Calculation Method for Excess Pore Water Pressure of Unsanded Pressurized Vacuum Preloading in Saturated Soft Soil

Abstract

The present invention discloses a method for calculating the excess pore water pressure of saturated soft soil under sand-free pressurized vacuum preloading, belonging to the technical field of foundation treatment, and comprising the following steps: Step S1: Determine the basic calculation parameters; Step S2: Obtain the calculation control equations for the excess pore water pressure in the foundation; Step S3: Obtain the average excess pore water pressure in the foundation. A general calculation expression for the average excess pore water pressure at any depth in the foundation is provided, providing a common quantitative theoretical basis for analyzing problems related to the sand-free pressurized vacuum preloading technology; calculation methods for the excess pore water pressure in the foundation under three typical pressurization modes are provided, which can reflect the influence of different pressurization depth ranges, cover the common pressurization modes in actual engineering, and can directly guide the actual engineering design; the solution principle and calculation process are clear, facilitating calculation using numerical analysis methods, and having good rationality and practical operability.

Description

Technical Field

[0001] The present invention relates to the technical field of foundation treatment, and particularly to a calculation method for excess pore water pressure in saturated soft soil by sandless pressurized vacuum preloading. Background Art

[0002] Deep soft soil layers with characteristics such as high water content, high compressibility, low permeability, and low bearing capacity are widely distributed in various regions of our country. The treatment of soft soil foundations is involved in many engineering constructions. The vacuum preloading method is a technical means for the drainage consolidation treatment of soft soil foundations. During the construction process, it is noise-free, vibration-free, and does not pollute the environment, with significant low-carbon environmental protection characteristics. However, traditional vacuum preloading generally reflects problems such as small pressurizing load, obvious vacuum degree attenuation, long consolidation time, large post-construction settlement, and even the reinforcement effect of vacuum preloading on soft foundations often only appears on the surface layer. The pressurized vacuum preloading technology is an improvement of the traditional vacuum preloading technology in recent years. For areas lacking sand and gravel materials, due to the high cost of laying sand cushions over a large area, the method of no sand cushion is adopted in the pressurized vacuum preloading technology, forming the sandless pressurized vacuum preloading technology.

[0003] For the sandless pressurized vacuum preloading technology, the reasonable calculation and analysis of excess pore water pressure in the foundation is an important issue in related engineering practices. However, due to the relatively late emergence of this technology and the fact that engineering applications have preceded theoretical research, there is currently no specific calculation method for the excess pore water pressure in saturated soft soil by sandless pressurized vacuum preloading. In previous studies on vacuum preloading, when analyzing the excess pore water pressure in the foundation, the characteristics of the well resistance changing simultaneously with time and depth were not fully considered. Moreover, the traditional variable well resistance model assumes that the final permeability coefficient of the drainage board is zero, significantly underestimating its drainage capacity, while the constant well resistance model will overestimate the degree of consolidation of the foundation. Therefore, there are still many defects in the traditional related calculation and analysis methods. In view of this, the present invention aims at the problems existing in previous studies, for the new sandless pressurized vacuum preloading technology, based on its specific layout characteristics and the spatio-temporal variation characteristics of the well resistance, as well as the operability of relevant parameter values in practice, adopts a new calculation and analysis model centered on the pressurizing pipe, considering two typical characteristics in the spatio-temporal variation characteristics of the well resistance of the drainage board, and combines the theoretical solution of drainage consolidation in the radial seepage mode of the foundation soil considering the sandless characteristics to provide a calculation method for the excess pore water pressure in saturated soft soil by sandless pressurized vacuum preloading. Summary of the Invention

[0004] The present invention takes into account two characteristics: the general non-linearity of the attenuation of the well resistance of the drainage board with time and the non-zero value of the final permeability coefficient of the drainage board, and provides a calculation method for the excess pore water pressure of saturated soft soil under the sandless pressurized vacuum preloading, which is convenient for numerical analysis operations and has good rationality. It can conveniently realize the design analysis and calculation of the excess pore water pressure problem of saturated soft soil under the sandless pressurized vacuum preloading, and can simply and efficiently and reasonably carry out the foundation treatment design related to the sandless pressurized vacuum preloading.

[0005] The present invention is realized through the following technical solutions:

[0006] A calculation method for the excess pore water pressure of saturated soft soil under the sandless pressurized vacuum preloading includes the following steps: Step S1: Determine the basic calculation parameters, including geometric parameters, soil properties of the foundation, smearing parameters, well resistance parameters, and preloading load; Step S2: Obtain the calculation control equations for the excess pore water pressure in the foundation. Based on the non-homogeneous partial differential control equation of the excess pore water pressure in the foundation, substitute the basic calculation parameters into the calculation expression representing the relationship between the excess pore water pressure in the foundation soil and the pore water pressure in the drainage board to obtain the calculation control equations for the excess pore water pressure in the foundation; Step S3: Obtain the average excess pore water pressure in the foundation. Combine the boundary conditions, initial conditions, and pressurization mode to solve the calculation control equations for the excess pore water pressure, obtain the average excess pore water pressure in the foundation, and use the average excess pore water pressure at any depth in the foundation to represent the average excess pore water pressure in the foundation within the influence range of a single pressurization pipe.

