CN111898176A - Method for calculating consolidation degree under layered foundation gradual loading condition - Google Patents

Method for calculating consolidation degree under layered foundation gradual loading condition Download PDF

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CN111898176A
CN111898176A CN201910628350.5A CN201910628350A CN111898176A CN 111898176 A CN111898176 A CN 111898176A CN 201910628350 A CN201910628350 A CN 201910628350A CN 111898176 A CN111898176 A CN 111898176A
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layer
consolidation
calculating
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coefficient
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CN111898176B (en
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陆伟岗
朱晶晶
刘益平
任亚群
韦华
陈念军
周伟
王志楠
何小飞
沈锦儒
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Jiangsu Keneng Geotechnical Engineering Co ltd
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    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
    • E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
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Abstract

The invention discloses a method for calculating consolidation under the condition of gradual loading of layered foundations, which adopts multi-stage instant loading, calculates the consolidation of each layered foundation step by step without adopting a deep and complex mathematical method, only needs to be operated by a common mathematical method, can finish calculation by using an electronic form, has small workload and meets the design requirement in precision, and can be proved by an example that the consolidation of the multi-layered foundations under the condition of gradual loading is calculated by a layered method, and the precision of the result completely meets the design requirement.

Description

Method for calculating consolidation degree under layered foundation gradual loading condition
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 consolidation degree of a layered foundation under a gradual loading condition.
Background art:
for the calculation of the consolidation degree of the surcharge preloading reinforcement soft foundation under the gradual loading condition, a sand base correction method and an improved handsome method can be adopted. When the method is used for multi-layer foundation, the average index method or the equivalent thickness method is still adopted to calculate according to a single soil layer. The method can simplify the calculation of the average consolidation degree of the whole soil layer, but cannot calculate the consolidation degree, the layered settlement and other results of each soil layer. 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 method for calculating the consolidation degree under the condition of gradual loading of a layered foundation, so as to solve the defects in the prior art.
A method for calculating the consolidation degree of a layered foundation under the condition of gradual loading, which comprises the following steps:
dividing the compression layer into a plurality of layers, and calculating the drainage distance and the vertical consolidation coefficient of the whole path of each layer;
loading the layering, and calculating to obtain a load ratio and an actual consolidation duration;
calculating the layering stress reduction coefficient and the layering contribution rate of each layer;
obtaining an initial value of the layered consolidation degree according to the load ratio and the actual consolidation duration;
obtaining a layering average consolidation degree contribution value according to the layering consolidation degree initial value, the layering contribution rate and the layering stress reduction coefficient;
and accumulating the contribution values of the average consolidation degrees of all the layers to obtain the total average consolidation degree of the whole layer.
Preferably, the method for calculating the drained water distance and the full-path vertical consolidation coefficient comprises the following steps:
distance of water discharge HiIs the distance from the bottom surface of the layer to the top surface of the compression layer:
Figure RE-GDA0002185527190000021
full path vertical consolidation coefficient: the calculation requires distinguishing between the vertical layer and the sub-well layer.
When the ith zone is located in a shaft zone:
Figure RE-GDA0002185527190000022
in the formula: c. 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 a vertical shaftThe ratio of the cross-sectional area to the cross-sectional area of the single well influence range is dimensionless, 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 RE-GDA0002185527190000031
Calculated using the formula:
Figure RE-GDA0002185527190000032
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 loading method comprises the following steps:
the method adopts a multi-level instant application mode, and changes the load linearly applied for many times into k-level instant application;
all levels of load values are respectively delta p1，Δp2……，Δpj，……，Δpk。
Preferably, the calculation method of the load ratio and the actual consolidation duration comprises the following steps:
the load ratio is as follows:
load ratio eta of j-th loadjCan be calculated by：
ηj＝Δpj/p
In the formula: Δ pjThe j-th load value is expressed in kPa, and p is the final stacking value expressed in kPa.
