Method for calculating ultra-static pore water pressure of sand-free supercharged vacuum preloading saturated soft soil

Abstract

The invention discloses a method for calculating ultra-static pore water pressure of sand-free supercharged vacuum preloading saturated soft soil, which belongs to the technical field of foundation treatment and comprises the following steps of: S1, determining basic calculation parameters; s2, obtaining a calculation control equation set of the hyperstatic pore water pressure in the foundation; and S3, the average hyperstatic pore water pressure in the foundation is obtained. A general calculation expression of the average hyperstatic pore water pressure at any depth in the foundation is provided, and a general quantitative theoretical basis is provided for analyzing the problems of a sand-free supercharged vacuum preloading technology; the method for calculating the hyperstatic pore water pressure in the foundation under three typical pressurization modes is provided, influences of different pressurization depth ranges can be reflected, common pressurization modes in actual engineering are covered, and actual engineering design can be directly guided; and the solution principle and the calculation process are clear, calculation can be conveniently carried out by adopting a numerical analysis method, and the method has relatively good rationality and actual operability.

Description

Technical Field

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

[0002] Deep and soft soil layers with high water content, high compressibility, low permeability and low bearing capacity are widely distributed throughout my country, and many engineering construction projects involve the treatment of soft soil foundations. The vacuum preloading method is a technical means of drainage and consolidation treatment of soft soil foundations. There is no noise, no vibration, and no pollution to the environment during the construction process, and it has significant low-carbon and environmental protection characteristics. However, traditional vacuum preloading generally reflects problems such as small pressurized load, obvious vacuum attenuation, long consolidation time, and large post-construction settlement. What's more, the reinforcement effect of vacuum preloading on soft foundations often only appears on the surface. The boosted vacuum preloading technology is an improvement on the traditional vacuum preloading technology in recent years. For areas lacking sand and gravel materials, the cost of laying sand cushion layers over a large area is high. Therefore, the method of no sand cushion layer is adopted in the boosted vacuum preloading technology, forming a sandless boosted vacuum preloading technology.

[0003] For the sandless booster vacuum preloading technology, the reasonable calculation and analysis of excess pore water pressure in the foundation is an important issue in related engineering practice. However, since this technology appeared relatively late and its engineering application was ahead of theoretical research, there is currently no special calculation method for excess pore water pressure in saturated soft soil for sandless booster vacuum preloading. Previous studies on vacuum preloading did not fully consider the characteristics of well resistance changing with time and depth when analyzing excess pore water pressure in the foundation. In addition, the traditional variable well resistance model assumes that the final permeability coefficient of the drainage board is zero, which significantly underestimates its drainage capacity, while the constant well resistance model overestimates the consolidation degree of the foundation. Therefore, the traditional related calculation and analysis methods still have many defects. In view of this, the present invention aims at the problems existing in previous studies, aims at a new sandless booster vacuum preloading technology, based on its specific layout characteristics and the temporal and spatial variation characteristics of well resistance, as well as the operability of the values ​​of relevant parameters in practice, and adopts a new calculation and analysis model with the booster pipe as the center, which takes into account two typical characteristics of the temporal and spatial variation characteristics of the well resistance of the drainage plate. Combined with the sandless characteristics, the theoretical solution of drainage consolidation under the radial seepage mode of foundation soil is analyzed, and a calculation method for the excess pore water pressure of saturated soft soil in sandless booster vacuum preloading is provided. Summary of the invention

[0004] The present invention takes into account the two characteristics of the general nonlinearity of the attenuation of the well resistance of the drainage plate at any time and the non-zero final permeability coefficient of the drainage plate, and provides a method for calculating the excess pore water pressure of saturated soft soil by sandless booster vacuum preloading. The method is convenient for numerical analysis operation and has good rationality. The design analysis and calculation of the excess pore water pressure problem of saturated soft soil by sandless booster vacuum preloading can be conveniently realized, and the foundation treatment design related to sandless booster vacuum preloading can be carried out simply, efficiently and rationally.

