CN111898177A - Calculation method of stratified foundation consolidation degree - Google Patents

Calculation method of stratified foundation consolidation degree Download PDF

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CN111898177A
CN111898177A CN201910628356.2A CN201910628356A CN111898177A CN 111898177 A CN111898177 A CN 111898177A CN 201910628356 A CN201910628356 A CN 201910628356A CN 111898177 A CN111898177 A CN 111898177A
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layer
consolidation
soil
vertical
coefficient
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CN111898177B (en
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朱晶晶
刘益平
任亚群
韦华
陈念军
周伟
陆伟岗
王志楠
何小飞
沈锦儒
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Jiangsu Keneng Geotechnical Engineering Co ltd
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Jiangsu Keneng Geotechnical Engineering Co ltd
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Abstract

The invention discloses a method for calculating the consolidation degree of a layered foundation, which starts from settlement calculation, analyzes the mutual relation between the settlement and the total settlement of each layer in a compression layer of the layered foundation, researches the difference between the actual stress born by each layer and the ground pre-pressing load, does not need to establish a new differential equation, avoids adopting a high-depth complex mathematical method, only needs to calculate by a common mathematical method and utilizes an electronic form to complete the calculation of the consolidation degree of the layered foundation, and has small workload and meeting the design requirement with precision.

Description

Calculation method of stratified foundation consolidation degree
Technical Field
The invention belongs to the technical field of soft soil foundation reinforcement in geotechnical engineering, and particularly relates to a method for calculating the consolidation degree of a layered foundation.
Background art:
for the calculation of the consolidation degree of the layered foundation, there are methods of using an average index method, such as the consolidation degree of the layered foundation suggested by gray, and using a weighted average consolidation coefficient; also, the equivalent thickness method is used. After treatment, all the soil layers are calculated according to a single soil layer. The method can simplify calculation, but only can calculate the average consolidation degree of the whole soil layer, and cannot calculate the consolidation degree, the layered settlement and the like of each soil layer, and the accuracy of the result is not ideal. In other methods for calculating the consolidation degree of the layered foundation, research results are more in recent years, the general theory and formula are complex, and the solution of the consolidation equation can be obtained by means of a deep and complex mathematical method. Some adopt numerical methods and some adopt analytical methods. The numerical method mainly uses a finite difference method and a finite element method, and the analytical method adopts methods of variable separation and Fourier expansion, a Lagrange interpolation method, Laplace integral transformation and the like. This is relatively complicated for designers, and is inconvenient for engineering practice.
Disclosure of Invention
The invention aims to provide a calculation method of the consolidation degree of a layered foundation, which aims to solve the problems of how to determine the path of water seepage movement in each soil layer and how to consider the effect of each soil layer in a drainage path, particularly the influence of a vertical shaft in an incomplete well foundation on a downhole layer.
A method of calculating the consolidation of a stratified foundation, the method comprising the steps of:
dividing the whole compression layer into a plurality of layers according to the natural layer, calculating the drainage distance of each layer and the vertical consolidation coefficient of the whole path, and obtaining drainage parameters;
obtaining an initial value of the layering consolidation degree of each layer according to the drainage parameters;
calculating a layered final sedimentation value and an entire layer final sedimentation value, and obtaining a layered stress reduction coefficient and a layered contribution rate;
obtaining the average layering consolidation degree according to the initial layering consolidation degree value and the stress reduction coefficient of layering;
obtaining a layering consolidation degree contribution value according to the layering average consolidation degree and the layering contribution rate;
and calculating the sum of the contribution values of the layering consolidation degrees to obtain the total average consolidation degree of the whole layering of the layered foundation.
Preferably, the drainage distance HiCalculated using the formula:
Figure RE-GDA0002185523940000021
the seepage movement of water in the soil from the bottom surface of the ith layer to the top surface of the compression layer should include the drainage distance HiAll layers within, hmIs the layer thickness of the mth soil layer in the unit of m.
Preferably, the full path vertical consolidation coefficient
Figure RE-GDA0002185523940000022
The calculation method comprises the following steps:
calculating to distinguish a vertical layer from a downhole layer, and when the ith layer is positioned in the vertical layer:
Figure RE-GDA0002185523940000023
in the formula: c. CvmIs the vertical consolidation coefficient of the m-th layer of soil, hmIs the thickness of the layer of the m-th soil, cm.
When the ith zone is located in the downhole formation:
calculating the composite vertical consolidation coefficient of each layer in the vertical well layer, and equating the vertical consolidation coefficient of the vertical well and the vertical consolidation coefficient of the soil between wells into the composite vertical consolidation coefficient of each layer by adopting an area ratio method, and calculating by using the following formula:
cwsi＝[1+μ(vi-1)]×cvi
in the formula: c. CwsiComposite vertical consolidation coefficient in cm for ith layer2S; mu is the ratio of the cross section area of the vertical well to the cross section area of the single well influence range, and has no dimension, wherein mu is Aw/A; v. ofiIs the ratio of the vertical consolidation coefficient of the vertical shaft to the vertical consolidation coefficient of the soil between the ith layered well, and has no dimension vi＝cw/cvi；
In the formula: a. thewIs the cross-sectional area of the shaft in m2(ii) a A is the cross-sectional area of the single-well influence range and the unit m2；cwIs vertical consolidation coefficient of vertical shaft, unit cm2/s；cviIs the vertical consolidation coefficient of the soil between the ith layering wells in cm2/s；
Full path vertical consolidation coefficient of each layer in underground layer
Figure RE-GDA0002185523940000031
Calculated using the formula:
Figure RE-GDA0002185523940000032
in the formula: c. CwsmIs the composite vertical consolidation coefficient of the mth layer in the vertical well layer in unit of cm2/s； cvmIs the vertical consolidation coefficient of the m-th layer soil in the underground layer in unit of cm2S; w is the serial number of the soil layer of the lowest layer of the vertical shaft layer, and the dimension is zero; w +1 is the soil layer serial number of the uppermost layer in the underground layer, and has no dimension, m in the calculation formula of the vertical consolidation coefficient of the whole path refers to the soil layer serial number, and is not the layering serial number.