Actual consolidation duration:
let the moment when the pre-pressing ends be TzThe time difference between the load application time of each level and the delay of the stacking start time is t1，t2,……，tj，……，tk；
Consolidation duration T for class j loadjCan be calculated using the following formula:
Tj＝Tz－tj
preferably, the method for calculating the delamination stress reduction coefficient and the delamination contribution rate includes the following steps:
the delamination stress reduction coefficient:
Figure RE-GDA0002185527190000041
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-GDA0002185527190000042
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, m.
The layering contribution rate:
Figure RE-GDA0002185527190000043
s' is the foundation deformation calculated by the layer summation method, si' amount of deformation, psi, of the i-th foundation calculated by the layer-by-layer summation methodsCalculation of empirical coefficient of Settlement, sifIs the final sedimentation value of the ith layer in cm, sfAnd the unit cm is the final sedimentation value of the whole layer, and n is the total number of the layering layers in the whole layer.
Preferably, the method for calculating the initial value of the layered consolidation degree comprises the following steps:
when the pre-pressing is finished, and the consolidation duration is TzIn time, the initial value of the layered consolidation degree of the ith layer foundation
Figure RE-GDA0002185527190000051
Figure RE-GDA0002185527190000052
In the formula:
Figure RE-GDA0002185527190000053
the initial value of the layering consolidation degree of the ith layering is dimensionless; etajThe load ratio of the j level load is dimensionless; α is a coefficient, α ═ π2/8；βiIs the coefficient of the ith layer, TzAt the end of the pre-compression, the unit d, tjDelay time difference of j-th load, unit d; k is the last stage of the grading load without dimension.
When the initial value of the layered consolidation degree of the ith layered foundation at a certain time T in the preloading process is calculated
Figure RE-GDA0002185527190000054
Figure RE-GDA0002185527190000055
In the formula: xi is the grade serial number of the last grade load in the T moment.
Preferably, the method for calculating the layered average consolidation degree contribution value comprises the following steps:
calculating to obtain the layered average consolidation degree U of the i-th layer of foundationi：
Figure RE-GDA0002185527190000056
Average consolidation degree U of each layeriMultiplying the layered contribution ratio lambdaiTo obtain the ith layerThe value of the contribution of the degree of consolidation in layers.
The invention has the advantages that: the method fills the content of calculating the consolidation degree of the multilayer foundation under the condition that the existing specification does not have gradual loading.
(1) The invention adopts a grading instant loading method. The calculation of the consolidation degree of the multilayer foundation under the condition of gradual loading is solved. The existing theory and formula of the layering method can be applied only by processing the load, and the solution with enough precision can be obtained by simple operation by using the Excel spreadsheet, thereby greatly simplifying the calculation process.
(2) The layered foundations are layered according to natural layers, and each layer is a homogeneous foundation, so that the problem of the multilayer foundations is converted into the problem of the homogeneous foundations.
(3) The method can calculate not only the total average consolidation degree of the whole layer, but also the consolidation degree of each layer, and also the average consolidation degree of any combination layer, such as a vertical well layer or a downhole layer.
Drawings
FIG. 1 is a flow chart of the consolidation degree calculation method under the condition of gradual loading of a multi-layer 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 diagram of a time course curve of multiple linear uniform loads according to the present invention.
FIG. 4 is a schematic diagram of a multi-stage instantaneous loading time course curve according to the present invention.
Fig. 5 is a cross-sectional view of an embankment construction according to embodiment 1 of the present invention.
FIG. 6 is a schematic diagram of a multi-stage transient loading time course curve according to embodiment 1 of the present invention.
FIG. 7 is a vertical cross-sectional view of a single well consolidation model according to example 2 of the present invention.
FIG. 8 is a graph of the actual and calculated loading time courses for inventive example 2.
FIG. 9 is a comparison of the solution of the present invention with other approximate solutions of the present invention in accordance with example 2 of the present invention.
