CN112966320B - Loess unloading collapse amount calculation method - Google Patents
Loess unloading collapse amount calculation method Download PDFInfo
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Abstract
The invention discloses a loess unloading collapsibleThe calculation method of the quantity comprises the following steps: step 1: calculating to obtain a collapsible completion ratio eta reflecting the degree of collapse of loess when unloading occurs 1 Calculating an unloading stress ratio K reflecting the reduction amplitude of the vertical pressure when the unloading action occurs in the loess collapse process, and step 2: by applying the wet-out completion ratio eta 1 The unloading stress ratio K calculates the unloading collapse coefficient delta us Step 3: by unloading the coefficient of collapse delta us Calculating loess modulus reduction coefficient Z under unloading condition u Step 4: calculating loess unloading collapse amount according to the loess modulus reduction coefficient under the unloading condition; the invention utilizes the modulus folding method of unloading effect, fully considers the actual stress change condition in the loess collapse process between piles, and develops the modulus folding coefficient Z under different unloading conditions u The stress change in the loess collapsible sinking between piles is caused to be consistent with the actual working condition, the unloading collapsible effect is successfully introduced into the loess collapsible deformation calculation between piles, the calculation flow is simple, and the loess collapsible deformation calculation result between piles is reasonable.
Description
Technical Field
The invention belongs to the field of loess unloading collapse amount calculation methods, and particularly relates to a loess unloading collapse amount calculation method.
Background
Because of the complexity of the loess collapsibility problem, the existing loess collapsibility evaluation method is not suitable for unloading collapsibility working conditions, and the unloading collapsibility working conditions refer to working conditions with unloading effect in the loess collapsibility deformation process of test pits, pipe ditches, inter-pile soil and the like. Because of the defect of loess collapsibility evaluation research under the unloading collapsibility working condition, quantitative analysis and prediction of the unloading collapsibility are difficult, a collapsibility calculated value obtained by simply applying an existing constant load condition loess collapsibility evaluation method is greatly different from an actual measurement value, so that the collapsibility calculated value analysis result is poor in reliability, engineering practice is difficult to guide, engineering diseases are frequently caused, or a too conservative engineering treatment method is adopted under a cautious principle, so that great waste is caused. Therefore, it is urgent how to scientifically and rapidly perform loess collapse amount calculation analysis with respect to the unloading collapse condition.
At present, the loess collapse amount calculating method includes a calculation and analysis method and a field pit immersion test method. The calculation analysis method calculates the loess collapse amount based on the constant pressure collapse coefficient measured in the indoor test. The field test pit immersion test method actually measures loess collapsible amount by excavating the immersion test pit, but the field test pit immersion test is high in cost, long in period and difficult to be adopted in a large amount, and the realization of the loess collapsible evaluation by the indoor test is still a main means, so that an accurate and rapid loess unloading collapsible amount calculating method is needed on the basis of the loess indoor unloading collapsible test, and the calculated loess collapsible amount is more approximate to an actual measured value.
Disclosure of Invention
The invention aims to provide a loess collapse amount calculating method, which aims to solve the problems that the existing calculating method is high in cost, and the influence of an unloading effect on the loess collapse process is ignored, so that the calculated value is larger.
The invention adopts the following technical scheme: a loess unloading collapse amount calculating method comprises the following steps:
step 1: calculating to obtain a collapsible completion ratio eta reflecting the degree of collapse of loess when unloading occurs 1 ,
Calculating to obtain unloading stress ratio K reflecting the reduction amplitude of vertical pressure when unloading action occurs in loess collapse process,
step 2: by applying the wet-out completion ratio eta 1 The unloading stress ratio K calculates the unloading collapse coefficient delta us ,
Step 3: by unloading the coefficient of collapse delta us Calculating loess modulus reduction coefficient Z under unloading condition u Wherein Z is calculated u The formula of (2) is:
Z u =0.001p 1 -0.512δ us -0.012,
wherein: p is p 1 Is the initial pressure (kPa);
step 4: and calculating loess unloading collapse amount according to the loess modulus reduction coefficient under the unloading condition.
Further, η is calculated in step 1 1 The formula of (2) is:
wherein: s is S 1 For the sample before unloading takes place at pressure p 1 The amount of collapse (mm) completed under action; s is testSample at pressure p 1 Total wet out (mm) under action.