[0007] In order to solve the above technical problems and achieve the corresponding technical effects, the present invention provides a general calculation expression for the average excess pore water pressure at any depth in the foundation, providing a common quantitative theoretical basis for analyzing problems of the sandless pressurized vacuum preloading technology; provides calculation methods for the excess pore water pressure in the foundation under 3 typical pressurization modes, which can reflect the influence of different pressurization depth ranges, cover the common pressurization modes in actual engineering, and can directly guide the actual engineering design; the solution principle and calculation process are clear, which is convenient for calculation using numerical analysis methods, and has good rationality and practical operability.

[0008] Further technical solutions:

[0009] In step S1, the geometric parameters include the thickness H of the soft soil layer, in m, the equivalent cylinder influence radius R e , in m, the radius r of the pressurization pipe p , in m, the length L of the pressurization pipe, in m, the cross-sectional area A of the drainage board d , in mm 2 , the equivalent number n of drainage boards in the unit d ;

[0010] The soil property parameters of the foundation include the volumetric deformation modulus E v , with the unit of MPa, Poisson's ratio v, and radial permeability coefficient k h , with the unit of m / s;

[0011] The smear parameters include the smear zone boundary radius r s , with the unit of m, and the permeability coefficient ratio x of the slightly disturbed zone to the smear zone;

[0012] The well resistance parameters include the initial permeability coefficient k of the drain d0 , with the unit of m / s, depth attenuation coefficient a, time attenuation coefficient b, with the unit of s -1 , and the final drainage stability index β;

[0013] The preloading load includes the vacuum load p v , with the unit of kPa, and the magnitude of the boosting load p r , with the unit of kPa;

[0014] Among them, r p ≤ r < r s The area is the undisturbed zone, and r s ≤ r ≤ R e The area is the equivalent annular smear zone.

[0015] Furthermore: In step S2, the calculation control equations for the excess pore water pressure in the foundation are as follows:

[0016]

[0017] Among them, t is the time, z is the depth from the ground surface, r s is the smear zone boundary radius, r p is the boosting pipe radius, R e is the influence radius of the equivalent cylinder, H is the thickness of the soft soil layer, L is the length of the boosting pipe, and L ≤ H. u s (r, z, t) is the excess pore water pressure of the soil mass, γ w is the unit weight of water, ε v (z, t) is the volumetric strain of the soil mass, u d (z, t) is the pore water pressure in the drain;

[0018] Considering the effectiveness of the boosting effect, let p r (z, t) = p ru h r (z)f r (t), where p ru is the full boosting value, h r (z) is the boosting coefficient related to the depth, f r(t) is the variation coefficient of the surcharge load with time, p r (z, t) is the radial surcharge load.

[0019] Furthermore: In formula (1), h d (z) is the depth attenuation exponent of the permeability coefficient of the drainage board, f d (t) is the time attenuation exponent of the permeability coefficient of the drainage board, and the expression is:

[0020]

[0021] f d (t) = β + (1 - β)e -bt (3)

[0022] Wherein, a is the depth attenuation coefficient, b is the time attenuation coefficient, a is a positive dimensionless quantity not greater than 1, b > 0, β is the ultimate drainage stability exponent, and β is the ratio of the stable value of the permeability coefficient of the drainage board after attenuation to the initial value; in the case of normal well resistance, a = 0, β = 1, and in the case where the drainage board is completely blocked and has no drainage capacity, β = 0.

[0023] Furthermore: In formula (1), λ, ρ 2 are intermediate parameters, and the expression is:

[0024]

[0025] k d0 is the permeability coefficient at the initial moment, E v is the volume deformation modulus of the soil body, ν is the Poisson's ratio; A d is the cross-sectional area of a single drainage board;

[0026] The intermediate variable F s has the following expression:

[0027]

[0028] Wherein, k r (ζ) is the horizontal permeability coefficient of the soil body varying radially. In the smeared zone, the value of k r (ζ) is k s , and in the undisturbed zone, the value of k r (ζ) is k h ; ξ is the integral variable of the radial distance.

[0029] Furthermore: Combining the continuity condition and the boundary condition of the radial seepage, the relationship between the excess pore water pressure u s (r, z, t) of the soil body and the pore water pressure u d (z, t) in the drainage board is:

[0030]

[0031] Among them, γ w is the unit weight of water; ε v (z, t) is the volumetric strain of the soil mass. The inhomogeneous partial differential control equation of the excess pore water pressure in the foundation is expressed as:

[0032]

[0033] By combining formulas (2) to (11), the calculation control equation set of the excess pore water pressure in the foundation is obtained.