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

[0006] The invention discloses a method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting, comprising the following steps: step S1: determining basic calculation parameters, including geometric parameters, soil parameters of foundation, smearing parameters, well resistance parameters and preloading load; step S2: obtaining a group of control equations for calculating excess pore water pressure in the foundation, substituting the basic calculation parameters into a calculation expression representing the relationship between the excess pore water pressure in the foundation soil and the pore water pressure in the drainage plate based on a non-homogeneous partial differential control equation of excess pore water pressure in the foundation, and 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 group of control equations for calculating excess pore water pressure in combination with boundary conditions, initial conditions and 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 represent the average excess pore water pressure in the foundation within the influence range of a single boosting pipe. In order to solve the above technical problems and achieve corresponding technical effects, the present invention provides a general calculation expression for the average excess pore water pressure at any depth in the foundation, which provides a common quantitative theoretical basis for analyzing problems of sandless booster vacuum preloading technology; provides a calculation method for excess pore water pressure in the foundation under three typical boosting modes, which can reflect the influence of different boosting depth ranges, covers the common boosting 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.

[0007] Further technical solutions:

[0008] In step S1, the geometric parameters include the thickness of the soft soil layer H, in m, the equivalent cylinder influence radius R e , unit is m, boost pipe radius r p , in m, booster pipe length L, in m, drainage board cross-sectional area A d , unit is mm 2 、Equivalent number of drainage panels in the unit n d ;

[0009] The soil parameters of the foundation include: volume deformation modulus E v , units are MPa, Poisson's ratio v, radial permeability coefficient k h , unit is m / s;

[0010] The smearing parameters include: the smearing area boundary radius r s , unit is m, the permeability ratio of the micro-disturbance area to the smearing area is x;

[0011] The well resistance parameters include the initial permeability coefficient k of the drainage board. d0 , in m / s, depth attenuation coefficient a, time attenuation coefficient b, in s -1 , drainage final stability index β;

[0012] The preload includes vacuum load p v , unit is kPa, boost load size p r , unit is kPa;

[0013] Among them, r p ≤r <r s The area is an undisturbed area, r s ≤r≤R e The area is an equivalent annular smear area.

[0014] Further: In step S2, the control equations for calculating the excess pore water pressure in the foundation are:

[0015]

[0016] Where t is time, z is the depth from the ground, r s is the boundary radius of the smear area, r p R is the radius of the boost pipe, e is the equivalent cylinder influence radius, H is the thickness of the soft soil layer, L is the length of the booster pipe, and L≤H, u s (r,z,t) is the excess pore water pressure of the soil, γ w is the density of water, ε v (z,t) is the volume strain of the soil, u d (z, t) is the pore water pressure in the drainage board;

[0017] Considering the effectiveness of the supercharging effect, let p r (z,t)=p ru h r (z)f r (t), where p ru is the boost full load value, h r (z) is the pressure increase coefficient related to depth, f r (t) is the coefficient of change of boost load with time, pr (z, t) is the radial pressure load.

[0018] Further: In formula (1), h d (z) is the depth attenuation index of the drainage board permeability coefficient, f d (t) is the time decay exponent of the permeability coefficient of the drainage board, and its expression is:

[0019]

[0020] f d (t) = β + (1-β) e -bt (3)

[0021] 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 stability index of drainage, 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 β=0 when the drainage board is completely blocked and has no drainage capacity.

[0022] Further: In formula (1), λ, ρ 2 、n、n p 、r d is the intermediate parameter, and its expression is:

[0023]

[0024] k d0 is the initial permeability coefficient, 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;

[0025] Intermediate variable F s The expression is:

[0026]

[0027] Among them, k r (r) is the radially varying horizontal permeability coefficient of the soil, and in the smear area k r (r) value is k s , in the undisturbed area k r (r) value is k h ; ξ is the integral variable of radial distance.