Preferably, the method for calculating the initial value of the layered consolidation degree comprises the following steps:
the initial value of the layering consolidation degree of the ith layering is that the ith layering in the foundation is regarded as the whole layer, when the foundation is subjected to ground pre-pressing load, the stress generated in the layer is assumed to be equal to the ground pre-pressing load from top to bottom, the consolidation degree is calculated by a general expression summarized by Zeng nationality, and the obtained initial value of the layering consolidation degree of the ith layering is:
Figure RE-GDA0002185523940000041
in the formula:
Figure RE-GDA0002185523940000042
the initial value of the layering consolidation degree of the ith layering is dimensionless; alpha is a parameter, alpha-pi2/8；βiParameters for the ith tier:
when the stratification is in a shaft layer:
Figure RE-GDA0002185523940000043
when the stratification is in the downhole layer:
Figure RE-GDA0002185523940000044
in the formula: c. ChiIs the radial consolidation coefficient of soil, cm2/s；
Figure RE-GDA0002185523940000045
Is the vertical consolidation coefficient of the soil; hiThe drainage distance of the ith soil layer is cm; t is consolidation duration, unit s, n is well diameter ratio, n is de/dw，deIs the effective drainage diameter of the shaft, cm; dwIs the diameter of the vertical shaft, cm; fiParameters related to the well diameter ratio, well resistance and smearing influence of the ith layer are defined; deThe diameter of the equivalent circle of a single well of the drainage well is cm.
When an ideal well: fi＝Fn；
When a non-ideal well: fi＝Fn+Fsi+Fri；
Wherein: fnThe well diameter ratio factor is used, all layers in the vertical well layer are the same, and the calculation is carried out according to the following formula:
Figure RE-GDA0002185523940000051
when the well diameter ratio is nwWhen F is not less than 15nCan be simplified as follows:
Fn＝ln(nw)-0.75
Fsireflecting the influence of the i-th layer smearing disturbance, and calculating according to the following formula:
Figure RE-GDA0002185523940000052
Si＝dsi/dw
in the formula: k is a radical ofhi、ksiRespectively the permeability coefficients of the i-th layer of undisturbed soil and the soil in the smearing area, cm/s; dwIs the diameter of the vertical shaft, cm; dsiIs the diameter of the smearing area, cm; siDiameter d of application area of ith layersiDiameter d of shaftwThe ratio of (A) to (B) is preferably 2 to 3. Taking a low value for medium sensitive cohesive soil and a high value for high sensitive cohesive soil;
Frireflecting the well resistance effect of the ith layer, calculating according to the following formula:
Figure RE-GDA0002185523940000053
Figure RE-GDA0002185523940000054
in the formula: hiThe drainage distance of the ith layer is cm; k is a radical ofwIs the vertical shaft permeability coefficient, cm/s; q. q.swFor water flow of vertical shaft, cm3/s；rwIs the radius of the cross section of the shaft, cm.
Preferably, the calculation method of the layering average consolidation degree comprises the following steps:
multiplying the initial value of the lamination consolidation degree by the stress reduction coefficient of the corresponding lamination, and multiplying the stress reduction coefficient omega of the ith lamination by the stress reduction coefficient of the corresponding laminationiCalculated using the formula:
Figure RE-GDA0002185523940000061
in the formula: z is a radical ofi、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the ith layer of soil and the (i-1) th layer of soil,
Figure RE-GDA0002185523940000062
Figure RE-GDA0002185523940000063
calculating the average additional stress coefficient h from the foundation bottom surface to the bottom surface of the i-th layer soil and the i-1 th layer soiliIs the thickness of the ith layer of soil.
Preferably, the calculation method of the contribution value of the layered consolidation degree is as follows:
hierarchical contribution ratio λ of ith hierarchyiCalculated using the formula:
Figure RE-GDA0002185523940000064
multiplying the layering average consolidation degree by the corresponding layering contribution rate to obtain a layering consolidation degree contribution value;
in the formula: siIs the final sedimentation value of the ith layer, si' is the deformation value of the ith layer calculated according to the layer summation method, and the unit is cm; s' is the value of the deformation of the entire layer calculated by the sum of layers, sfThe final sedimentation value of the whole layer is in cm.
Preferably, the calculation method of the layered final sedimentation value is as follows:
layering final sedimentation value:
Figure RE-GDA0002185523940000065
p0for additional pressure acting on the base bottom surface, EsiThe compressive modulus of the i-th layer of soil below the bottom surface of the foundation,
Figure RE-GDA0002185523940000066
is a base bottom surfaceCalculating the average additional stress coefficient, z, in the range from the point to the bottom surface of the i-th layer of soil and the i-1 th layer of soili、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the ith layer of soil and the (i-1) th layer of soil.
Preferably, the method for calculating the final sedimentation value of the whole layer is as follows:
final sedimentation value of the whole layer:
Figure RE-GDA0002185523940000071
p0for additional pressure acting on the base bottom surface, EsiCompressive modulus of the i-th layer of soil under the foundation bed, psisThe empirical coefficient is calculated for the settlement,
Figure RE-GDA0002185523940000072
calculating the average additional stress coefficient, z, from the foundation bottom surface to the i-th layer soil and the i-1 th layer soil bottom surfacei、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the i-th layer of soil and the i-1 st layer of soil, and n is the total number of the layered layers in the whole layer.
