force on the particle group is balanced with the corresponding buoyancy weight. The critical hydraulic gradient calculation formula when particle size groups less than or equal to the starting particle size d are simultaneously subjected to seepage force is derived.

[0098] The most critical issue is determining the initiating particle size d that causes soil failure when seepage failure occurs.

[0099] For the case of a single particle initiation, let γ w Let γ be the unit weight of water, J be the seepage gradient acting on the soil, and γ be the total seepage force per unit volume of soil under the action of the seepage gradient. w J. Since permeability is directly proportional to particle surface area, for a single soil particle of diameter d, the permeability force it experiences is the product of the ratio of its surface area to the total surface area of ​​all particles per unit volume and the total permeability force, which is:

[0100]

[0101] Under vertically upward seepage, the critical condition for the initiation of a single soil particle with diameter d is that the seepage force it experiences is in equilibrium with its buoyancy weight.

[0102]

[0103] And it can be deduced

[0104]

[0105] In the formula,

[0106] γ s This indicates the unit weight of soil particles.

[0107] J c This represents the critical hydraulic gradient of a single soil particle with a particle size of d.

[0108] As can be seen from the above formula, using a smaller starting particle size will result in the calculated critical hydraulic gradient value being lower than the experimental value.

[0109] Appendix G.0.6 of GB50487-2008 Code for Geological Investigation of Water Conservancy and Hydropower Projects considers the initiation of piping by a single soil particle. According to Appendix G.0.6 of GB50487-2008 Code for Geological Investigation of Water Conservancy and Hydropower Projects, the critical hydraulic gradient formula (6) for piping is as follows. In this embodiment, the critical hydraulic gradient J for piping in uneven soil of the embankment foundation is calculated. c =0.302.

[0110]

[0111] In the formula,

[0112] n represents the porosity of soil per unit volume (as a decimal).

[0113] G s This represents the average relative density of coarse and fine particles.

[0114] d5 represents the particle size (mm) of particles that constitute 5% or more of the total soil weight by weight.

[0115] d 20 This indicates the particle size (mm) of the soil particles that constitute 20% or more of the total soil weight.

[0116] However, in engineering practice, seepage does not occur from the initiation of a single soil particle, but rather through a group of particles. At lower seepage rates, finer particles initiate seepage first, while coarser particles initiate it as seepage rate increases. Under normal conditions, the coarse particles I, forming the framework, are relatively stable, while the fine particles II are in a state of free accumulation. For non-uniform soils, with fine particle size distributions of II-1, II-2, ..., II-n, the loss pattern of these fine particles is as follows:

[0117] The first step is that at a certain water level, the finest particles, Class II-1 particles, begin to be lost first. If the water level does not rise further at this point, and all Class II-1 particles are lost, no more particles will be lost, and the soil will remain stable.

[0118] The second step involves the rising water level, followed by the loss of the finer particles, specifically the II-2 grade particles, and the process of the first step is repeated; ...

[0119] In step n, when the water level rises to a certain value, all the last stage II-n fine particles are lost. If the water level continues to rise, the finest part of the coarse particles I, stage I-1, will be in a critical state of loss initiation. Once the coarse particles that form the skeleton become unstable, the soil will collapse.

[0120] For safety reasons, the water level at which all the last stage II-n particles (i.e., the particles that distinguish the particle size d0) are lost is defined as the critical water level or the failure water level. From this, the critical hydraulic gradient or the failure hydraulic gradient can be obtained. At this time, d0 is the maximum particle size d when the soil undergoes seepage failure.

[0121] When a particle group initiates simultaneously, the surface area of ​​the initiated particle group with particle size d per unit volume of soil is:

[0122]

[0123] The osmotic force on a particle group is the product of the ratio of the surface area of ​​particles with a diameter less than or equal to d to the total surface area of ​​all particles per unit volume, and the total osmotic force.

[0124]

[0125] When a group of particles starts up simultaneously, under the action of vertical upward seepage, the critical condition is that the seepage force on the particle group is balanced with its buoyancy weight.

[0126] Specifically, when the critical condition is that the permeation force on the particle group is in equilibrium with the corresponding buoyancy, the following formula (2) is obtained.