[0028] Further: 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:

[0029]

[0030] Among them, γ w is the density of water; v (z, t) is the volume strain of the soil, and the non-homogeneous partial differential governing equation of the excess pore water pressure in the foundation is expressed as:

[0031]

[0032] Formula (2) to Formula (11) are combined to obtain the control equation group for calculating the excess pore water pressure in the foundation.

[0033] Further: 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:

[0034]

[0035] 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.

[0036] Further: The boundary conditions and initial conditions that formula (1) needs to satisfy are:

[0037] z=0,u d (0,t)=-p v (13)

[0038]

[0039] 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:

[0040]

[0041] Among them, ω is the time integral variable; p v is the vacuum load; f r ′ is f r The first-order derivative of ; m is the number of calculations of different eigenvalues; η m are the calculated values ​​corresponding to each eigenvalue;

[0042] Using MATLAB to solve the non-zero solution of the nonlinear equation (17), we get m different η m Value, the nonlinear equation (17) is:

[0043]

[0044] 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;

[0045] In formula (16), the eigenfunction system composed of the first-order 0th-order Bessel function system and the second-order 0th-order Bessel function system is for:

[0046]

[0047] In formula (16), A mv is the vacuum load p v The expansion coefficients on the eigenfunction system, A mr is the boost load p r The expansion coefficient on the eigenfunction system is given by:

[0048]

[0049] In formulas (19) and (20), the eigenfunction system composed of the first-order Bessel function system of the first kind and the second-order Bessel function system of the first kind is for:

[0050]

[0051] In formula (16), C m , D m 、E m are the calculation intermediate variables corresponding to each eigenvalue, and the formula is:

[0052]

[0053] E m =1-D m (twenty four).

[0054] Further: in step S3, the boost mode includes: 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.

[0055] Further: Under the boosting mode I, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0056]

[0057] Under the boosting mode II, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0058]

[0059] Under the pressure-boosting mode III, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0060]

[0061] In formulas (25) to (27), t0 is the time interval from the start of vacuum preloading to the start of pressurization, t 1i is the instantaneous loading moment in the i-th intermittent supercharging cycle; is all the instantaneous loading moments of supercharging before the calculation time point t; t 2j is the instantaneous unloading moment in the jth intermittent supercharging cycle; t 2j :t 11 ,t 12 ,…,t 2jm are all the instantaneous unloading moments of supercharging before the calculation time point t.

[0062] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0063] The method for calculating the excess pore water pressure of saturated soft soil with sandless boosting vacuum preloading of the present invention fully considers the generality of the time-attenuation in the spatiotemporal variation characteristics of the well resistance of the actual drainage board and the non-zero characteristics of the final permeability coefficient of the drainage board, and clearly gives the calculation method of the excess pore water pressure in the foundation under three typical boosting modes, which is convenient for numerical analysis operation and has good rationality, and can conveniently realize the design analysis and calculation of the excess pore water pressure problem of saturated soft soil with sandless boosting vacuum preloading, and can simply, efficiently and rationally carry out the foundation treatment design related to sandless boosting vacuum preloading, which provides an effective method and scientific basis for such engineering design calculations, and has important technical significance and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0065] Figure 1 It is a general composition diagram of sandless booster vacuum preloading saturated soft soil foundation;

[0066] Figure 2 It is a schematic diagram of the basic analytical model of radial seepage in sandless booster vacuum preloading saturated soft soil foundation;

[0067] Figure 3 This is the pulse schematic diagram of boost mode I;

[0068] Figure 4 This is the pulse schematic diagram of boost mode II;

[0069] Figure 5 This is the pulse schematic diagram of boost mode III;

[0070] Figure 6 The calculation results of the average excess pore water pressure at a depth of 0.5 m in the foundation under the boosting mode I in Example 2 are as a function of time;

[0071] Figure 7 The calculation results of the average excess pore water pressure at a depth of 2.0 m in the foundation under the boosting mode I in Example 2 are as a function of time;

[0072] Figure 8 The calculation results of the average excess pore water pressure at a depth of 7.0 m in the foundation under the boosting mode I in Example 2 are as a function of time;