The invention has the advantages that: the method for calculating the consolidation degree of the layered foundation comprises the following steps:
(1) the method is clear and simple, does not need to establish a partial differential equation additionally, avoids adopting a deep and complex mathematical theory to solve, applies the existing theory and formula, utilizes an Excel spreadsheet, can obtain a solution with sufficient precision by only using an exponential function and four arithmetic operations, and greatly simplifies the calculation process;
(2) the method can calculate the total average consolidation degree of the whole layer, the consolidation degree of each layer and the average consolidation degree of any combination layer, such as a vertical well layer or a downhole layer;
(3) the foundation of the vertical shaft without the perforated compression layer is called as an incomplete well foundation, the definition is clear, the naming is simple, the number of words is reduced, the narration is convenient, the space of an article is saved, the work efficiency is improved, the incomplete well foundation is divided into a vertical shaft layer and a downhole layer, and the measures and the methods for improving the consolidation degree of the compression layer are convenient to analyze and study;
(4) reducing the calculated initial value of the layering consolidation degree by adopting a stress reduction coefficient so as to eliminate errors;
(5) whether the vertical shaft layer or the underground layer is layered according to natural layers, each layer is a homogeneous foundation, the layered consolidation degree of each layer can be calculated by using a ready consolidation degree formula, and the contribution of the layer to the total average consolidation degree of the whole compression layer can be calculated by using the layered contribution rate, so that the layered foundation problem is converted into a homogeneous foundation problem;
(6) the invention defines the drainage distance of each layer from the bottom of the layer to the top of the whole layer. And all the layers in the drainage distance path participate in seepage movement, the layer thickness of the layer is taken as the drainage distance, the seepage movement is carried out to the bottom surface of the adjacent upper layer to enter the upper layer, and the rest is done in the same way, and finally the seepage movement is carried out to the top surface of the vertical shaft layer to be discharged. The equivalent consolidation coefficient is called the 'full-path vertical consolidation coefficient' and is 1/h2The weighted average has clear and clear principle, convenient calculation and enough precision;
(7) the invention provides a new concept of a full-path vertical consolidation coefficient through a vertical well layer. The drainage shaft plays an important role in the seepage movement of pore water in soil in the lower layer of the well. When calculating the full path vertical consolidation coefficient of each layer of the underground layer, the function of the vertical shaft must be taken into account.
Drawings
FIG. 1 is a flow chart for calculating the consolidation of a stratified foundation according to the present invention.
FIG. 2 is a schematic vertical sectional view of a single well consolidation model of the incomplete well foundation of the present invention.
FIG. 3 is a schematic vertical section of the single well pore water seepage movement of the non-integral well foundation of the present invention.
FIG. 4 is a graph of additional stress in soil according to the present invention.
Fig. 5 is a cross-sectional view of an embankment according to embodiment 1 of the present invention.
FIG. 6 is a vertical cross-sectional view of a single well consolidation model according to example 2 of the present invention.
FIG. 7 is a comparison of the calculation results of the embodiment of the present invention and the calculation results of other solutions.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
As shown in fig. 1, a method for calculating the consolidation degree of a layered foundation includes the following steps:
(1) defining a complete well foundation and an incomplete well foundation:
the condition that the drainage vertical shaft does not penetrate through the pressed soil layer is called as an incomplete well foundation, and the condition is called as a complete well foundation otherwise;
(2) dividing a compression layer into a vertical well layer and a downhole layer based on the definition of the incomplete well foundation;
(3) and (3) layering the vertical well layer and the downhole layer according to the natural layer, and numbering the vertical well layer and the downhole layer from top to bottom in sequence (as shown in figure 2). Each layer in the vertical well layer is a complete well foundation, and each layer in the underground well layer is a well-free foundation;
(4) defining whole, stratified, combined and stratigraphic layers:
the whole compressed layer is called 'whole layer', and the whole layer consolidation degree is called 'whole layer total average consolidation degree'
Figure RE-GDA0002185523940000094
The minimum layer of the division is called 'layering', and the layering is characterized by: each layer is a single homogeneous foundation, and the consolidation degree of each layer is called as layered average consolidation degree;
secondly, a plurality of adjacent layers are combined together to form a 'combined layer', and the method is characterized in that: the composite layer is located at a location throughout the layer and comprises a plurality of distinct sub-layers, e.g. downhole, the degree of consolidation of which is referred to as the "composite layer average degree of consolidation" and is designated by the depth of the top and bottom of the composite layer from the surface, e.g.
Figure RE-GDA0002185523940000091
Average consolidation degree of the bonding layer of 2.0m to 5.5m from the ground;
thirdly, the combined layer taking the whole layer top as the top surface is called as a stratum, such as a vertical well layer; the consolidation of the formation is called the average consolidation of the formation, which is given by its layer thickness, for example
Figure RE-GDA0002185523940000092
The average consolidation degree of the stratum with the depth of the bottom layer of 8.2m, and if the strata are numbered sequentially from top to bottom, the strata can also be subscripted by the Roman number sequence, for example
Figure RE-GDA0002185523940000093
……；
(5) Initial value of layering consolidation degree, layering average consolidation degree and contribution value of layering consolidation degree:
the calculation formula of the average consolidation degree of the foundation under different drainage conditions is as follows:
Figure RE-GDA0002185523940000101
firstly, an initial value of layering consolidation degree:
regarding the ith layer in the foundation as the whole layer, when the foundation is subjected to ground preloading, the stresses generated in the layers are equal from top to bottom, calculating the consolidation degree by using the formula (1), and obtaining the initial value of the layered consolidation degree of the ith layer so as to obtain the final value of the layered consolidation degree of the ith layer
Figure RE-GDA0002185523940000102
And (4) showing. This is called the initial value of the degree of consolidation for a layer because it is not realistic to assume that the stresses in the layer are uniform and equal to the ground load. As can be seen from fig. 4, the additional stress patterns are gradually reduced from top to bottom, the additional stress pattern of each layer is approximately in the shape of an inverted trapezoid, and the average stress of the layers farther away from the ground is smaller. If this difference is not taken into account, a large error will occur. Therefore, the initial value of the layering consolidation degree must be corrected to obtain the real layering average consolidation degree.