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 consolidation degree under gradual loading condition of a layered foundation includes the following steps:
(1) and dividing the compression layer into a plurality of layers according to the rule of a layering method, and calculating the drainage distance and the vertical consolidation coefficient of the whole path of each layer. And calculating the layering contribution rate and the layering stress reduction coefficient of each layer.
(2) The preloading under the gradual loading condition has two load applying modes. The two load application modes are as follows: multiple linear uniform loading (fig. 3) and multiple instant application (fig. 4).
Firstly, in a linear and uniform loading mode, the preset load value can be reached after several days of loading each time, and a slope is displayed on a loading time course curve graph; and maintaining for several days after one stacking application, applying the next stacking again, and repeating the steps until the maintenance is finished. When the load is applied for many times, a plurality of oblique lines exist on a load time course curve chart, the loading rate of each time is different, and the slope of the oblique lines is different.
And secondly, a multi-stage instant application mode, wherein the application of each stacking is finished instantly, and a stepped graph is displayed on a loading time course curve chart.
The invention adopts a multi-stage instant application mode to replace a multi-time linear uniform loading mode. Fig. 4 is a graph showing the load time course of the instant load.
(3) The multi-stage instant application mode is as follows: the load applied linearly for multiple times is changed into k-level instant application. All levels of load values are respectively delta p1，Δp2……，Δpj，……，Δpk. Calculating the ratio of the load of each stage to the final load, called as the load ratio, and the load ratio eta of the j-th stage loadjCan be calculated using the following formula:
ηj＝Δpj/p (1)
in the formula: Δ pjThe value is the j-level load value, and the value is the final stacking value, namely kPa;
obviously, the consolidation duration of the 1 st stage load is longest, and the consolidation duration T of the later stages of loadsjAnd gradually shortened.
Let the moment when the pre-pressing ends be TzThe time difference between the load application time of each level and the delay of the stacking start time is t1，t2,……，tj，……，tm. Consolidation duration T for the jth loadjCan be calculated using the following formula:
Tj＝Tz－tj(2)
when the consolidation duration is T, the initial value of the layered consolidation degree of the ith layer of foundation
Figure RE-GDA0002185527190000081
Figure RE-GDA0002185527190000082
In the formula: xi is the serial number with the maximum load of each stage in the T time;
Figure RE-GDA0002185527190000083
and the grade value is the initial value of the layered consolidation degree of the jth grade load of the ith layer of foundation. Calculated using the formula:
Figure RE-GDA0002185527190000084
when the pre-pressing is finished, the consolidation duration is TzIn time, the initial value of the layered consolidation degree of the ith layer foundation
Figure RE-GDA0002185527190000085
Figure RE-GDA0002185527190000086
(1) Average layering consolidation degree U of ith foundationiCalculated by the following formula;
Figure RE-GDA0002185527190000087
(2) the contribution value of the layered consolidation degree of the i-th layer foundation is the average consolidation degree Uit of each layer multiplied by the contribution rate lambda of each layeri；
(3) The total average consolidation degree of the whole layer is the sum of the contribution values of the consolidation degrees of all the layers;
Figure RE-GDA0002185527190000088
(4) when the grading load is delta pjThe precision can be obtained when the pressure is less than or equal to 24 kPa.
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).
The soft foundation engineering of the dike (see figure 5) adopts a bagged sand well for treatment, the soil layer thickness is 20m, 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 secondary constant velocity load as shown in figure 3. Finding TzAverage consolidation of soil layer at 120d (without considering well resistance and smearing effect).
The calculation method 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) this example is a complete well foundation, with only 1 layer, a single soil texture, layer thickness of 20 m.
(1.2) shaft floor parameters
Diameter d of sand wellw＝7cm
Equivalent diameter d of shafte＝1.05×1.4＝1.47m
Shaft depth hw＝20m
Step (2)
(2.1) in this example, there are only 1 segment whose segment contribution λ is 1.0;
(2.2) it is assumed that the stress in the earth is uniform. The delamination stress reduction factor ω is 1.0.