[0127]

[0128] From the above formula (2), the critical hydraulic gradient calculation formula (3) is derived when a group of particle sizes less than or equal to the starting particle size d is simultaneously subjected to seepage force. Formula (3) is shown below.

[0129]

[0130] In the formula,

[0131] J c This represents the critical hydraulic gradient when a group of particles with a diameter less than or equal to the starting particle size d are simultaneously subjected to osmotic forces.

[0132] n represents the porosity of soil per unit volume.

[0133] γw Indicates the density of water.

[0134] γ s This indicates the unit weight of soil particles.

[0135] dp represents the cumulative volume percentage of the starting particle size d.

[0136] d(p) represents the starting particle size d corresponding to a volume percentage content of p.

[0137] p(d) represents the cumulative volume percentage of the particle size group that is less than or equal to the starting particle size d, G s This indicates the average relative density of coarse and fine particles.

[0138] Specifically, when the starting particle size of the soil per unit volume is d, that is, when all particles start simultaneously, which is when uniform soil undergoes fluid seepage deformation, p(d) = 1, and at this time formula (3) simplifies to:

[0139] J c =(1-n)(G s -1) (5)

[0140] Formula (5) is the classic Terzaghi soil formula, which is adopted by Chinese standards. Generally, the porosity of fine sand is n = 0.4, and the specific gravity of soil particles is G. s When = 2.65, the critical hydraulic gradient J for silty fine sand to undergo seepage deformation is obtained from formula (4). c =0.99, close to 1.0. When the safety factor is 2, the allowable hydraulic gradient for silty fine sand to undergo seepage deformation is 0.5.

[0141] Based on the definition of critical hydraulic gradient of soil, this invention considers the coarsest particle size that may be activated when seepage failure occurs when deriving the formula for critical hydraulic gradient of soil. It regards the finest particle size to the coarsest particle size that may be activated as the entire particle size group for soil seepage failure, thus avoiding the defect of the current semi-theoretical and semi-empirical formula that only considers the activation of a single soil particle, which leads to an underestimation of the critical hydraulic gradient of soil.

[0142] The above step S5) considers the critical hydraulic gradient calculation method when the particle group with starting particle size d starts simultaneously. It assumes that all particles with a particle size less than or equal to d are simultaneously subjected to seepage force. However, in reality, when the soil per unit volume is non-uniform in particle size, as the seepage gradient increases, the particles will be gradually lost from fine to coarse, eventually leading to seepage failure. Therefore, the assumption that all particles with a particle size less than or equal to d are simultaneously subjected to seepage force is not in line with reality. When the starting particle size d starts, all particles smaller than that size have already been lost and no longer bear the seepage force. The critical hydraulic gradient calculated by formula (3) for the simultaneous start of the particle group with the largest particle size d is too high. Formula (3) needs to be adjusted so that the lost particles are no longer considered.

[0143] S6) The formula for calculating the critical hydraulic gradient when particle size groups smaller than or equal to the starting particle size d are simultaneously subjected to seepage force is adjusted. Particle size groups smaller than the starting particle size d are considered to be in a loss state. Coarse particles and particle size groups equal to the starting particle size d are considered to jointly bear the seepage force. When the starting particle size d is infinitely close to the distinguishing particle size d0, the formula for calculating the critical hydraulic gradient when piping occurs in the non-uniform soil is obtained (1). The calculated critical hydraulic gradient value is taken as the closest to the true critical hydraulic gradient value.

[0144] Taking the particle size of the last stage II-n of fine particles in step S5) above as the research object. Since the stages II-1, II-2, ..., II-(n-1) before the last stage II-n of fine particles have all migrated and been lost at this time, the coarse particles I and the last stage II-n of fine particles share the seepage force. Once the seepage force borne by the last stage II-n of fine particles is greater than or equal to the sum of the resistance caused by its own weight and the constraint resistance, the last stage II-n of fine particles will be completely lost, and the coarse particles I will be in the critical state of loss initiation, that is, the soil will be in the critical state of seepage failure. According to step S5), when the particle size of the last stage II-n of fine particles is infinitely close to the distinguishing particle size d0, the hydraulic gradient value obtained at this time is closest to the true critical hydraulic gradient value.

[0145] Formula (1) is shown below.