The layering average consolidation degree:
as can be seen from fig. 4, the area of the additional stress pattern of the ith layer is 3: the area of the graph abcd is phiThe initial value of the layering consolidation degree is obtained according to the calculation result, and the value is larger than the actual value; the graph cdef (hatched in the graph) is the actual load area, the value of which is based on the averageThe force times the layer thickness is calculated as ωiphi. The layering consolidation degree calculated by the method is the real layering average consolidation degree. From the initial value of the degree of consolidation in layers calculated by the formula (1)
Figure RE-GDA0002185523940000103
Need to multiply the corresponding stress reduction coefficient omegaiThis is the true average degree of consolidation in layers, denoted Ui. the mean degree of consolidation for a slice at time t is the value of the sedimentation s for that slice at time titWith the layered final sedimentation value siThe ratio of. This can be demonstrated by the following formula:
Figure RE-GDA0002185523940000111
in the formula: lambda [ alpha ]iFor delamination contribution, p is the additional stress of the ith delamination, hiThe layer thickness of the ith layer is described in detail below.
③ contribution value of layering consolidation degree:
the average layering consolidation degree is multiplied by the contribution rate of the layer to obtain the contribution value lambda of the layering consolidation degreeiUi。
(6) Defining the layered contribution rate:
because the layering is only one part of the whole layer, the ratio of the layering consolidation to the total average consolidation of the whole layer is related to the ratio of the deformation of the layering in the total deformation, namely the layering contribution rate, and in the combined layer comprising n layered foundations, each layering has different parameters such as layer thickness, geology and the like, so that different layering consolidation and layering contribution rates can be obtained; while the settlement of the compression layer is calculated, the settlement value of each layer is divided by the cumulative settlement value of the integration layer to obtain the contribution rate lambda of the layer to the integration layeri：
Figure RE-GDA0002185523940000112
In the formula: si' is the deformation value of the ith layer, s, calculated by the layer summation methodiFor the i-th layerSedimentation value, cm; s' is the value of the deformation of the entire layer calculated by the sum of layers, sfIs the final sedimentation value of the integration layer, cm.
Each layer has different contribution rates depending on the contribution objects, for example, a layer is one of the vertical layers and one of the whole layers, and the vertical layer and the whole layer have different contribution rates.
(7) Defining a stress reduction coefficient:
generally, when general expression (1) is applied, the stress in the compression layer is considered to be uniformly distributed along the depth, which is equivalent to the condition that the foundation is consolidated under the action of self weight, the foundation area is large, and the compression layer is thin (namely H/B < 0.5). This is not the case and such an approximation necessarily results in some error. To eliminate errors, a stress reduction factor ω is used according to the position of each layer in the compression layeriAnd (5) reducing the calculated initial value of the layering consolidation degree. Stress reduction factor omegaiCalculated by the following method:
the load with limited area is piled on the surface of the semi-infinite elastic body, the distribution of the additional stress along the depth of the foundation is gradually reduced due to diffusion, and the stress reduction coefficient omega of each layer is calculated by taking the average stress at the midpoint of each layeri：
Figure RE-GDA0002185523940000121
zi、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the ith layer of soil and the (i-1) th layer of soil,
Figure RE-GDA0002185523940000122
calculating the average additional stress coefficient h from the foundation bottom surface to the bottom surface of the i-th layer soil and the i-1 th layer soiliIs the thickness of the ith layer of soil.
(8) Calculation of the final sedimentation value:
the final settlement value of the compression layer during preloading is calculated according to a settlement formula of a layering summation method of national standard GB50007-2011 building foundation design standard, and symbols in the formula are shown in the standard:
Figure RE-GDA0002185523940000123
in the process of calculating the settlement, the layer contribution rate lambda can be calculated by the wayiAnd stress reduction factor omegai；
(9) The value-taking principle of the vertical seepage drainage distance is provided:
for the subject of single-side drainage, the final outlet of pore water seepage movement in the foundation is necessarily the top surface of the whole compression layer, and obviously the distance from the bottom surface of each layer to the top surface of the vertical well layer is taken as the drainage distance of the layer, for example, the drainage distance H of the ith layeri(see FIG. 2) is calculated using the following formula:
Figure RE-GDA0002185523940000131
(10) the principle of calculating the vertical consolidation coefficient of the whole path is put forward
When all-path vertical consolidation coefficients are calculated in each layer of the vertical well layer, only H is involvediThe vertical consolidation coefficient of each layer of soil within the distance does not count the influence of the vertical well on the vertical consolidation coefficient; when the vertical consolidation coefficient of the whole path is calculated in each layer in the underground layer, not only the H is involvediThe vertical consolidation coefficient of each layer of soil within the distance is also taken into account, and the influence of the vertical well on the vertical consolidation coefficient is also taken into account.
(11) Calculation method for determining all-path vertical consolidation coefficients of each layer in vertical well layer
The full-path vertical consolidation coefficient is calculated for each layer in the vertical well layer by the following formula:
Figure RE-GDA0002185523940000132
in the formula: c. CvmIs the vertical consolidation coefficient of the m-th layer soil, cm2/s；hmIs the thickness of the mth layer of soil, m.
(12) The calculation method for determining the all-path vertical consolidation coefficient of each layer in the underground layer comprises the following steps:
(12.1) calculating the composite vertical consolidation coefficient of each layer in the vertical well layer
The vertical consolidation coefficient of the vertical shaft and the vertical consolidation coefficient of the soil between the shafts are equivalent to the composite vertical consolidation coefficient of each layer by adopting an area ratio method, and the calculation is carried out by using the following formula:
cwsi＝[1+μ(νi-1)]×cvi(8)
in the formula: c. CwsiComposite vertical consolidation coefficient, cm, for the ith layer2S; mu is the ratio of the cross section area of the vertical well to the cross section area of the single well influence range, has no dimension and is calculated by the formula (9); v. ofiThe ratio of the vertical consolidation coefficient of the vertical shaft to the vertical consolidation coefficient of the soil between the ith layering wells is zero dimension and is calculated by the formula (10).