Further, the formula for calculating K in the step 1 is that,
wherein: p is p 1 Is the initial pressure (kPa); Δp is the vertical pressure (kPa) that the sample is unloaded when unloading occurs during collapse; p is p r Is the vertical pressure (kPa) remaining after the sample is unloaded during the collapse.
Further, delta is calculated in step 2 us The formula of (2) is:
δ us =δ s [1-(1-η 1 )(1-1.067K 1.695 )],
wherein: delta s Is the collapsible coefficient of the undisturbed loess.
Further, the loess unloading collapsible amount delta is calculated in the step 4 us The formula of (2) is:
wherein Δp i Adding average additional stress generated by volume weight in the ith layer of soil to the yellow soil body in the loess collapse process; alpha is a correction coefficient of the collapsible deformation modulus, and 1.1 to 1.5 is taken; e (E) 0i A deformation modulus (MPa) before immersing and collapsing the ith layer of collapsible loess; h i Is the thickness of the i-th layer collapsible loess.
The beneficial effects of the invention are as follows: the invention utilizes the modulus folding method of unloading effect, fully considers the actual stress change condition in the loess collapse process between piles, and develops the modulus folding coefficient Z under different unloading conditions u The stress change in the loess collapsible sinking between piles is caused to be consistent with the actual working condition, the unloading collapsible effect is successfully introduced into the loess collapsible deformation calculation between piles, the calculation flow is simple, and the loess collapsible deformation calculation result between piles is reasonable.
Drawings
FIG. 1 is a schematic diagram of the loess test pit soaking unloading wet collapse condition of the present invention;
FIG. 2 is a schematic diagram of loess unloading and collapsing conditions among piles according to the present invention;
FIG. 3 is a comparison of calculated soil collapsible amounts between piles according to the method for calculating different loess collapsible amounts of the present invention;
FIG. 4 is a schematic diagram of unload wet collapse according to the present invention;
FIG. 5 is a schematic diagram of the unload wet out test procedure of the present invention;
FIG. 6 is a diagram of eta of the present invention 2 /(1-η 1 ) A relationship curve with K;
FIG. 7 is a graph showing the trend of the test influencing factor indicators according to the present invention;
FIG. 8 shows delta of the present invention us Calculating a comparison curve with the test result;
FIG. 9 is a graph showing the calculation of the collapsible amount of undisturbed loess by modulus folding and subtracting method according to the present invention;
FIG. 10 shows delta of the present invention s Schematic diagram of the relationship with Z;
FIG. 11 is a graph showing the comparison of the calculated loess unloading collapsible amount and the actual measured value;
FIG. 12 is a view showing a loess deformation modulus reduction coefficient determining method under the unloading collapsing condition in accordance with the present invention;
FIG. 13 is a result of verifying deterioration of loess collapsible amount by modulus folding and subtracting method of the present invention;
FIG. 14 is a graph showing the comparison of calculated and measured values of the side friction of loess unloading collapsible piles among ZH4 piles according to the present invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a loess unloading collapse amount calculating method, which comprises the following steps:
step 1: calculating to obtain a collapsible completion ratio eta reflecting the degree of collapse of loess when unloading occurs 1 Calculating eta 1 The formula of (2) is:
wherein: s is S 1 For the sample before unloading takes place at pressure p 1 The amount of collapse (mm) completed under action; s is the pressure p of the sample 1 Total wet out (mm) under action.
The unloading stress ratio K reflecting the reduction amplitude of the vertical pressure when the unloading action occurs in the loess collapse process is calculated, the formula for calculating K is as follows,
wherein: p is p 1 Is the initial pressure (kPa); Δp is the vertical pressure (kPa) that the sample is unloaded when unloading occurs during collapse; p is p r Is the vertical pressure (kPa) remaining after the sample is unloaded during the collapse.
Step 2: by applying the wet-out completion ratio eta 1 The unloading stress ratio K calculates the unloading collapse coefficient delta us Calculate delta us The formula of (2) is:
δ us =δ s [1-(1-η 1 )(1-1.067K 1.695 )]
wherein: delta s Is the collapsible coefficient of the undisturbed loess.
Step 3: by unloading the coefficient of collapse delta us Calculating loess modulus reduction coefficient Z under unloading condition u Calculate Z u The formula of (2) is:
Z u =0.001p 1 -0.512δ us -0.012
wherein: p is p 1 Is the initial pressure (kPa).