[0034] Furthermore, in step S3, the expression of the average excess pore water pressure at any depth in the foundation within the effective influence range of a single pressure-increasing pipe is:

[0035]

[0036] Substitute formula (10) into formula (12), and the average excess pore water pressure in the foundation within the effective influence range of a single pressure-increasing pipe can be characterized by the average excess pore water pressure at any depth in the foundation.

[0037] Furthermore, the boundary conditions and initial conditions that formula (1) needs to satisfy are:

[0038] z = 0, u d (0, t) = -p v (13)

[0039]

[0040] By combining formula (1) and formulas (13) to (15), and using the method of eigenfunction expansion to solve, the general expression of the average excess pore water pressure at any depth in the foundation is obtained as:

[0041]

[0042] Among them, ω is the time integral variable; p v is the vacuum load; f r ′ is the first derivative of f r ; m is the number of calculations of different eigenvalues; η m is the calculated value corresponding to each eigenvalue;

[0043] Using MATLAB to solve the non-zero solution of the nonlinear equation (17), m different η m values are obtained. The formula of the nonlinear equation (17) is:

[0044]

[0045] Among them, J0 is the Bessel function of the first kind of order 0, J1 is the Bessel function of the first kind of order 1, Y0 is the Bessel function of the second kind of order 0, and Y1 is the Bessel function of the second kind of order 1;

[0046] In formula (16), the eigenfunction system composed of the Bessel function systems of the first kind of order 0 and the second kind of order 0 is:

[0047]

[0048] In formula (16), A mv is the expansion coefficient of the vacuum load p v on the eigenfunction system, and A mr is the expansion coefficient of the surcharge load p r on the eigenfunction system. The formula is:

[0049]

[0050] In formulas (19) and (20), the eigenfunction system composed of the Bessel function systems of the first kind of order 1 and the second kind of order 1 is:

[0051]

[0052] In formula (16), C m , D m , and E m are respectively the calculation intermediate variables corresponding to each eigenvalue. The formula is:

[0053]

[0054] E m = 1 - D m (24).

[0055] Furthermore: In step S3, the surcharge modes include: surcharge mode I, surcharge mode II, and surcharge mode III. The surcharge mode I is constant surcharge when the vacuum preloading starts. The surcharge mode II is constant surcharge after a period of time after the vacuum preloading starts. The surcharge mode III is intermittent surcharge after a period of time after the vacuum preloading starts.

[0056] Furthermore: Under the surcharge mode I, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0057]

[0058] Under the surcharge mode II, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0059]

[0060] Under the pressurization mode III, the calculation expression of the average excess pore water pressure at any depth in the foundation is as follows:

[0061]

[0062] In formulas (25) to (27), t0 is the time interval from the start of vacuum preloading to before pressurization, t 1i is the instantaneous loading moment at the i-th intermittent pressurization cycle; are all the instantaneous pressurization loading moments before the calculation time point t; t 2j is the instantaneous unloading moment at the j-th intermittent pressurization cycle; t 2j : t 11 、t 12 、…、t 2jm are all the instantaneous pressurization unloading moments before the calculation time point t.

[0063] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0064] The calculation method of the excess pore water pressure of the non-sand pressurized vacuum preloading saturated soft soil of the present invention fully considers the generality of the attenuation with time and the non-zero characteristic of the final permeability coefficient of the drainage board in the actual time-space variation characteristics of the well resistance of the drainage board, and clearly gives the calculation methods of the excess pore water pressure in the foundation under three typical pressurization modes, which is convenient for numerical analysis operations and has good rationality. It can conveniently realize the design analysis and calculation of the excess pore water pressure problem of the non-sand pressurized vacuum preloading saturated soft soil, and can simply, efficiently and reasonably carry out the foundation treatment design related to the non-sand pressurized vacuum preloading, providing an effective method and scientific basis for the design calculation of such projects, and having important technical significance and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts. In the drawings:

[0066] Figure 1 is a schematic diagram of the general composition of a non-sand pressurized vacuum preloading saturated soft soil foundation;

[0067] Figure 2 is a schematic diagram of the basic analysis model of radial seepage in a non-sand pressurized vacuum preloading saturated soft soil foundation;

[0068] Figure 3 It is a schematic diagram of the pulse in supercharging mode I;

[0069] Figure 4 It is a schematic diagram of the pulse in supercharging mode II

[0070] Figure 5 It is a schematic diagram of the pulse in supercharging mode III.