Figure RE-GDA0002185523940000141
Figure RE-GDA0002185523940000142
In the formula: a. thewIs the cross-sectional area of the shaft, m2(ii) a A is the cross-sectional area of the single-well influence range, m2；cwVertical consolidation coefficient of vertical shaft, cm2/s；cviIs the vertical consolidation coefficient of the soil between the ith layering wells in cm2/s。
Due to cw＞＞cvi，cwsiCan be calculated using the following formula:
Cwsi≈μcw(11)
(12.2) calculating the full-path vertical consolidation coefficient of each layer in the underground layer
Full-path vertical consolidation coefficient L of each layer in underground layercvjCalculated using the formula:
Figure RE-GDA0002185523940000143
in the formula: c. CwsmIs the average vertical consolidation coefficient of the mth layer in the vertical well layer, cm2/s；cvmIs the vertical consolidation coefficient of the m-th layer soil in the underground layer, cm2S; w is the serial number of the soil layer of the lowest layer of the vertical shaft layer, and the dimension is zero; w +1 is the serial number of the uppermost soil layer in the underground layer, and has no dimension.
(13) Calculating an initial value of the layering consolidation degree:
the initial value of the consolidation degree of each layer in the vertical well layer and the underground well layer is calculated by adopting a general expression, and the initial value is calculated by taking ABCD in figure 4 as the area of an additional stress diagram:
Figure RE-GDA0002185523940000144
in the formula:
Figure RE-GDA0002185523940000145
the initial value of the layering consolidation degree of the ith layering is dimensionless; α is a coefficient, α ═ π2/8；βiThe coefficient of the ith layering is shown, t is consolidation duration, and s; wherein beta isiCalculating by adopting different formulas according to the positions of the layers;
the formula adopted for layering in the vertical well layer is as follows:
Figure RE-GDA0002185523940000151
the formula adopted for layering in the downhole layer is as follows:
Figure RE-GDA0002185523940000152
in the formula: c. ChiIs the radial consolidation coefficient of the ith layer, cm2/s；deThe diameter of the influence range of the shaft, m;
Figure RE-GDA0002185523940000153
full path vertical consolidation coefficient, cm, for the ith layer2/s；HiIs the drainage distance of the ith layer, m; fiParameters relating to well diameter ratio, well resistance and smear impact are given for the ith layer.
When an ideal well: fi＝Fn； (15)
When a non-ideal well: fi＝Fn+Fsi+Fri。 (16)
In the formula: fnThe well diameter ratio factor is used, all layers in the vertical well layer are the same, and the calculation is carried out according to the following formula:
Figure RE-GDA0002185523940000154
when the well diameter ratio is nwWhen F is not less than 15nCan be simplified as follows:
Fn＝ln(nw)-0.75 (18)
Fsireflecting the smearing disturbance effect, the following formula is calculated:
Figure RE-GDA0002185523940000155
Si＝dsi/dw(20) in the formula: k is a radical ofhi、ksiRespectively the permeability coefficients of the i-th layer of undisturbed soil and the soil in the smearing area, cm/s; dwIs the diameter of the vertical shaft, cm; dsIs the diameter of the smearing area, cm; s is the diameter d of the coating areasDiameter d of shaftwThe ratio of (A) to (B) is preferably 2 to 3. Taking a low value for medium sensitive cohesive soil and a high value for high sensitive cohesive soil;
Fsrireflecting the well resistance effect of the ith layer, calculating according to the following formula:
Figure RE-GDA0002185523940000161
Figure RE-GDA0002185523940000162
in the formula: hiThe drainage distance of the ith layer is cm; k is a radical ofwIs the vertical shaft permeability coefficient, cm/s; q. q.swFor water flow of vertical shaft, cm3/s；rwIs the radius of the cross section of the shaft, cm.
(14) Initial value of degree of consolidation in layers
Figure RE-GDA0002185523940000163
Multiplying the stress reduction factor omega of the layeriObtaining the average consolidation degree U of the layersiIt is calculated by cdef in fig. 4 as the area of the additional stress map;
Figure RE-GDA0002185523940000164
(15) average degree of consolidation in layers UiMultiplying the contribution of the hierarchy by λiObtaining the contribution value lambda of the layer consolidation degreeiUi；
(16) Total average degree of consolidation of the entire layer
Figure RE-GDA0002185523940000165
A contribution to the consolidation of each layeriUiThe sum of the above;
Figure RE-GDA0002185523940000166
based on the above, the following examples are adopted for experimental analysis in the invention:
example 1: this example is taken from the handbook of ground treatment (second edition).
One embankment soft foundation engineering adopts a bagged sand well for treatment, the thickness of a pressed soil layer is 30m, and the consolidation coefficient c of soil ish＝cv＝1.8×10-2cm2And s. Diameter d of sand wellwThe sand well spacing is 1.4m, the sand well depth is 20m, and the sand well plane is arranged in an equilateral triangle. The embankment load is a momentary load, as shown in fig. 5. And (4) calculating the average consolidation degree of the compressed soil layer at 120d (not considering the influence of well resistance and smearing).
The calculation theory provided by the invention comprises the following steps:
and (1) designing and calculating various parameters required by geotechnical engineering data according to the prepressing scheme. The method specifically comprises the following substeps:
(1.1) the example is a single soil incomplete well foundation, 2 layers are divided by taking the bottom of a vertical well as a boundary, the upper layer is a vertical well layer with the thickness of 20m, and the lower layer is a downhole layer with the thickness of 10 m.
(1.2) shaft floor parameters
Diameter d of sand wellw＝7cm，
Equivalent diameter d of shafte＝1.05×1.4＝1.47m，
Well diameter ratio nw＝21，
Shaft depth hw＝20m；
Step (2)
In this example, there were 2 layers, and the layer contribution ratio and the stress reduction coefficient obtained by calculating the sedimentation by the layer summation method are shown in Table 1.1.