Step (3) drawing a load time course curve chart
(3.1) the original quadratic linear uniform loading is replaced by 6-stage instantaneous loading, which is shown in figure 6.
And (3.2) determining the load values, the load ratios, the delay time difference and the consolidation duration of all levels, wherein the values are listed in the table 1.1.
TABLE 1.1 load parameter Table
Figure RE-GDA0002185527190000101
And calculating the grading value of the initial value of the layering consolidation degree of each layer in different consolidation time lengths by using a general expression induced by professor Zeng national longevity. The method specifically comprises the following substeps:
(3.3) calculating the drainage distance H of each layeriFull path vertical consolidation coefficient
Figure RE-GDA0002185527190000102
And the coefficients a are listed in table 1.2.
TABLE 1.2 drainage distance HiFull path vertical consolidation coefficient
Figure RE-GDA0002185527190000103
And coefficient alpha list
Figure RE-GDA0002185527190000104
Figure RE-GDA0002185527190000105
(3.4) calculating the grading value of the initial value of the layering consolidation degree of each layer with different consolidation time lengths
Figure RE-GDA0002185527190000106
The grade values of the initial values of the layered consolidation for the layers of different consolidation durations are calculated by equation (4), and the results are shown in Table 1.3.
TABLE 1.3 rating of initial values of consolidation for layers at different consolidation durations
Figure RE-GDA0002185527190000107
Figure RE-GDA0002185527190000108
Figure RE-GDA0002185527190000111
(3.5) calculating the initial value of the degree of consolidation in layers
Figure RE-GDA0002185527190000112
Figure RE-GDA0002185527190000113
And (4) calculating the average layering consolidation degree and the average total consolidation degree of the whole layer.
Since the layer separation contribution ratio λ is 1.0 and the layer separation stress reduction coefficient ω is 1.0 in this example, the layer separation average consolidation degree and the entire layer total average consolidation degree are equal to 0.9347.
Table 1.4 is a comparison of the results of the calculations of the present invention with the results of the taisha-based correction method, the modified handsome method. It can be seen that the calculation results of the method of the present invention are completely consistent with the calculation results of the taishaji correction method and the improved handsome method.
TABLE 1.4 comparison table of results calculated by three methods
Name of method Hair brushMing dynasty Method for correcting space base Improved method for handsome
Total average degree of consolidation 0.93 0.93 0.93
Example 2: the example is taken from engineering calculation example in Yan rich Lagrange interpolation solution for consolidation of layered and unbroken sand well foundation-overload prepressing consolidation test of soft foundation of field way in Zhoushan airport
The test area was 78m × 120m, and the soil layer parameters of the test site are given in table 2.1. The test adopts the surcharge preloading treatment of the bagged sand well, the diameter of the sand well is 7cm, the distance between the sand wells is 1.4m, the sand well is arranged in a regular triangle, and the sand well is 20m long.
TABLE 2.1 soil layer parameter Table
Figure RE-GDA0002185527190000114
Figure RE-GDA0002185527190000121
FIG. 7 shows a vertical cross-section of the single well consolidation model of the present case. The invention provides a method for calculating the consolidation degree of a layered foundation under the condition of gradual loading, which comprises the following steps:
and (1) designing and calculating various parameters required by geotechnical engineering data according to the preloading scheme. The method specifically comprises the following substeps:
(1.1) shaft parameters
The following parameters were calculated from the size and spacing and shape of the sand wells in the plan layout:
diameter d of sand wellw＝7cm
Equivalent diameter d of shafte＝1.47m
Shaft depth hw＝20m
(1.2) calculation of consolidation coefficients for the layers (see Table 2.1)
(1.3) calculating parameters of well resistance and smearing effect influence
Well diameter ratio nw＝de/dw＝21.0
Well diameter ratio factor Fn＝2.295
Let S be ds/dw＝2.0
Suppose Kh/KsSmearing effect F ═ 2s＝0.693
The remaining parameters are listed in table 2.2.