Step 4: calculating loess collapse amount according to loess modulus reduction coefficient under unloading condition, and calculating loess collapse amount delta us The formula of (2) is:
wherein Δp i Increasing the volume of yellow soil body in loess collapse processThe average additional stress generated in the ith layer of soil is heavy; e (E) si The compression modulus of the collapsible loess of the i-th layer; h i Is the thickness of the i-th layer collapsible loess.
Wherein:
E si =αE' 0
wherein, alpha is a correction coefficient of the collapse deformation modulus, and 1.1 to 1.5 are taken.
Wherein E is 0 Deformation modulus (MPa) of the clay before wet sinking; e (E) 0 ' is the deformation modulus (MPa) of the bentonite after wet-sinking; z is Z u To reduce the modulus of loess under unloading condition,
according to
Z u =0.001p 1 -0.512δ us -0.012
The formula for calculating loess unloading collapse amount by using loess modulus reduction coefficient is as follows:
namely:
wherein alpha is a correction coefficient of the collapse deformation modulus, and 1.1 to 1.5 is taken; e (E) 0i The deformation modulus (MPa) of the ith layer before the collapsible loess is immersed in water.
The present loess collapse conditions and reasons for considering the loess collapse process unloading effect, as well as verification tests, are set forth below.
1. Loess unloading and collapsing conditions
As shown in fig. 1, in the loess test pit immersion test, under the influence of a seepage funnel, collapsible soil distribution and boundary effect, the soil layer from the center to the outer edge of the test pit forms a staggered platform due to non-uniform collapsible deformation, when the self-weight stress of the soaked loess soil layer cannot overcome the perimeter resistance, the collapsible soil layer around the test pit is incomplete or even not collapsible, the relative displacement of the non-uniform collapsible soil body can cause frictional resistance, and the effect can inhibit the development of collapsible deformation caused by the immersion of loess.
The soil layer is subjected to an initial stress p 1 The soil body in the pit is immersed in water to sink, and vertical stress applied to the soil body is converted from p in the sinking process due to the difference of sinking amount and the action of friction resistance tau of surrounding soil body 1 Reduced to p r The larger the collapse deformation amplitude is, the larger the vertical stress reduction amplitude is. The phenomenon is similar to that loess is subjected to a dragging effect in the vertical direction in the process of collapsing, the reduction of the vertical stress of the soil body in the process of collapsing can be called as unloading effect, and the soil body stress in the process of collapsing is subjected to the unloading effect to be redistributed.
For another example, the self-weight collapsible loess field plain concrete pile composite foundation has smaller pile distance because the stress state and the collapsible characteristics of the loess soaking and collapsing process between piles are different from those of a natural field, and the loess (shown in fig. 2) between piles is influenced by the sharing effect of the piles and the negative friction of the pile sides in the loaded soaking process, has different stress distribution from that of a common soil layer, and has the accompanying process of unloading and collapsing.
2. Considering the reason of the unloading effect in loess collapse process
According to the test data of the water immersion load of the non-compaction pile composite foundation in the dead weight collapsible loess field in different loess areas, the on-site test results of the non-compaction pile side negative friction resistance are shown in table 1.
TABLE 1 non-compaction pile negative friction resistance field test for self-weight collapsible loess field
Consider the soil between piles to be immersed in waterAnd the change condition of the vertical stress in the loading process, and the characteristics of unloading and collapsibility in the loess collapsibility process are combined, the unloading collapsibility coefficient delta is provided us The collapsible amount of loess between piles is calculated as follows:
wherein, alpha and beta are respectively the water soaking probability, soil property, foundation stress state, region and other factors correction coefficients. Delta us The calculation method of (2) is as shown in the formula:
δ us =δ s [1-(1-η 1 )(1-0.7K 1.5 )] (2)
wherein: delta us Is the unloading collapse coefficient; delta s Taking the initial pressure p 1 A corresponding collapse coefficient; η (eta) 1 Is the completion ratio for the collapse; k is the unloading stress ratio, and eta is determined by the simultaneous occurrence of unloading and collapse deformation 1 And 0. And taking the average value of the pile side negative friction resistance by the unloading amount deltap in the calculation of the unloading stress ratio K.