[0146]

[0147] In the formula,

[0148] J c 'Indicates the critical hydraulic gradient at which piping occurs in heterogeneous soil.'

[0149] n represents the porosity of soil per unit volume.

[0150] G s This represents the average relative density of coarse and fine particles.

[0151] dp represents the cumulative volume percentage of the starting particle size d.

[0152] d(p) represents the starting particle size d corresponding to a volume percentage content of p.

[0153] p(d0) represents the cumulative volume percentage of the particle size group that distinguishes particle size d0.

[0154] Specifically, when the critical condition is that the seepage force borne by the particle group equal to the starting particle size d is equal to the sum of the resistance and constraint caused by its own weight, the following formula (4) is obtained. From formula (4), the critical hydraulic gradient calculation formula (1) for piping in uneven soil is derived.

[0155] The formula (4) is as follows:

[0156]

[0157] In the formula,

[0158] J c 'Indicates the critical hydraulic gradient at which piping occurs in heterogeneous soil.'

[0159] n represents the porosity of soil per unit volume.

[0160] G s This represents the average relative density of coarse and fine particles.

[0161] dp represents the cumulative volume percentage of the starting particle size d.

[0162] d(p) represents the starting particle size d corresponding to a volume percentage content of p.

[0163] p(d0) represents the cumulative volume percentage of the particle size group that distinguishes particle size d0.

[0164] In this embodiment, the critical hydraulic gradient value for piping in the uneven soil of the embankment foundation is calculated using formula (1), where n = 0.4 and p(d0) = 0.27.

[0165]

[0166] When performing a balance analysis of permeability and buoyancy on a particle group, this invention only considers the remaining soil particles involved in the permeation movement, based on the actual engineering conditions, and excludes soil particles that have already migrated and been lost in the early stages, thus avoiding overestimation of the critical hydraulic gradient of the soil.

[0167] Appendix G.0.6 of GB50487-2008 Code for Geological Investigation of Water Conservancy and Hydropower Projects states that the formula for the critical hydraulic gradient of piping considers the initiation of a single soil particle, thus obtaining the critical hydraulic gradient J of piping.c =0.302; The critical hydraulic gradient J for piping in uneven soil is calculated using formula (1) obtained by this invention. c =0.318, which considers the initiation of particle groups. The latter value is greater than the former, indicating that considering only the initiation of a single soil particle will lead to an underestimation of the critical hydraulic gradient of the soil.

[0168] In this embodiment, if calculated according to formula (3) in step S5), J is obtained. c =0.352, which is greater than 0.318, indicating that including soil particles that have already migrated and been lost in the early stages will overestimate the critical hydraulic gradient value for piping in the uneven soil of the embankment foundation.

[0169] This invention provides a critical hydraulic gradient calculation method based on particle size distribution curves, which can more accurately calculate the critical hydraulic gradient value closest to the actual value, and obtain the critical hydraulic gradient of soil that conforms to engineering practice. This provides theoretical and technical support for seepage control design of embankment foundations and has important theoretical and engineering practical significance.

[0170] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for calculating critical hydraulic gradient based on particle size distribution curves, characterized in that, Includes the following steps: S1) Determine all soil particle size groups that may be activated when soil seepage failure occurs. All soil particle size groups include the finest soil particle size to the coarsest soil particle size that may be activated. S2) Plot the soil particle size-soil weight content curve, where the horizontal axis represents the soil particle size and the vertical axis represents the cumulative soil weight percentage of particles with a particle size less than or equal to a certain size. S3) Transform the soil particle size-soil weight content curve into a particle size-volume content curve, where the vertical axis represents the cumulative volume percentage of soil particles that are less than or equal to the corresponding particle size. S4) For continuously graded soil, calculate the distinguishing particle size d0 between coarse and fine particles, where the coarse particles are in a stable skeleton state and the fine particles are in a free-stacking state. And determine the initiating particle size d that causes soil failure when seepage failure occurs, and d≤d0; S5) For non-uniform graded continuous soil, all particle size groups less than or equal to the starting particle size d are considered to be simultaneously subjected to seepage failure. The critical condition is that the seepage force on the particle group is balanced with the corresponding buoyancy weight. The critical hydraulic gradient calculation formula when particle size groups less than or equal to the starting particle size d are simultaneously subjected to seepage force is derived. S6) The critical hydraulic gradient calculation formula for particle size groups that are smaller than or equal to the starting particle size d and are simultaneously subjected to seepage force is adjusted. Particle size groups smaller than the starting particle size d are regarded as loss state, and coarse particles and particle size groups equal to the starting particle size d are considered to jointly bear the seepage force. When the starting particle size d is infinitely close to the distinguishing particle size d0, the critical hydraulic gradient calculation formula (1) for piping occurs in the non-uniform soil is obtained. The calculated critical hydraulic gradient value is taken as the closest to the true critical hydraulic gradient value. Formula (1) is shown below. In the formula, J c ’ This represents the critical hydraulic gradient at which piping occurs in heterogeneous soil. n represents the porosity of soil per unit volume. G s This represents the average relative density of coarse and fine particles. dp represents the cumulative volume percentage of the starting particle size d. d(p) represents the starting particle size d corresponding to a volume percentage content of p. p(d0) represents the cumulative volume percentage of the particle size group that distinguishes particle size d0.