[0073] Fig. 9 The calculation results of the variation of the average excess pore water pressure along the depth in Example 2 under pressurization mode I for 10 days;

[0074] Fig.10 The calculation results of the variation of the average excess pore water pressure along the depth after pressurization for 300 days in the pressurization mode I of Example 2;

[0075] Fig.11 The calculation results of the average excess pore water pressure changing with time in the boosting mode II of Example 2;

[0076] Fig.12 The calculation results of the average excess pore water pressure variation along the depth in the boosting mode II of Example 2;

[0077] Fig.13 The results of the average excess pore water pressure variation over time at a foundation depth of 0.5 m under pressurization mode III in Example 2 after pressurization for 50 days;

[0078] Fig.14 The results of the average excess pore water pressure variation over time at a foundation depth of 0.5 m under boosting mode III in Example 2 after boosting for 100 days;

[0079] Fig.15 The results of the average excess pore water pressure variation over time at a foundation depth of 3.5 m in boosting mode III of Example 2 for 50 days;

[0080] Fig.16The results of the average excess pore water pressure variation over time at a foundation depth of 3.5 m under boosting mode III in Example 2 after boosting for 100 days;

[0081] Fig.17 The results of the average excess pore water pressure variation over time at a foundation depth of 7 m in boosting mode III in Example 2 after boosting for 50 days;

[0082] Fig.18 The results of the average excess pore water pressure variation over time at a foundation depth of 7 m in boosting mode III of Example 2 after boosting for 100 days;

[0083] Fig.19 The calculation results of the present invention in Example 2 are compared with the calculation results of the FLAC3D vertical simulation method. DETAILED DESCRIPTION

[0084] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0085] 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 apparent to one of ordinary skill in the art that these specific details are not necessarily employed to practice the present invention. In other embodiments, in order to avoid obscuring the present invention, well-known structures, circuits, materials, or methods are not specifically described.

[0086] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "one embodiment," "an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. In addition, it will be appreciated by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0087] In the description of the present invention, the directions or positional relationships indicated by terms such as “front”, “rear”, “left”, “right”, “up”, “down”, “vertical”, “horizontal”, “high”, “low”, “inside” and “outside” are based on the directions or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they should not be understood as limiting the scope of protection of the present invention.

[0088] Embodiment 1:

[0089] The method for calculating excess pore water pressure of saturated soft soil by sandless boosting vacuum preloading of the present invention comprises the following steps: step S1: determining basic calculation parameters, including geometric parameters, soil parameters of the foundation, smearing parameters, well resistance parameters and preloading load; step S2: obtaining a group of calculation control equations for excess pore water pressure in the foundation, substituting the basic calculation parameters into a calculation expression characterizing the relationship between the excess pore water pressure in the foundation soil and the pore water pressure in the drainage plate based on a non-homogeneous partial differential control equation for excess pore water pressure in the foundation, and obtaining a group of calculation control equations for excess pore water pressure in the foundation; step S3: obtaining the average excess pore water pressure in the foundation, solving the group of calculation control equations for excess pore water pressure in combination with boundary conditions, initial conditions and 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.

[0090] According to Figure 1 to Figure 5 The actual object shown in the figure is determined by other geological survey data and test results combined with engineering experience to determine the basic calculation parameters such as geometric parameters, soil parameters of the foundation, smear parameters, well resistance parameters and preload. Specifically, the geometric parameters include the thickness of the soft soil layer H, in meters, the equivalent cylinder influence radius R e , unit is m, boost pipe radius r p , in m, booster pipe length L, in m, drainage board cross-sectional area A d , unit is mm 2 、Equivalent number of drainage panels in the unit n d The soil parameters of the foundation include volume deformation modulus E v , units are MPa, Poisson's ratio v, radial permeability coefficient k h , in m / s; the smearing parameters include the smearing area boundary radius r s , in m, the permeability ratio of the micro-disturbance area to the smear area x; well resistance parameters include the initial permeability coefficient of the drainage board k d0 , in m / s, depth attenuation coefficient a, time attenuation coefficient b, in s -1, drainage final stability index β; preload includes vacuum load p v , unit is kPa, boost load size p r , unit is kPa; where r p ≤r <r s The area is an undisturbed area, r s ≤r≤R e The area is an equivalent annular smear area.