TABLE 2 physical Properties of collapsible loess in different regions
To illustrate the necessity of considering the unloading effect when calculating the loess collapse amount, the loess collapse amount between piles in different loess areas (table 2) is calculated using formula (1) and compared with the loess collapse amount calculation method recommended by the loess specifications and literature (see table 3), and the collapse amount of loess between non-compaction piles in the self-weight collapsible loess field is calculated, and the result is shown in fig. 3.
TABLE 3 loess collapsible amount calculation expression based on different correction methods
As can be seen from fig. 3:
(1) 04 loess standardization when calculating the collapsible volume of loess between the stake, because the actual stress change condition in the loess collapsible process between the stake is not considered, closely carries out mechanical stack with collapsible volume, has neglected the influence of off-load effect to loess collapsible process, makes its calculated value bigger.
(2) In order to compensate the defect that only the soil quality difference is corrected in the calculation of the collapsible quantity of 04 loess standard, the collapsible quantity is reduced by 18 loess standard introduction of foundation soil soaking probability coefficient alpha, and Zheng Jianguo and the yellow snow peak and the like respectively consider the non-uniformity of collapsible loess distribution and the lower limit depth of occurrence of collapsible, and further evaluate the coefficient by using the discontinuous distribution coefficient k of collapsible soil and the lower limit depth of collapsibleThe loess collapsible amount is reduced again in order to make the calculated collapsible amount closer to reality.
(3) In the above-mentioned calculation of loess collapsible amount between piles in three regions, if the machine uses the method of Table 3, the collapsible coefficient delta under constant load condition is used s The calculated value of the slump is the same. If the pile-to-pile loess collapse unloading device is blindly used for unloading working conditions of loess collapse among piles, the reliability of the pile-to-pile loess collapse unloading device is greatly questioned.
For example, under the condition that the neutral point depth and the wet soil layer thickness of the H4 and H7 measuring points in the Binxian region are the same, the wet soil amount calculated by the prior method is the same, but when calculated by the formula (1), the wet soil coefficient delta is due to unloading us The calculation of (1) follows the actual change characteristics of the soil stress in the loess collapse process, and introduces the difference of negative friction resistance into delta through the unloading stress ratio K us The method fully reflects the influence of the unloading effect on the collapse deformation in the loess collapse process, and compared with the pile side negative frictional resistance born by the H7 measuring point, the method has the advantages that the unloading effect on the loess among piles is more severe, so that the collapse deformation of the soil among piles at the H7 position under the influence of the strong unloading effect is smaller. PileThe difference of the collapsible amount calculation of the two side measuring points is the best embodiment of the unloading effect in the loess collapsible process.
The general trend of the existing loess collapsible amount calculation is that the collapsible amount is macroscopically reduced in a moderate manner at all angles, but the specific influence of the unloading effect on the loess collapsible deformation in the collapsible process can not be quantified by adjusting according to various experience coefficients in the face of the unloading collapsible working condition, and the limitation of the adjusting means in the process of coping with the common phenomenon of stress change in the loess collapsible process is exposed. Therefore, it is necessary to use the unload sag coefficient δ us The modulus folding method for calculating the loess collapse amount is obtained, and the rapid calculation and analysis method for the loess collapse amount is explored, so that the loess collapse amount under the influence of the unloading effect can be calculated according to a method and can be circulated according to the method.
3. Factor of unloading action
According to the working condition of loess field unloading collapsibility, the loess collapsibility process under the influence of unloading mainly considers two factors: the completion degree of loess collapsible when unloading effect occurs; the unloading amount during unloading. Thus, to clarify the unloading collapse process, the following relevant parameters are defined.
(1) Wet collapse completion ratio eta 1
Definition eta 1 To reflect the extent to which loess has completed collapsing when the unloading action occurs.
Wherein: s is S 1 For the sample before unloading takes place at pressure p 1 The amount of collapse (mm) completed under action; s is the pressure p of the sample 1 Total wet out (mm) under action.
(2) Unloading stress ratio K
K is defined to reflect the magnitude of decrease in vertical pressure when unloading occurs during loess collapse.
Wherein: p is p 1 Is the initial pressure (kPa); Δp is the vertical pressure (kPa) that the sample is unloaded when unloading occurs during collapse; p is p r Is the vertical pressure (kPa) remaining after the sample is unloaded during the collapse.
(3) Unloading collapse ratio eta 2
Definition eta 2 To reflect the extent of sample collapse after unloading.