[0071] Figure 6 It is the calculation result of the variation of the average excess pore water pressure with time at a depth of 0.5 m in the foundation under supercharging mode I in Example 2;

[0072] Figure 7 It is the calculation result of the variation of the average excess pore water pressure with time at a depth of 2.0 m in the foundation under supercharging mode I in Example 2;

[0073] Figure 8 It is the calculation result of the variation of the average excess pore water pressure with time at a depth of 7.0 m in the foundation under supercharging mode I in Example 2;

[0074] Figure 9 It is the calculation result of the variation of the average excess pore water pressure along the depth under supercharging mode I in Example 2 after 10 days of pressure application;

[0075] Figure 10 It is the calculation result of the variation of the average excess pore water pressure along the depth under supercharging mode I in Example 2 after 300 days of pressure application;

[0076] Figure 11 It is the calculation result of the variation of the average excess pore water pressure with time under supercharging mode II in Example 2;

[0077] Figure 12 It is the calculation result of the variation of the average excess pore water pressure along the depth under supercharging mode II in Example 2

[0078] Figure 13 It is the result of the variation of the average excess pore water pressure with time at a depth of 0.5 m in the foundation under supercharging mode III in Example 2 after 50 days of pressure increase;

[0079] Figure 14 It is the result of the variation of the average excess pore water pressure with time at a depth of 0.5 m in the foundation under supercharging mode III in Example 2 after 100 days of pressure increase;

[0080] Figure 15 It is the result of the variation of the average excess pore water pressure with time at a depth of 3.5 m in the foundation under supercharging mode III in Example 2 after 50 days of pressure increase;

[0081] Figure 16 It is the result of the variation of the average excess pore water pressure with time at a depth of 3.5 m in the foundation under supercharging mode III in Example 2 after 100 days of pressure increase;

[0082] Figure 17 The results of the variation of the average excess pore water pressure with time at a foundation depth of 7 m under a pressure increase of 50 d in Example 2 in pressurization mode III;

[0083] Figure 18 The results of the variation of the average excess pore water pressure with time at a foundation depth of 7 m under a pressure increase of 100 d in Example 2 in pressurization mode III;

[0084] Figure 19 The comparison results between the calculation results of the present invention and the calculation results of the FLAC3D vertical simulation method in Example 2. Detailed implementation manners

[0085] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the embodiments and the drawings. The illustrative embodiments and descriptions thereof of the present invention are only used to explain the present invention and do not limit the present invention.

[0086] In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that the present invention does not have to adopt these specific details. In other embodiments, well-known structures, circuits, materials or methods are not specifically described in order to avoid obscuring the present invention.

[0087] Throughout the specification, the reference to "an embodiment", "embodiment", "an example" or "example" means that the specific features, structures or characteristics described in connection with the embodiment or example are included in at least one embodiment of the present invention. Therefore, the phrases "an embodiment", "embodiment", "an example" or "example" that appear throughout the specification do not necessarily all refer to the same embodiment or example. In addition, the specific features, structures or characteristics can be combined in any appropriate combination and / or sub-combination in one or more embodiments or examples. In addition, those of ordinary skill in the art should understand that the drawings provided herein are for illustrative purposes only and are not necessarily drawn to scale. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0088] In the description of the present invention, the orientation or positional relationship indicated by the terms "front", "rear", "left", "right", "upper", "lower", "vertical", "horizontal", "high", "low", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be construed as limiting the protection scope of the present invention.

[0089] Example 1:

[0090] The calculation method of the excess pore water pressure of saturated soft soil by the sandless pressurized vacuum preloading of the present invention includes the following steps: Step S1: Determine the basic calculation parameters, including geometric parameters, soil properties of the foundation, smearing parameters, well resistance parameters, and preloading load; Step S2: Obtain the calculation control equations of the excess pore water pressure in the foundation. Based on the non-homogeneous partial differential control equation of the excess pore water pressure in the foundation, substitute the basic calculation parameters into the calculation expression representing the relationship between the excess pore water pressure in the foundation soil and the pore water pressure in the drainage board to obtain the calculation control equations of the excess pore water pressure in the foundation; Step S3: Obtain the average excess pore water pressure in the foundation. Combine the boundary conditions, initial conditions, and pressurization mode to solve the calculation control equations of the excess pore water pressure, obtain the average excess pore water pressure in the foundation, and use the average excess pore water pressure at any depth in the foundation to represent the average excess pore water pressure in the foundation within the influence range of a single pressurization pipe.

[0091] According to the Figures 1 - 5 shown actual object, determine the basic calculation parameters such as geometric parameters, soil properties of the foundation, smearing parameters, well resistance parameters, and preloading load from other geological exploration data and test results and combined with engineering experience. Specifically, the geometric parameters include the thickness H of the soft soil layer, in m, the equivalent cylinder influence radius R e , in m, the pressurization pipe radius r p , in m, the pressurization pipe length L, in m, the cross-sectional area A of the drainage board d , in mm 2 , the equivalent number n of drainage boards in the unit d ; the soil properties of the foundation include the volume deformation modulus E v , in MPa, the Poisson's ratio v, the radial permeability coefficient k h , in m / s; the smearing parameters include the boundary radius r of the smeared area s , in m, the permeability coefficient ratio x of the slightly disturbed area to the smeared area; the well resistance parameters include the initial permeability coefficient k of the drainage board d0 , in m / s, the depth attenuation coefficient a, the time attenuation coefficient b, in s -1 , the drainage final stability index β; the preloading load includes the vacuum load p v , in kPa, the magnitude p of the pressurization load r , in kPa; where, in the area of r p ≤r<r s is the undisturbed area, and in the area of r s ≤r≤R e is the equivalent annular smeared area.