[0091] In step S2, the control equations for calculating the excess pore water pressure in the foundation are:

[0092]

[0093] Where t is time, z is the depth from the ground, r s is the boundary radius of the smear area, r p R is the radius of the boost pipe, e is the equivalent cylinder influence radius, H is the thickness of the soft soil layer, L is the length of the booster pipe, and L≤H, u s (r,z,t) is the excess pore water pressure of the soil, γ w is the density of water, ε v (z,t) is the volume strain of the soil, u d (z, t) is the pore water pressure in the drainage board;

[0094] Considering the effectiveness of the supercharging effect, let p r (z,t)=p ru h r (z)f r (t), where p ru is the boost full load value, h r (z) is the pressure increase coefficient related to depth, f r (t) is the coefficient of change of boost load with time, p r (z, t) is the radial pressure load.

[0095] The derivation process of the control equations for calculating excess pore water pressure in the specific foundation is as follows:

[0096] In formula (1), h d (z) is the depth attenuation index of the drainage board permeability coefficient, f d (t) is the time decay exponent of the permeability coefficient of the drainage board, and its expression is:

[0097]

[0098] f d (t) = β + (1-β) e -bt (3)

[0099] 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 stability index of drainage, 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 β=0 when the drainage board is completely blocked and has no drainage capacity.

[0100] In formula (1), λ, ρ 2 、n、n p 、r d is the intermediate parameter, and its expression is:

[0101]

[0102] k d0 is the initial permeability coefficient, 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;

[0103] Intermediate variable F s The expression is:

[0104]

[0105] Among them, k r (r) is the radially varying horizontal permeability coefficient of the soil, and in the smear area k r (r) value is k s , in the undisturbed area k r (r) value is k h ;.

[0106] 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:

[0107]

[0108] Among them, γ w is the density of water; v (z,t) is the volume strain of the soil.

[0109] 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:

[0110]

[0111] Formula (2) to Formula (11) are combined to obtain the control equation group for calculating the excess pore water pressure in the foundation.

[0112] The specific derivation method of the calculation expression of the average excess pore water pressure at any depth in the foundation is as follows:

[0113] 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:

[0114]

[0115] 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.

[0116] The boundary conditions and initial conditions that formula (1) needs to satisfy are:

[0117] z=0,u d (0,t)=-p v (13)

[0118]

[0119] 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:

[0120]

[0121] Among them, ω is the time integral variable; p v is the vacuum load; f r ′ is f r The first-order derivative of ; m is the number of calculations of different eigenvalues; η m are the calculated values ​​corresponding to each eigenvalue;

[0122] Using the non-zero solution of MATLAB nonlinear equation (17), we can obtain m different η m Value, the nonlinear equation (17) is:

[0123]

[0124] 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;

[0125] In formula (16), the eigenfunction system composed of the first-order 0th-order Bessel function system and the second-order 0th-order Bessel function system is for:

[0126]

[0127] In formula (16), A mv is the vacuum load p v The expansion coefficients on the eigenfunction system, A mr is the boost load p r The expansion coefficient on the eigenfunction system is given by:

[0128]

[0129] In formulas (19) and (20), the eigenfunction system composed of the first-order Bessel function system of the first kind and the second-order Bessel function system of the first kind is for:

[0130]

[0131] In formula (16), C m , D m 、E m are the calculation intermediate variables corresponding to each eigenvalue, and the formula is:

[0132]

[0133] E m =1-D m (twenty four).