TABLE 1.1 hierarchical contribution λiAnd stress reduction factor omegaiWatch (A)
Number of layers i 1 2
Contribution ratio of stratification λi 0.6754 0.3246
Stress reduction factor omegai 0.9936 0.9552
Step (3) calculating the composite vertical consolidation coefficient of the vertical well layer
Permeability coefficient k of sand wellw＝2×10-5m/s＝1.73m/d，
Compression modulus E of sand wells＝5MPa，
Vertical consolidation coefficient c of sand wellw＝1.73×5×1000/9.8＝882m2/d，
Vertical consolidation coefficient c of interwell soilv1＝cv2＝1.555×10-2m2/d，
Area ratio mu is 1/nw 2＝0.00227，
Composite average consolidation coefficient cwsi≈882×0.00227＝2.0m2/d，
The vertical consolidation coefficient of the whole path is that,
layering 1:
Figure RE-GDA0002185523940000181
layering 2:
Figure RE-GDA0002185523940000182
step (4) calculating the drainage distance H of each layeriFull path vertical consolidation coefficient
Figure RE-GDA0002185523940000183
And coefficients alpha, betai. The results of the calculations are set forth in Table 1.2.
TABLE 1.2 drainage spacing HiFull path vertical consolidation coefficient
Figure RE-GDA0002185523940000184
And coefficients alpha, betaiList of
Figure RE-GDA0002185523940000185
And (4) calculating the initial value of the layering consolidation degree of each layer by using a general expression summarized by professor Zeng national xi. The method of the invention is used for calculating the layering average consolidation degree and the contribution value of each layer.
The method specifically comprises the following substeps:
(4.1) calculating the initial value of the degree of consolidation in layers
Figure RE-GDA0002185523940000186
The initial values of the consolidation in layers were calculated by the formula (13), and the results are shown in Table 1.3.
(4.2) calculation of the average degree of consolidation in layers Ui
The average consolidation level for each layer was calculated using equation (15), and the results are shown in Table 1.3.
(4.3) calculating the contribution value lambda of the degree of consolidation in layersiUi
The average consolidation degree U of each layeriMultiplying by respective layer contribution rates λiThe values of the contribution of the consolidation degree by delamination were obtained, and the results are shown in Table 1.3.
TABLE 1.3 Table of layered consolidation levels
Figure RE-GDA0002185523940000191
And (4) calculating the average value of the total consolidation degree of the whole layer.
The total average consolidation degree of the whole layer is calculated by the formula (16)
Figure RE-GDA0002185523940000192
The results of the calculation of the layering method and the results of the calculation of the Xikang and the improvement method are listed in Table 1.4, and it can be seen that the results of the calculation of the present invention are not much different from the results of the calculation of the Xikang and the improvement method.
TABLE 1.4 comparison of the results
Figure RE-GDA0002185523940000193
Example 2: this example was taken from Yan richly, "Lagrange's interpolation method for consolidation of a layered, unbroken sand well foundation".
Taking a single soft soil layer with the thickness of 30m, wherein the sand well penetration ratio is 2/3, and the horizontal and vertical permeability coefficients are respectively 2.73 multiplied by 10-9And 1.48X 10-9m/s, horizontal and vertical consolidation coefficients of 8.63 × 10-2And 4.71X 10-2m2S, radius of sand well rw14cm, the well diameter ratio n is 20, S is 1, and the sand well permeability coefficient kw＝2.0×10-5m/s. Constant load q (t) 100kPa, single-sided drainage.
FIG. 6 shows a vertical cross-section of the single well consolidation model of the present case. The calculation theory of the consolidation degree of the layered foundation provided by the invention comprises the following steps:
and (1) designing and calculating various parameters required by geotechnical engineering data according to the prepressing scheme. The method specifically comprises the following substeps:
(1.1) the example is a single-soil incomplete well foundation, and the compression layer originally in a single soil layer is divided into 2 layers by taking a vertical well bottom as a boundary, wherein the upper layer is a vertical well layer with the thickness of 20m, and the lower layer is a downhole layer with the thickness of 10 m.
(1.2) shaft floor parameters
Diameter d of sand wellw＝14cm，
Equivalent diameter d of shafte＝2.8m，
Shaft depth hw＝20m；
(1.3) calculating parameters of well resistance and smearing effect influence
Well diameter ratio nw＝de/dw＝20，
Well diameter ratio factor Fn＝2.25，
S＝ds/dw＝1
Smearing effect Fs＝0，
Fr＝8.75，
F＝11.0；
And (2) calculating the final sedimentation value of each layer and the whole layer by adopting a national standard GB50007 layered sum method, and meanwhile, calculating the layered contribution rate and the layered stress reduction coefficient. The method specifically comprises the following substeps:
(2.1) final sedimentation value s of each layeri' and cumulative Settlement Σ si’
The results are shown in Table 2.1, and none of the values is multiplied by the empirical coefficients of sedimentation.
(2.2) hierarchical contribution ratio λi
The calculations are listed in table 2.1.
(2.3) reduction coefficient of layered stress ωi
The results of the calculations are given in table 2.1.
TABLE 2.1 Segregation si', cumulative Settlement Σ si', layer contribution ratio lambdaiAnd a summary of the reduction factor of the delamination stress
Figure RE-GDA0002185523940000211
Step (3) calculating the composite vertical consolidation coefficient of the vertical well layer
Let the permeability coefficient of the sand well be kw＝2×10-5m/s＝1.73m/d，
The compression modulus Es of the sand well is 5MPa,
vertical consolidation coefficient c of sand wellw＝882m2/d，
Vertical consolidation coefficient c of interwell soilv1＝cv2＝4.07×10-2m2/d，
Well diameter area ratio mu of 1/202＝0.0025，
Composite average consolidation coefficient cwsi≈882×0.0025＝2.2m2/d，
Full path vertical consolidation coefficient
Layering 1:
Figure RE-GDA0002185523940000221
layering 2:
Figure RE-GDA0002185523940000222
and (4) calculating initial values of the layering consolidation degrees of the layers in different consolidation durations by using a general expression summarized by professor Zeng national xi. The method specifically comprises the following substeps:
(4.1) calculating the drainage distances H of the respective layersiFull path vertical consolidation coefficient
Figure RE-GDA0002185523940000223
And coefficients alpha, betai. The results of the calculations are shown in Table 2.2.