Wherein: s is S 2 For the sample after unloading at pressure p r The amount of collapse (mm) achieved under action.
(4) Loess unloading to reduce the collapsible coefficient delta r
Since loess is reduced in vertical pressure during the unloading and collapsing process, its collapsing deformation should be smaller than that under constant pressure. To represent the size of the incomplete collapsible amount S of the undisturbed loess under the influence of unloading effect r And an initial height h 0 Is defined as the loess unloading reduction collapse coefficient delta r :
Wherein: s is S r An incomplete collapsible amount (mm) of the undisturbed loess sample under the influence of unloading; h is a 0 Is the original height (mm) of the original Huang Tuyang.
The unload wet collapse process is shown in fig. 4. In the figure, line segment bf represents the sample at p 1 The amount of collapse upon complete collapse under action. In the whole collapse process, the product of the collapse amount and the vertical pressure is A 1 Then
A 1 =p 1 S (5)
Line bc represents the sample at p 1 Under the action of the action, the partial collapse S is completed 1 At this point the vertical load Δp is immediately removed and the sample is then at p r Is subjected to the action of the collapse amount S 2 The sample height change is indicated by line segment de. Let the product of the collapse amount and the vertical stress be A 2 Then:
A 2 =p 1 S 1 +p r S 2 (S 1 ≤S,S 2 ≤S) (6)
due to the vertical unloading during the collapse, then:
A 1 >A 2 (7)
i.e.
p 1 S>p 1 S 1 +p r S 2 (8)
Formula (8) can be expressed as
And due to p r ≤p 1 Then:
S>S 1 +S 2 (10)
as can be seen from the formula (10), a portion of loess is not collapsed during collapse due to unloading, and the collapse amount can be reduced by the collapse coefficient delta by unloading, compared with the collapse amount under the constant pressure r And (3) representing.
Reduction of the sag factor delta for explicit unloading r Coefficient of collapse delta s By substituting the formulae (1) and (3) into the formula (4)
According to the specification to delta s In turn, formula (11) can be written as
δ r =δ s (1-η 1 -η 2 ) (12)
Formula (12) can be expressed as
Wherein:
in the formula (14), S 2 /(S-S 1 ) The values of (2) relate to 3 wet set deformation: the sample is at an initial pressure p 1 Total number of wetlands under action S; before unloading takes place, the sample is under pressure p 1 The amount of collapse S 1 The method comprises the steps of carrying out a first treatment on the surface of the After the unloading action has taken place, the sample is under pressure p r Amount of collapse under action S 2 . K and eta can be used according to the definition of each influencing factor in the unloading and collapsing process 1 And p 1 To describe the magnitudes of the above 3 deformations, which are equal to S 2 /(S-S 1 ) The correlation between these can be expressed by the following formula:
4. loess unloading collapse coefficient delta us
Based on the physical significance of each influencing factor in the loess unloading and collapsing process. To express the loess collapsibility under the influence of the unloading effect, the unloading collapsibility coefficient delta us Can be defined as
δ us =δ s -δ r (16)
Substitution of formulas (13) to (15) into formula (16) can be obtained
δ us =δ s [1-(1-η 1 )(1-f(K,η 1 ,P 1 )] (17)
Equation (17) establishes a loess collapse coefficient delta by comprehensively considering the collapse effect in the loess collapse process us Is an expression of (2). As can be seen, δ us Is to delta s To a certain extent, 3 influencing factors in the unloading and collapsing process are mainly considered during the collapse: initial pressure p to which the sample is subjected when initial collapse begins 1 Is of a size of (2); the completion degree of loess collapse, i.e. the collapse completion ratio, before the unloading effect occursη 1 The method comprises the steps of carrying out a first treatment on the surface of the The magnitude of the unloading amount when the unloading action occurs is the unloading stress ratio K.
Delta derived for validation during loess unloading and collapsing us Is required to perform an unloading collapsibility test to explore the rule of loess collapsibility deformation under the influence of unloading effect, thereby determining f (K, eta) 1 ,p 1 ) Expression of (2) to obtain delta us Is a calculation formula of (2).
5. Loess unloading collapsibility test
5.1 test procedure
To determine delta us The present invention performed a conventional collapsibility test followed by an unload collapsibility test. In the unload wet test, the initial pressure p was measured with emphasis 1 And the completion ratio of the collapse eta 1 Under the condition, unloading stress ratio K and unloading wet collapse deformation S 2 Correlation between the above.