[0134] The boost modes include: boost mode I, boost mode II and boost mode III. The boost mode I is constant boost when vacuum pre-pressurization starts, boost mode II is constant boost after a period of time after vacuum pre-pressurization starts, and boost mode III is intermittent boost after a period of time after vacuum pre-pressurization starts. Figure 3 to Figure 5 As shown, the corresponding average excess pore water pressure at any depth in the foundation within the effective influence range of a single booster pipe can be further obtained from formula (16). Specifically,

[0135] Under the pressure-boosting mode I, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0136]

[0137] Under the boosting mode II, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0138]

[0139] Under the pressure-boosting mode III, the calculation expression of the average excess pore water pressure at any depth in the foundation is:

[0140]

[0141] In formulas (25) to (27), t0 is the time interval from the start of vacuum preloading to the start of pressurization, t 1i is the instantaneous loading moment in the i-th intermittent supercharging cycle; is all the instantaneous loading moments of supercharging before the calculation time point t; t 2j is the instantaneous unloading moment in the jth intermittent supercharging cycle; t 2j :t 11 ,t 12 ,…,t 2jm are all the instantaneous unloading moments of supercharging before the calculation time point t.

[0142] Embodiment 2:

[0143] 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:

[0144] 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;

[0145] 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).

[0146] According to the average excess pore water pressure in the foundation defined by formula (12), and the average excess pore water pressure calculation expressions (25), (26), and (27) derived from boundary conditions, initial conditions, and different pressurization modes, the relevant basic calculation parameters are substituted into the calculation expressions to obtain the average excess pore water pressure at any depth in the foundation under pressurization modes I, II, and III. Among them, for pressurization mode III, there are three specific pressurization modes: mode 1: vacuum preloading 50d pressurization start and cycle once; mode 2: vacuum preloading 80d pressurization start and cycle once; mode 3: vacuum preloading 50d pressurization start and cycle 5 times.

[0147] The calculation results of the average excess pore water pressure at a typical depth in the foundation under supercharging mode I are as follows: Figure 6 to Figure 8 As shown in Figure 2, it can be seen that with the extension of time, the excess pore pressure decreases nonlinearly. Compared with the case without pressurization, the pore water pressure in the foundation under pressurization is significantly increased, which is conducive to accelerating the consolidation of the foundation soil. The calculated results are in line with the general laws of reality and are reasonable.

[0148] The calculation results of the average excess pore water pressure in the foundation along the depth at typical moments under supercharging mode I are as follows: Fig. 9 , Fig.10 As shown in Figure 2, it can be seen that with the extension of time, the excess pore pressure in the foundation increases nonlinearly along the depth.

[0149] The calculation results of the change of excess pore water pressure under supercharging mode II are as follows: Fig.11 , Fig.12 As shown in Figure 2, in addition to the nonlinear increase of the excess pore pressure in the foundation along the depth, it also reflects the variation characteristics of the excess pore pressure that changes synchronously with the boost load.

[0150] Figure 13 to Figure 18 The calculation results of the average excess pore water pressure at depths of 0.5m, 3.5m, and 7m in the foundation under supercharging mode III are shown respectively when the total supercharging time is 50d and 100d. It can be seen that the longer the total supercharging time is, the higher the degree of dissipation of the excess pore pressure in the foundation is; under the same total supercharging time and supercharging load conditions, the later the supercharging ends, the relatively smaller the excess pore pressure in the foundation is in the short time after the supercharging ends, and as the time is further extended, there is basically no difference in the later period.

[0151] To further illustrate the rationality of the method of the present invention, the pressure boosting mode I, i.e., constant pressure boosting during vacuum pre-pressure startup, is taken as a typical example. For the embodiment, L=7m, t=300d are taken as a typical example. The calculation results of the method of the present invention are compared with the calculation results of the FLAC3D numerical simulation method. Fig.19 It can be seen that the distribution pattern of excess pore 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.

[0152] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. The method for calculating the excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting is characterized by: 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: Obtain the average excess pore water pressure in the foundation, solve the calculation control equation group of excess pore water pressure in combination with boundary conditions, initial conditions and boosting mode, 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 characterize the average excess pore water pressure in the foundation within the influence range of a single boosting pipe.

2. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 1 is characterized in that: In step S1, the geometric parameters include the thickness of the soft soil layer H, in m, the equivalent cylinder influence radius R e , in m, boost pipe radius r p , in m, booster pipe length L, in m, drainage board cross-sectional area A d , unit is mm 2 、Equivalent number of drainage panels in the unit n d ; The soil parameters of the foundation include: volume deformation modulus E v , units are MPa, Poisson's ratio v, radial permeability coefficient k h , unit is m / s; The smearing parameters include: the smearing area boundary radius r s , unit is m, the permeability ratio of the micro-disturbance area to the smearing area is x; The well resistance parameters include the initial permeability coefficient k of the drainage board. d0 , in m / s, depth attenuation coefficient a, time attenuation coefficient b, in s -1 , drainage final stability index β; The preload includes vacuum load p v , unit is kPa, boost load size p r , unit is kPa; Among them, r p ≤r <r s The area is undisturbed, r s ≤r≤R e The area is an equivalent annular smear area.

3. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 2 is characterized in that: 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, r s is the boundary radius of the smear area, r p R is the radius of the boost pipe, e is the equivalent cylinder influence radius, H is the thickness of the soft soil layer, L is the length of the booster pipe, and L≤H, u s (r,z,t) is the excess pore water pressure of the soil, γw is the density of water, ε v (z, t) is the soil ε v Volumetric strain at (z, t), u d (z,t) is the pore water pressure in the drain plate, ξ is the integral variable of the radial distance; Considering the effectiveness of the supercharging effect, let p r (z,t)=p ru h r (z)f r (t), where p ru is the boost full load value, h r (z) is the pressure increase coefficient related to depth, f r (t) is the coefficient of change of boost load with time, p r (z, t) is the radial pressure load.

4. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 3 is characterized in that: In formula (1), h d (z) is the depth attenuation index of the drainage board permeability coefficient, f d (t) is the time decay exponent of the permeability coefficient of the drainage board, and its expression is: f d (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 stability index of drainage, 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 β=0 when the drainage board is completely blocked and has no drainage capacity.

5. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 4 is characterized in that: In formula (1), λ, ρ 2 、n、n p 、r d is the intermediate parameter, and its expression is: k d0 is the initial permeability coefficient, 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; Intermediate variable F s The expression is: Among them, k r (r) is the radially varying horizontal permeability coefficient of the soil, and in the smear area k r (r) value is k s , in the undisturbed area k r (r) value is k h ; ξ is the integral variable of radial distance.

6. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 5 is characterized in that: 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: Among them, γ w is the density of water; v (z, t) is the volume strain of the soil, and the non-homogeneous partial differential governing 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.

7. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 6 is characterized in that: 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.

8. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 7 is 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: Among them, ω is the time integral variable; p v is the vacuum load; f r ' is f r The first-order derivative of ; m is the number of calculations of different eigenvalues; η m are the calculated values ​​corresponding to each eigenvalue; Using MATLAB to solve the non-zero solution of the nonlinear equation (17), we get m different η m Value, the nonlinear equation (17) formula 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-order 0th-order Bessel function system and the second-order 0th-order Bessel function system is for: In formula (16), A mv is the vacuum load p v The expansion coefficients on the eigenfunction system, A mr is the boost load p r The expansion coefficient on the eigenfunction system is given by: In formulas (19) and (20), the eigenfunction system composed of the first-order Bessel function system of the first kind and the second-order Bessel function system of the first kind is for: In formula (16), C m , D m 、E m are the calculation intermediate variables corresponding to each eigenvalue, and the formula is: E m =1-D m (24)。 9. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 8 is 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.

10. The method for calculating excess pore water pressure of saturated soft soil by vacuum preloading without sand boosting according to claim 9 is 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 the start of pressurization, t 1i is the instantaneous loading moment in the i-th intermittent supercharging cycle; is all the instantaneous loading moments of supercharging before the calculation time point t; t 2j is the instantaneous unloading moment in the jth intermittent supercharging cycle; t 2j :t 11 ,t 12 ,…,t 2jm are all the instantaneous unloading moments of supercharging before the calculation time point t.

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