Table 2.2 summary of coefficients of floors in shaft
Figure RE-GDA0002185527190000131
(1.4) calculating the composite consolidation coefficient of the vertical well layer
Permeability coefficient of sand well is kw＝10×10-5m/s＝8.64m/d
Compression modulus E of sand wells＝12MPa
Vertical consolidation coefficient c of sand wellw＝10580m2/d
Area ratio mu is 1/nw 2＝0.00227
Composite consolidation coefficient cwsi≈10580×0.00227＝27.8m2/d(i＝1、2、3)
Layering according to natural layers; the method specifically comprises the following substeps:
(2.1) the depth of the compressed layer was determined to be 55.0m under the condition that the additional stress was 0.1 times or less the self-weight stress.
(2.2) this example is an incomplete well foundation. The compression layer is divided into two combined layers, a vertical well layer and a downhole layer, by taking the bottom of the drainage well as a boundary.
And (2.3) dividing the vertical well layer and the underground layer according to the natural layer, wherein the vertical well layer comprises 3 layers, and the underground layer comprises 2 layers. Numbered consecutively from top to bottom for a total of 5 layers (see fig. 7).
And (3) 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:
(3.1) calculating the final sedimentation value s of the entire layerc
Compressive modulus equivalent value:
Figure RE-GDA0002185527190000132
because the stacking load is slowly increased and can not exceed the bearing capacity of the foundation all the time, the settlement empirical coefficient psi is calculated by an interpolation method according to GB50007-2011s
Figure RE-GDA0002185527190000141
sf＝1.032×151.7＝156.5cm
(3.2) final sedimentation value s of each layeri' and cumulative Settlement Σ si’
The results are shown in Table 2.3, and none of the values is multiplied by the empirical coefficients of sedimentation.
(3.3) hierarchical contribution ratio λi
The calculations are listed in table 2.3.
(3.4) reduction coefficient of layered stress ωi
The results of the calculations are given in table 2.3.
TABLE 2.3 Segregation si', cumulative Settlement Σ si', layer contribution ratio lambdaiAnd a summary of the reduction factor of the delamination stress
Figure RE-GDA0002185527190000142
Step (4) drawing a loading time course curve, and calculating load values delta p of all levelsjLoad ratio etajDelay time difference tjAnd a consolidation duration Tj。
The sand cushion construction period and the permanent cushion construction period are simplified into a linear loading section, the rest are constant loading sections, and the time course curve of gradual loading is shown as an actual loading time course curve in figure 8. The total number of stacking is 3, the 1 st stacking is applied instantly, the other 2 times are linear uniform loading, the original 2 times linear uniform loading mode is replaced by the 6-level instant loading mode, and a loading time course curve chart is shown in fig. 8. The total stacking duration 781d and the loading parameters are detailed in Table 2.4.
TABLE 2.4 load parameter Table
Figure RE-GDA0002185527190000158
Step (5) calculating the grading value of the initial value of the layering consolidation degree of each layer in different consolidation time lengths by using a general expression induced by professor Zeng national xi
Figure RE-GDA0002185527190000151
The method specifically comprises the following substeps:
(5.1) calculating the composite consolidation coefficient of each layer in the vertical well layer, and calculating the drainage distance H of each layer of the compression layeriComposite consolidation coefficient cwsiFull path vertical consolidation coefficient
Figure RE-GDA0002185527190000152
And exponential coefficients alpha, betai. The results of the calculations are shown in Table 2.5.
TABLE 2.5 drainage spacing HiList of parameters
Figure RE-GDA0002185527190000153
(5.2) calculating the original initial value of the layering consolidation degree of each layer under the condition of gradual loading
Figure RE-GDA0002185527190000154
Initial value of layering consolidation degree of each layer under gradual loading condition
Figure RE-GDA0002185527190000155
By using the formula(4) The results are shown in Table 2.6.