[0092] In step S2, the calculation control equations for the excess pore water pressure in the foundation are as follows:

[0093]

[0094] where t is time, z is the depth from the ground surface, r s is the radius of the smeared zone boundary, r p is the radius of the pressure-increasing pipe, R e is the influence radius of the equivalent cylinder, H is the thickness of the soft soil layer, L is the length of the pressure-increasing pipe, and L ≤ H. u s (r, z, t) is the excess pore water pressure of the soil mass, γ w is the unit weight of water, ε v (z, t) is the volumetric strain of the soil mass, u d (z, t) is the pore water pressure in the drain board;

[0095] Considering the effectiveness of the pressure-increasing effect, let p r (z, t) = p ru h r (z)f r (t), where p ru is the full-load value of the pressure increase, h r (z) is the pressure-increasing coefficient related to the depth, f r (t) is the variation coefficient of the pressure-increasing load with time, and p r (z, t) is the radial pressure-increasing load.

[0096] The specific derivation process of the calculation control equations for the excess pore water pressure in the foundation is as follows:

[0097] In formula (1), h d (z) is the depth attenuation exponent of the permeability coefficient of the drain board, and f d (t) is the time attenuation exponent of the permeability coefficient of the drain board, and the expression is:

[0098]

[0099] f d (t) = β + (1 - β)e -bt (3)

[0100] where a is the depth attenuation coefficient, b is the time attenuation coefficient, a is a positive dimensionless quantity not greater than 1, b > 0, and β is the final drainage stability index, which is the ratio of the stable value of the permeability coefficient of the drain board after attenuation to the initial value; in the case of normal well resistance, a = 0 and β = 1, and in the case where the drain board is completely blocked and has no drainage capacity, β = 0.

[0101] In formula (1), λ and ρ 2 are intermediate parameters, and the expression is:

[0102]

[0103] k d0 is the permeability coefficient at the initial moment, E v is the volume deformation modulus of the soil, ν is the Poisson's ratio; A d is the cross-sectional area of a single drain board;

[0104] Intermediate variable F s The expression is:

[0105]

[0106] Among them, k r (ζ) is the radially varying horizontal permeability coefficient of the soil. r (ζ) value is k s , in the undisturbed area k r (ζ) value is k h ; ξ is the integral variable of radial distance.

[0107] Combining the continuity condition and boundary condition of radial seepage, the excess pore water pressure u of the soil can be obtained: s (r, z, t) and the pore water pressure u in the drainage board d The relationship between (z, t) is:

[0108]

[0109] Among them, γ w is the density of water; v (z,t) is the volume strain of the soil.

[0110] based on Figure 1 , Figure 2 The actual object model can be used to derive the nonhomogeneous partial differential governing equation of excess pore water pressure in the foundation, which is expressed as follows:

[0111]

[0112] Formula (2) to Formula (11) are combined to obtain the control equation group for calculating the excess pore water pressure in the foundation.

[0113] The specific derivation method of the calculation expression of the average excess pore water pressure at any depth in the foundation is as follows:

[0114] In step S3, the expression of the average excess pore water pressure at any depth in the foundation within the effective influence range of a single booster pipe is:

[0115]

[0116] Substituting Equation (10) into Equation (12), the average excess pore water pressure within the effective influence range of a single pressure-increasing pipe can be characterized by the average excess pore water pressure at any depth in the foundation.

[0117] The boundary conditions and initial conditions that Equation (1) needs to satisfy are:

[0118] z = 0, u d (0, t) = -p v (13)

[0119]

[0120] Combining Equation (1) and Equations (13) - (15), and solving using the method of eigenfunction expansion, the general expression for the average excess pore water pressure at any depth in the foundation is obtained as:

[0121]

[0122] where ω is the time integration variable; p v is the vacuum load; f r ′ is the first derivative of f r ; m is the number of calculations for different eigenvalues; η m is the calculated value corresponding to each eigenvalue;

[0123] Using the non-zero solutions of the MATLAB non-linear equation (17), m different η m values are obtained. The formula for the non-linear equation (17) is:

[0124]

[0125] where J0 is the Bessel function of the first kind of order 0, J1 is the Bessel function of the first kind of order 1, Y0 is the Bessel function of the second kind of order 0, and Y1 is the Bessel function of the second kind of order 1;

[0126] In Equation (16), the eigenfunction system composed of the Bessel function system of the first kind of order 0 and the Bessel function system of the second kind of order 0 is:

[0127]

[0128] In Equation (16), A mv is the expansion coefficient of the vacuum load p v on the eigenfunction system, and A mr is the expansion coefficient of the pressurized load p r on the eigenfunction system. The formula is:

[0129]

[0130] In formulas (19) and (20), the eigenfunction system composed of the first-kind and second-kind Bessel function systems of the first order is as follows:

[0131]

[0132] In formula (16), C m , D m , and E m are respectively the calculation intermediate variables corresponding to each eigenvalue, and the formulas are as follows:

[0133]

[0134] E m = 1 - D m (24).