2. The critical hydraulic gradient calculation method based on particle size distribution curve according to claim 1, characterized in that: In S2), the abscissa of the particle size-soil weight content curve is divided according to the soil particle size group.

3. The critical hydraulic gradient calculation method based on particle size distribution curve according to claim 2, characterized in that: In S3), the cumulative soil weight percentage of the ordinate of the curve is converted into the cumulative volume percentage using the following formula. In the formula, V s This indicates the cumulative volume percentage of soil particles. m s Indicates the cumulative mass of soil particles. G s This represents the average relative density of coarse and fine particles. ρ w This indicates the density of water.

4. The critical hydraulic gradient calculation method based on particle size distribution curve according to claim 3, characterized in that: In S4), the particle size d0 is distinguished by calculating the particle size-soil weight content curve in step S2).

5. The critical hydraulic gradient calculation method based on particle size distribution curve according to claim 4, characterized in that: In S4), the distinguishing particle size d0 between coarse and fine particles is calculated using the following formula. In the formula, d0 represents the particle size that distinguishes between coarse and fine particles. d 10 This indicates the particle size that represents 10% or more of the total soil weight by weight. d 70 This indicates the particle size that accounts for 70% of the total soil weight of the cumulative soil weight, and is less than or equal to this particle size.

6. The critical hydraulic gradient calculation method based on particle size distribution curve according to claim 1, characterized in that: In S5), when the critical condition is that the permeation force on the particle group is in equilibrium with the corresponding buoyancy weight, the following formula (2) is obtained. From the above formula (2), the critical hydraulic gradient calculation formula (3) is derived when a group of particle sizes less than or equal to the starting particle size d is simultaneously subjected to seepage force. Formula (3) is shown below. In the formula, J c This represents the critical hydraulic gradient when a group of particles with a diameter less than or equal to the starting particle size d are simultaneously subjected to osmotic forces. n represents the porosity of soil per unit volume. γ w Indicates the density of water. γ s This indicates the unit weight of soil particles. dp represents the cumulative volume percentage of the starting particle size d. d(p) represents the starting particle size d corresponding to a volume percentage content of p. p(d) represents the cumulative volume percentage of the particle size group that is less than or equal to the starting particle size d. G s This indicates the average relative density of coarse and fine particles.

7. The critical hydraulic gradient calculation method based on particle size distribution curve according to claim 6, characterized in that: In S6), when the critical condition is that the seepage force borne by the particle group equal to the starting particle size d is equal to the sum of the resistance and constraint caused by its own weight, the following formula (4) is obtained. From formula (4), the critical hydraulic gradient calculation formula (1) for piping in uneven soil is derived. The formula (4) is as follows: In the formula, J c ’ This represents the critical hydraulic gradient at which piping occurs in heterogeneous soil. n represents the porosity of soil per unit volume. G s This represents the average relative density of coarse and fine particles. dp represents the cumulative volume percentage of the starting particle size d. d(p) represents the starting particle size d corresponding to a volume percentage content of p. p(d0) represents the cumulative volume percentage of the particle size group that distinguishes particle size d0.

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