TABLE 2.6 grading values for initial values of the degree of consolidation in layers under gradual loading
Figure RE-GDA0002185527190000156
Figure RE-GDA0002185527190000157
Figure RE-GDA0002185527190000161
(5.3) calculating the initial value of the layering consolidation degree of each layer under the condition of gradual loading
Figure RE-GDA0002185527190000162
Initial value of layering consolidation degree of each layer under gradual loading condition
Figure RE-GDA0002185527190000163
The results are calculated by equation (3) as follows:
layer (1)
Figure RE-GDA0002185527190000164
Layer 2
Figure RE-GDA0002185527190000165
Layer III
Figure RE-GDA0002185527190000166
Layer iv
Figure RE-GDA0002185527190000167
Layer five
Figure RE-GDA0002185527190000168
Step (6) calculating gradual additionAverage consolidation U of the layers under loadiAnd a contribution value lambda of the degree of consolidation in layersiUi。
(6.1) calculating the average consolidation degree U of each layer under the condition of gradual loadingi。
Average consolidation U of each layer under gradual loadingiThe result and the contribution value lambda of the degree of consolidation in layers are calculated by the formula (6)iUiAre listed in Table 2.7.
TABLE 2.7 average consolidation level in layers UiContribution λiUiList of
Figure RE-GDA0002185527190000169
Figure RE-GDA0002185527190000171
(6.2) calculating the total average consolidation degree of the whole layer under the condition of gradual loading
Figure RE-GDA0002185527190000172
Total average consolidation degree of whole layer under gradual loading condition
Figure RE-GDA0002185527190000173
Calculated using equation (7), which is calculated as follows.
Figure RE-GDA0002185527190000174
With the total average consolidation degree of the whole layer
Figure RE-GDA0002185527190000175
Multiplying by the final sedimentation value s of the whole layerfWhen the thickness is 156.5cm, the settlement s of the whole layer at different consolidation time lengths can be obtainedtSee table 2.8.
TABLE 2.8 Whole layer sedimentation value s under gradual loadingt
Setting time t/d 133 267 401 516 565 615 652 781
Total sedimentation value st/cm 9.8 27.2 44.9 62.1 77.5 101.2 119.6 141.2
Fig. 9 shows curves drawn by the results of calculations of the layering method, the handsome correction method, the xikang correction method, and the Lagrange interpolation method of the present invention, and curves drawn by data measured in the field. It should be noted that equivalent methods of the handsome correction method and the xiekang correction method for the value of the drainage distance and the vertical consolidation coefficient are the same as the layering method. As can be seen, the shapes of the 4 curves are comparable, indicating that the values are all relatively close.
Compared with the measured value curve, the settlement of the 4 calculation methods is larger than the measured value before t is 500d, the slope of the curve before t is 400d is smaller than that after t is 500d, and the reason for analyzing that the loading is performed after t is 500d is probably that the simplified loading time course curve of the permanent bedding construction period has larger difference with the actual situation. When the stacking is finished, the load stage is maintained (t is more than or equal to 640d), and the 4 curves are close to the measured value. The loading time course curve after the description is consistent with the actual situation. When t is 781d, the 4 calculated sedimentation values and measured values and errors thereof are shown in table 2.9, and it can be seen from the table that the sedimentation values and measured values of the gau correction method, the xiekang correction method and the layer separation method are all relatively close to each other, the absolute values of the errors are all not enough to be 2%, the error of the Lagrange interpolation method is slightly larger, the absolute value of the error exceeds 5%, and the result of the layer separation method has enough accuracy.
TABLE 2.9 comparison of measured values with sedimentation values calculated by various methods when t 781d
Figure RE-GDA0002185527190000181
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.