[0135] The pressurization modes include: pressurization mode I, pressurization mode II, and pressurization mode III. Pressurization mode I is constant pressurization when vacuum preloading starts. Pressurization mode II is constant pressurization after a period of time after vacuum preloading starts. Pressurization mode III is intermittent pressurization after a period of time after vacuum preloading starts. As Figures 3 - 5 shown, from formula (16), the calculation expression of the average excess pore water pressure at any depth in the foundation within the effective influence range of a single pressurization pipe can be further obtained. Specifically,

[0136] Under pressurization mode I, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0137]

[0138] Under pressurization mode II, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0139]

[0140] Under pressurization mode III, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0141]

[0142] In formulas (25) to (27), t0 is the time interval from the start of vacuum preloading to before pressurization, and t 1i is the instantaneous loading moment at the i-th intermittent pressurization cycle; is all the instantaneous pressurization loading moments before the calculation time point t; t 2j is the instantaneous unloading moment at the j-th intermittent pressurization cycle; t 2j : t 11 , t12 ,…,t 2jm are all the instantaneous unloading moments of supercharging before the calculation time point t.

[0143] Embodiment 2:

[0144] A foundation is mainly composed of fluid plastic to soft plastic saturated clay, soft to plastic saturated silty clay, and strongly weathered sandy mudstone from top to bottom. The thickness of the saturated soft clay layer (including the first two soil layers) is 7m. The specific steps of processing according to the method in Example 1 are as follows:

[0145] For this calculation and analysis object, based on other geological survey data and test results combined with engineering experience, the relevant basic calculation parameters are determined as follows: soft soil layer thickness H = 7m, equivalent cylinder influence radius R e =0.9m, boost pipe radius r p =0.0125m, booster pipe length L≤H, drainage board cross-sectional area A d =400mm 2 、Equivalent number of drainage panels in the unit n d =2, volume deformation modulus E v =1.318MPa, Poisson's ratio v=0.45, radial permeability coefficient k h =5.30×10 -7 m / s, smear area boundary radius r s = 0.89m, the permeability ratio of the micro-disturbance area to the smearing area is x = 0.2, and the initial permeability coefficient of the drainage board is k d0 =1.00×10 -5 m / s, depth attenuation coefficient a = 0.5, time attenuation coefficient b = 3.60 × 10 -7 s -1 , drainage final stability index β = 0.5, vacuum load p v =80kPa, boost load size p r =20kPa;

[0146] Based on the non-homogeneous partial differential control equation of excess pore water pressure in the foundation shown in formula (11), the above basic calculation parameters are substituted into the calculation expression of the relationship between the excess pore water pressure in the soil and the pore water pressure in the drainage plate shown in formula (10), and the calculation control equation group of excess pore water pressure in the foundation determined by formula (2) to formula (11) can be specifically obtained, that is, formula (1).

[0147] According to the average excess pore water pressure in the foundation soil defined by formula (12), and the calculation expressions (25), (26), and (27) of the average excess pore water pressure derived from the boundary conditions, initial conditions, and different pressure increase modes, by substituting the relevant basic calculation parameters into the calculation expressions, the average excess pore water pressure at any depth in the foundation soil under pressure increase modes I, II, and III can be obtained. Among them, for pressure increase mode III, it specifically includes three pressure increase methods: Method 1: Vacuum preloading for 50 days, starting pressure increase and cycling once; Method 2: Vacuum preloading for 80 days, starting pressure increase and cycling once; Method 3: Vacuum preloading for 50 days, starting pressure increase and cycling 5 times.

[0148] The calculation results of the variation of the average excess pore water pressure at a typical depth in the foundation soil under pressure increase mode I with time are as Figures 6 - 8 shown. It can be seen that with the extension of time, the excess pore pressure decreases non-linearly. Compared with the case without pressure increase, the pore water pressure in the foundation soil under pressure increase is significantly increased, which is beneficial to accelerating the consolidation of the foundation soil. The calculated results are in line with the general actual law and are reasonable.

[0149] The calculation results of the variation of the average excess pore water pressure along the depth in the foundation soil at a typical moment under pressure increase mode I are as Figure 9 、 Figure 10 shown. It can be seen that with the extension of time, the excess pore pressure in the foundation soil shows a non-linear increasing distribution characteristic along the depth.