TABLE 2.2 drainage spacing HiFull path vertical consolidation coefficient
Figure RE-GDA0002185523940000229
And coefficients alpha, betaiList of
Figure RE-GDA0002185523940000224
(4.2) calculating initial values of the layering consolidation degree of each layer with different consolidation time lengths
Figure RE-GDA0002185523940000225
Initial value of layering consolidation degree of each layer with different consolidation duration
Figure RE-GDA0002185523940000226
The results are shown in Table 2.3, calculated by formula (13).
TABLE 2.3 initial values of degree of consolidation for different consolidation durations
Figure RE-GDA0002185523940000227
Figure RE-GDA0002185523940000228
And (5) different layering average consolidation degrees exist for different consolidation time lengths t.
(5.1) calculating the average consolidation degree U of each layer in different time periodsi。
Average consolidation degree of each layeriThe result and the contribution value λ of the degree of consolidation in layers are calculated by the formula (23)iUiAre listed in table 2.4.
TABLE 2.4 average consolidation level U in layers for different consolidation durationsiList of
Figure RE-GDA0002185523940000231
(5.2) calculating the contribution lambda of the layered consolidation degree in different time periodsiUi。
The results of the calculations are shown in Table 2.5.
TABLE 2.5 layered consolidation contribution lambda for different consolidation durationsiUiList of
Figure RE-GDA0002185523940000232
(5.3) calculating the total average consolidation degree of the whole layer at different time periods
Figure RE-GDA0002185523940000233
The results are shown in Table 2.6.
TABLE 2.6 Overall average consolidation for different consolidation durations
Figure RE-GDA0002185523940000234
Fig. 7 shows a graph obtained by plotting the hierarchical method of the present invention and the results of calculations such as the domestic conventional simplification method, Hart method, xiekang and improvement method, and the Lagrange interpolation method enriched in Yan. As can be seen, prior to consolidation
Figure RE-GDA0002185523940000241
The curve of the method is very close to the curves of the domestic common simplified method, Hart method, Xikang and improved method and the like, and reaches the middle stage of consolidation
Figure RE-GDA0002185523940000242
The curve of the method is relatively close to the curves of the domestic common simplified method, Yan rich Lagrange interpolation method and the like
Figure RE-GDA0002185523940000243
The curve of the method is closer to the curve of the domestic common simplified method. When in use
Figure RE-GDA0002185523940000244
The curve of the method is at the top of all the curves and almost coincides with the curve of the domestic common simplified method. Therefore, the method for calculating the consolidation degree of the layered foundation can completely meet the design requirement.
It will be appreciated by those skilled in the art that the invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The embodiments disclosed above are therefore to be considered in all respects as illustrative and not restrictive. All changes which come within the scope of or equivalence to the invention are intended to be embraced therein.

Claims (8)

1. A method for calculating the consolidation degree of a layered foundation, which is characterized by comprising the following steps:
dividing the whole compression layer into a plurality of layers according to the natural layer, calculating the drainage distance of each layer and the vertical consolidation coefficient of the whole path, and obtaining drainage parameters;
obtaining an initial value of the layering consolidation degree of each layer according to the drainage parameters;
calculating a layered final sedimentation value and an entire layer final sedimentation value, and obtaining a layered stress reduction coefficient and a layered contribution rate;
obtaining the average layering consolidation degree according to the initial layering consolidation degree value and the stress reduction coefficient of layering;
obtaining a layering consolidation degree contribution value according to the layering average consolidation degree and the layering contribution rate;
and calculating the sum of the contribution values of the layering consolidation degrees to obtain the total average consolidation degree of the whole layering of the layered foundation.
2. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the drainage distance HiCalculated using the formula:
Figure FDA0002127892960000011
the seepage movement of water in the soil from the bottom surface of the ith layer to the top surface of the compression layer should includeDistance of water discharge HiAll layers within; h ismIs the layer thickness of the mth soil layer in the unit of m.
3. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the full path vertical consolidation coefficient
Figure FDA0002127892960000012
The calculation method comprises the following steps:
calculating to distinguish a vertical well layer and a downhole layer, wherein when the ith layer is positioned in the vertical well layer:
Figure FDA0002127892960000021
cvmis the vertical consolidation coefficient of the m-th layer of soil, hmIs the thickness of the mth layer of soil;
when the ith layer is in the downhole layer:
calculating the composite vertical consolidation coefficient of each layer in the vertical well layer;
the vertical consolidation coefficient of the vertical shaft and the vertical consolidation coefficient of the soil between the vertical shafts are equivalent to composite vertical consolidation coefficients of all layers by adopting an area ratio method, and the composite vertical consolidation coefficients are calculated by the following formula:
cwsi＝[1+μ(vi-1)]×cvi；
in the formula: c. CwsiComposite vertical consolidation coefficient in cm for ith layer2S; mu is the ratio of the cross section area of the vertical well to the cross section area of the single well influence range, and has no dimension, mu is Aw/A；viIs the ratio of the vertical consolidation coefficient of the vertical shaft to the vertical consolidation coefficient of the soil between the ith layering well, v is zero dimensioni＝cw/cvi；
In the formula: a. thewIs the cross-sectional area of the shaft in m2(ii) a A is the cross-sectional area of the single-well influence range and the unit m2；cwIs vertical consolidation coefficient of vertical shaft, unit cm2/s；cviIs the vertical consolidation coefficient of the soil between the ith layering wells in cm2/s；
Full path vertical consolidation coefficient of each layer in underground layer
Figure FDA0002127892960000022
Calculated using the formula:
Figure FDA0002127892960000023
in the formula: c. CwsmIs the composite vertical consolidation coefficient of the mth layer in the vertical well layer in unit of cm2/s；cvmIs the vertical consolidation coefficient of the m-th layer soil in the underground layer in unit of cm2S; w is the serial number of the soil layer of the lowest layer of the vertical shaft layer, and the dimension is zero; w +1 is the serial number of the uppermost soil layer in the underground layer, and has no dimension.
4. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the method for calculating the initial value of the layering consolidation degree comprises the following steps:
the initial value of the layered consolidation degree of the ith layer is that the ith layer in the foundation is regarded as the whole layer, when the ground pre-pressing load is applied, the stress generated in the layer is assumed to be equal to the ground pre-pressing load from top to bottom, the consolidation degree is calculated by using a general expression, and the initial value of the layered consolidation degree of the ith layer is obtained:
Figure FDA0002127892960000031
in the formula:
Figure FDA0002127892960000032
the initial value of the layering consolidation degree of the ith layering is dimensionless; alpha is a parameter, alpha-pi2/8；βiParameters for the ith tier:
when the stratification is in a shaft layer:
Figure FDA0002127892960000033
when the stratification is in the downhole layer:
Figure FDA0002127892960000034
in the formula: c. ChiIs the radial consolidation coefficient of soil, cm2/s；
Figure FDA0002127892960000035
Is the vertical consolidation coefficient of the soil; hiThe drainage distance of the ith soil layer is cm; t is consolidation duration in units of s; fiParameters related to the well diameter ratio, well resistance and smearing influence of the ith layer are defined;
when an ideal well: fi＝Fn；
When a non-ideal well: fi＝Fn+Fsi+Fri；
Wherein: fnThe well diameter ratio factor is used, all layers in the vertical well layer are the same, and the calculation is carried out according to the following formula:
Figure FDA0002127892960000041
when the well diameter ratio is nwWhen F is not less than 15nCan be simplified as follows:
Fn＝ln(nw)-0.75；
Fsireflecting the influence of the i-th layer smearing disturbance, and calculating according to the following formula:
Figure FDA0002127892960000042
Si＝dsi/dw；
in the formula: k is a radical ofhi、ksiRespectively the permeability coefficients of the i-th layer of undisturbed soil and the soil in the smearing area, cm/s; dwIs the diameter of the vertical shaft, cm; dsiIs the diameter of the smearing area, cm; siDiameter d of application area of ith layersiDiameter d of shaftwThe ratio of (a) to (b),taking the S value as 2-3, taking the low value for medium sensitive cohesive soil, and taking the high value for high sensitive cohesive soil;
Frireflecting the well resistance effect of the ith layer, calculating according to the following formula:
Figure FDA0002127892960000043
Figure FDA0002127892960000044
in the formula: hiThe drainage distance of the ith layer is cm; k is a radical ofwIs the vertical shaft permeability coefficient, cm/s; q. q.swFor water flow of vertical shaft, cm3/s；rwIs the radius of the cross section of the shaft, cm.
5. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the calculation method of the layering average consolidation degree comprises the following steps:
multiplying the initial value of the lamination consolidation degree by the stress reduction coefficient of the corresponding lamination, and multiplying the stress reduction coefficient omega of the ith lamination by the stress reduction coefficient of the corresponding laminationiCalculated using the formula:
Figure FDA0002127892960000051
in the formula: z is a radical ofi、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the ith layer of soil and the (i-1) th layer of soil;
Figure FDA0002127892960000052
Figure FDA0002127892960000053
calculating the average additional stress coefficient from the foundation bottom surface to the bottom surface of the i-th layer of soil and the i-1 st layer of soil; h isiIs the thickness of the ith layer of soil, m.
6. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the calculation method of the contribution value of the layering consolidation degree comprises the following steps:
hierarchical contribution ratio λ of ith hierarchyiCalculated using the formula:
Figure FDA0002127892960000054
multiplying the layering average consolidation degree by the corresponding layering contribution rate to obtain a layering consolidation degree contribution value;
in the formula: siIs the final sedimentation value of the ith layer; si' is the deformation value of the ith layer calculated according to the layer summation method, and the unit is cm; s' is the deformation value of the whole layer calculated according to the layering summation method; sfIs the final sedimentation value of the whole layer, unit cm; psisAnd (4) calculating an empirical coefficient by sedimentation.
7. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the calculation method of the layered final sedimentation value is as follows:
layering final sedimentation value:
Figure FDA0002127892960000055
p0for additional pressure acting at the base bottom surface; esiThe compressive modulus of the i-th layer of soil below the bottom surface of the foundation;
Figure FDA0002127892960000061
calculating the average additional stress coefficient from the foundation bottom surface to the bottom surface of the i-th layer of soil and the i-1 st layer of soil; z is a radical ofi、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the ith layer of soil and the (i-1) th layer of soil.
8. The method for calculating the consolidation degree of a layered foundation according to claim 1, wherein: the final sedimentation value s of the whole layerfThe calculation method of (2) is as follows:
final sedimentation value of the whole layer:
Figure FDA0002127892960000062
p0for additional pressure acting at the base bottom surface; esiThe compressive modulus of the i-th layer of soil below the bottom surface of the foundation; psisCalculating an empirical coefficient by settlement;
Figure FDA0002127892960000063
calculating the average additional stress coefficient from the foundation bottom surface to the bottom surface of the i-th layer of soil and the i-1 st layer of soil; z is a radical ofi、zi-1The distance from the bottom surface of the foundation to the bottom surfaces of the ith layer of soil and the (i-1) th layer of soil; n is the total number of layers in the whole layer.
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