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 (10)

1. A method for calculating the consolidation degree of a layered foundation under the condition of gradual loading is characterized by comprising the following steps:
dividing the compression layer into a plurality of layers, and calculating the drainage distance and the vertical consolidation coefficient of the whole path of each layer;
loading the layering, and calculating to obtain a load ratio and an actual consolidation duration;
calculating the layering stress reduction coefficient and the layering contribution rate of each layer;
obtaining an initial value of the layered consolidation degree according to the load ratio and the actual consolidation duration;
obtaining a layering average consolidation degree contribution value according to the layering consolidation degree initial value, the layering contribution rate and the layering stress reduction coefficient;
and accumulating the contribution values of the average consolidation degrees of all the layers to obtain the total average consolidation degree of the whole layer.
2. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 1, wherein: the method for calculating the drainage distance comprises the following steps:
distance of water discharge HiIs the distance from the bottom surface of the layer to the top surface of the compression layer:
Figure FDA0002127892420000011
in the formula: h ismThe unit m, i represents the th layer of the mth layer of soil.
3. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 1, wherein: the full path vertical consolidation coefficient
Figure FDA0002127892420000012
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 FDA0002127892420000013
in the formula: c. 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 FDA0002127892420000021
Calculated using the formula:
Figure FDA0002127892420000022
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.
4. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 1, wherein: the loading method comprises the following steps:
the method adopts a multi-level instant application mode, and changes the load linearly applied for many times into k-level instant application;
all levels of load values are respectively delta p1，Δp2……，Δpj，……，Δpk。
5. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 4, wherein: the calculation method of the load ratio comprises the following steps:
load ratio eta of j-th loadjCan be calculated using the following formula:
ηj＝Δpj/p
in the formula: Δ pjThe j-th load value is expressed in kPa, and p is the final stacking value expressed in kPa.
6. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 4, wherein: the method for calculating the actual consolidation duration comprises the following steps:
let the moment when the pre-pressing ends be TzThe time difference between the load application time of each level and the delay of the stacking start time is t1，t2，……，tj，……，tk；
Consolidation duration T for class j loadjCan be calculated using the following formula:
Tj＝Tz－tj。
7. the method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 1, wherein: the method for calculating the laminated stress reduction coefficient comprises the following steps:
Figure FDA0002127892420000031
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 FDA0002127892420000032
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, m.
8. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 1, wherein: the method for calculating the layering contribution rate comprises the following steps:
Figure FDA0002127892420000033
in the formula: s ' is the foundation deformation, s ' calculated by the layer summation method 'iThe deformation, psi, of the i-th foundation calculated by the layer-by-layer summation methodsCalculation of empirical coefficient of Settlement, sifIs the final sedimentation value of the ith layer in cm, sfAnd the unit cm is the final sedimentation value of the whole layer, and n is the total number of the layering layers in the whole layer.
9. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 7, wherein: the method for calculating the initial value of the layering consolidation degree comprises the following steps:
when the pre-pressing is finished, and the consolidation duration is TzIn time, the initial value of the layered consolidation degree of the ith layered foundation
Figure FDA0002127892420000034
Figure FDA0002127892420000035
In the formula:
Figure FDA0002127892420000036
the initial value of the layering consolidation degree of the ith layering is dimensionless; etajThe load ratio of the j level load is dimensionless; α is a coefficient, α ═ π2/8；βiIs the coefficient of the ith layer, TzAt the end of the pre-compression, the unit d, tjThe delay time difference of the j-th level load is shown, and the unit d and k are the last level of the graded load without dimension;
when the initial value of the layered consolidation degree of the ith layered foundation at a certain time T in the preloading process is calculated
Figure FDA0002127892420000037
Figure FDA0002127892420000038
In the formula: xi is the grade serial number of the last grade load in the T moment.
10. The method for calculating the consolidation degree under the condition of gradual loading of the layered foundation as claimed in claim 9, wherein: the method for calculating the layered average consolidation degree contribution value comprises the following steps:
calculating to obtain the layered average consolidation degree U of the i-th layer of foundationi：
Figure FDA0002127892420000041
Average consolidation degree U of each layeriMultiplying the layered contribution ratio lambdaiAnd obtaining the contribution value of the layered consolidation degree of the ith layer.
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