[0150] The calculation results of the variation of the excess pore water pressure under pressure increase mode II are as Figure 11 、 Figure 12 shown. It can be seen that in addition to showing the non-linear increasing distribution characteristic of the excess pore pressure in the foundation soil along the depth, it also reflects the variation characteristic of the excess pore water pressure that changes synchronously with the pressure increase load.

[0151] Figures 13 - 18 respectively show the calculation results of the variation of the average excess pore water pressure with time at depths of 0.5 m, 3.5 m, and 7 m in the foundation soil under pressure increase mode III when the total pressure increase duration is 50 days and 100 days. It can be seen that the greater the total pressure increase duration, the higher the dissipation degree of the excess pore pressure in the foundation soil; under the same total pressure increase duration and pressure increase load conditions, the later the pressure increase ends, the relatively smaller the excess pore pressure in the foundation soil in the short time after the pressure increase ends, and with the further extension of time, there is basically no difference in the later stage.

[0152] To further illustrate the rationality of the method of the present invention, taking pressure increase mode I - constant pressure increase when vacuum preloading starts as a typical example, for the embodiment, taking L = 7 m and t = 300 d as typical, the calculation results of the method of the present invention are compared with the calculation results of the FLAC3D numerical simulation method, as shown in Figure 19It can be seen that the distribution pattern of the excess pore water pressure along the depth in the foundation obtained by the method of the present invention is basically consistent with the result obtained by numerical simulation using FLAC3D, and the maximum deviation between the two in terms of quantity is 4.98%. This shows that the method of the present invention has good rationality.

[0153] The specific embodiments described above have further elaborated on the purpose, technical solution and beneficial effects of the present invention. It should be understood that the above description is only the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A calculation method for the excess pore water pressure of saturated soft soil by sand-free pressurized vacuum preloading, characterized in that, The steps include: Step S1: Determine basic calculation parameters, including geometric parameters, soil parameters of foundation, smear parameters, well resistance parameters and preload; Step S2: obtaining a group of control equations for calculating excess pore water pressure in the foundation, and based on the nonhomogeneous partial differential control equations for excess pore water pressure in the foundation, substituting basic calculation parameters into a calculation expression representing the relationship between excess pore water pressure in the foundation soil and pore water pressure in the drainage plate, obtaining a group of control equations for calculating excess pore water pressure in the foundation; Step S3: obtaining the average excess pore water pressure in the foundation, solving the calculation control equations of the excess pore water pressure in combination with the boundary conditions, initial conditions and the boosting mode, obtaining the average excess pore water pressure in the foundation, and using the average excess pore water pressure at any depth in the foundation to characterize the average excess pore water pressure in the foundation within the influence range of a single boosting pipe; In step S1, the geometric parameters include the thickness H of the soft soil layer, in m, the equivalent cylindrical influence radius R e , in m, the radius r of the pressure-increasing pipe p , in m, the length L of the pressure-increasing pipe, in m, the cross-sectional area A of the drainage board d , in mm 2 , the equivalent number n of drainage boards within the unit d ; The soil property parameters of the foundation include the volumetric deformation modulus E v , with the unit of MPa, Poisson's ratio v, and radial permeability coefficient k h , with the unit of m / s; The smearing parameters include the boundary radius r of the smearing area s , with the unit of m, and the permeability ratio x of the micro-disturbance area to the smearing area; The well resistance parameters include the initial permeability coefficient k of the drain board d0 , with the unit of m / s, the depth attenuation coefficient a, and the time attenuation coefficient b, with the unit of s -1 , and the final drainage stability index β; The preloading load includes a vacuum load p v , with the unit of kPa, and a boosting load magnitude p r , with the unit of kPa; where r p ≤ r < r s the region is an undisturbed area, r s ≤ r ≤ R e the region is an equivalent annular smear area; In step S2, the control equations for calculating the excess pore water pressure in the foundation are: where t is time, z is the depth from the ground surface, r s is the boundary radius of the smeared zone, r p is the radius of the pressure-increasing pipe, R e is the influence radius of the equivalent cylinder, H is the thickness of the soft soil layer, L is the length of the pressure-increasing pipe, and L ≤ H, u s (r, z, t) is the excess pore water pressure of the soil mass, γ w is the unit weight of water, ε v (z, t) is the volumetric strain of the soil mass, u d (z, t) is the pore water pressure in the drain board, and ξ is the integration variable of the radial distance; Considering the effectiveness of the pressurization effect, let p r (z,t) = p ru h r (z)f r (t), where p ru is the full-load value of the pressurization, h r (z) is the pressurization coefficient related to the depth, f r (t) is the variation coefficient of the pressurization load with time, and p r (z,t) is the radial pressurization load; In Equation (1), h d (z) is the depth attenuation index of the permeability coefficient of the drainage board, and f d (t) is the time attenuation index of the permeability coefficient of the drainage board, and the expression is: f d f(t) = β+(1-β)e -bt (3) Among them, a is the depth attenuation coefficient, b is the time attenuation coefficient, a is a positive dimensionless quantity not greater than 1, b>0, β is the final drainage stability index, β is the ratio of the stable value of the drainage board permeability coefficient after attenuation to the initial value; under normal well resistance, a=0, β=1, and under the condition that the drainage board is completely blocked and has no drainage capacity, β=0; In formula (1), λ and ρ 2 are intermediate parameters, and the expressions are as follows: k d0 is the permeability coefficient at the initial time, E v is the bulk modulus of soil deformation, ν is the Poisson's ratio; A d is the cross-sectional area of a single drainage board; Intermediate variable F s The expression is: where k r (ζ) is the horizontal permeability coefficient of the soil mass varying radially. In the smeared zone, the value of k r (ζ) is k s , and in the undisturbed zone, the value of k r (ζ) is k h ; ξ is the integral variable of the radial distance.

2. The calculation method of the excess pore water pressure of saturated soft soil by sand-free pressurized vacuum preloading according to claim 1, characterized in that, Combining the continuity condition and the boundary condition of radial seepage, the excess pore water pressure u of the soil mass can be obtained s (r, z, t) and the pore water pressure u in the drainage board d (z, t) The relationship between them is as follows: Among them, γ w is the unit weight of water; ε v (z, t) is the volumetric strain of the soil mass. The non-homogeneous partial differential control equation of the excess pore water pressure in the foundation is expressed as: Formula (2) to Formula (11) are combined to obtain the control equation group for calculating the excess pore water pressure in the foundation.

3. The calculation method of the excess pore water pressure of saturated soft soil with sand-free pressurized vacuum preloading according to claim 2, wherein, In step S3, the expression of the average excess pore water pressure at any depth in the foundation within the effective influence range of a single booster pipe is: Substituting formula (10) into formula (12), the average excess pore water pressure at any depth in the foundation can be used to characterize the average excess pore water pressure in the foundation within the effective influence range of a single booster pipe.

4. The calculation method of excess pore water pressure of saturated soft soil by sand-free pressurized vacuum preloading according to claim 3, characterized in that The boundary conditions and initial conditions that formula (1) needs to satisfy are: z = 0, u d (0, t) = -p v (13) By combining formula (1) and formula (13) to formula (15), and solving them using the eigenfunction expansion method, we can obtain the general expression of the average excess pore water pressure at any depth in the foundation: where ω is the time integration variable; p v is the vacuum load; f r ' is the first derivative of f r ; m is the number of calculations of different eigenvalues; η m is the calculated value corresponding to each eigenvalue; Using MATLAB to solve the non-zero solutions of the non-linear equation (17), m different η m values are obtained. The formula for the non-linear equation (17) is: Where J0 is the first kind 0th order Bessel function, J1 is the first kind 1st order Bessel function, Y0 is the second kind 0th order Bessel function, Y1 is the second kind 1st order Bessel function; In formula (16), the eigenfunction system composed of the first-kind Bessel functions of order zero and the second-kind Bessel functions of order zero is as follows: In formula (16), A mv is the expansion coefficient of the vacuum load p v on the eigenfunction system, and A mr is the expansion coefficient of the boost load p r on the eigenfunction system. The formula is as follows: In formulas (19) and (20), the eigenfunction system composed of the first-kind Bessel functions of the first order and the second-kind Bessel functions of the first order is as follows: In formula (16), C m , D m , E m are respectively the calculation intermediate variables corresponding to each eigenvalue, and the formula is: E m = 1 - D m (24).

5. The calculation method of the excess pore water pressure of saturated soft soil by sand-free pressurized vacuum preloading according to claim 4, characterized in that, In step S3, the boost modes include: boost mode I, boost mode II and boost mode III, wherein boost mode I is constant boost when vacuum pre-pressurization is started, boost mode II is constant boost after a period of time after vacuum pre-pressurization is started, and boost mode III is intermittent boost after a period of time after vacuum pre-pressurization is started.

6. The method for calculating the excess pore water pressure of saturated soft soil by sand-free pressurized vacuum preloading according to claim 5, characterized in that, Under the pressure-boosting mode I, the calculation expression of the average excess pore water pressure at any depth in the foundation is: Under the boosting mode II, the calculation expression of the average excess pore water pressure at any depth in the foundation is: Under the pressure-boosting mode III, the calculation expression of the average excess pore water pressure at any depth in the foundation is: In Formulas (25) to (27), t0 is the time interval from the start of vacuum preloading to before pressurization, t 1i is the instantaneous loading moment at the i-th intermittent pressurization cycle; are all the instantaneous loading moments of pressurization before the calculation time point t; t 2j is the instantaneous unloading moment at the j-th intermittent pressurization cycle; t 2j : t 11 、t 12 、…、t 2jm are all the instantaneous unloading moments of pressurization before the calculation time point t.

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