First, the samples were measured at different p 1 The following coefficient of sag. Determination of as-is Huang Tuyang at p by double-line method 1 Coefficient of collapse delta at 200, 250, 300, 350, 400kPa, respectively s 。(p 1 The value range of the formula (I) is the common vertical stress range in the loess foundation of the multilayer-high building in the loess area at present, and the corresponding delta is s Reflecting the size of loess collapsibility under a certain pressure).
And then carrying out an unloading collapsibility test. At p 1 Under the action, the sample is compressed and stabilized under natural humidity. The sample after the pressure sinking stabilization is subjected to the collapsible deformation under the saturated state of water, and when the sample completes different collapsible amounts S 1 When the test is finished, vertical unloading is carried out to different degrees, the test is stopped until the sample is additionally sunken and stabilized after unloading, and the collapse deformation S of the sample after unloading is measured 2 (in the unload wet test, no considerable rebound phenomenon occurs, and the unload rebound deformation is negligible). When the unloading collapse test is carried out, the vertical initial pressure p of the sample is applied 1 The values are 200, 250, 300, 350 and 400kPa respectively. η (eta) 1 Considered as 20%, 40%, 60%, 80% of the total collapse of the sample under the initial pressure, respectively, when the collapse is completedI.e. unloading. In the collapse process, the method for determining the vertical stress after unloading comprises the following steps: (1) when p is 1 The unloading amounts Δp are 25, 50, 75, 100, 125, 150, 175kPa at 200kPa and 250kPa, respectively; (2) when p is 1 The unloading amounts Δp were 50, 75, 100, 125, 150, 175, 200, 225, 250kPa, respectively, at 300, 400kPa, respectively. The unload wet test protocol is shown in Table 1.
Table 1 unload wet collapse test protocol
The unload wet test procedure is shown in FIG. 5. Fig. 5 (a) shows a conventional collapse process. I.e. the sample is at a constant initial pressure p 1 Under the action, the wet sinking deformation S is completed; fig. 5 (b) shows an unloading collapse process. The sample is first at an initial pressure p 1 Under the action, partial collapse deformation S is completed 1 (S 1 <S), at which point the vertical load Δp is immediately removed and the sample is subsequently subjected to vertical pressure (p 1 - Δp) to complete the collapse deformation S 2 . In this example the heavy spots were measured at different p 1 η 1 Under the condition, the sample is subjected to wet collapse deformation S after unloading 2 Law of variation with K and K, eta 1 And eta 2 /(1-η 1 ) Correlation between the above.
5.2 preparation of test samples and determination of physical indicators
The test undisturbed loess sample is taken from a construction foundation pit of a certain building in copper of Shaanxi, the soil depth is 5.0-8.5 m, the test undisturbed loess sample is brown yellow and has a hard plastic state, and the physical properties are shown in Table 2.
TABLE 2 physical Properties of undisturbed Clay sample for testing
5.3 different initiationPressure p 1 Corresponding loess collapse coefficient delta s
The experiment shows that different p 1 The collapse coefficient delta of the undisturbed loess under action s The results are shown in Table 3. When p is 1 In the range of 0 to 200kPa, the initial collapse pressure of the test undisturbed loess sample was measured to be 75kPa, and the saturated density of the soil covered on the sample was found to be ρ according to Table 2 s =1.67g/cm 3 . When the soil sampling depth is 5m, the saturation dead weight stress of the upper covering soil is 83.5kPa and is larger than the initial collapsible pressure, so when the soil sampling depth is 5-8.5 m, the sampled soil sample is dead weight collapsible loess, p 1 When=200 kPa, δ s >0.07, and judging that the collapsibility of the taken soil sample is strong according to the specification.
Table 3 delta of samples at different initial pressures s
5.4 results of unload wet collapse test and analysis
To determine f (K, eta 1 The expression of p 1) is first determined at different p1 and eta 1 Under the condition, the unloading wet collapse deformation S2 of the sample is carried out, and the unloading wet collapse deformation S2 is further carried out according to S2/(S-S1) and eta 2 /(1-η 1 ) Equivalent relation of (a) to obtain eta 2 /(1-η 1 ) -K, as shown in fig. 6.
As can be seen from fig. 6:
(1) Corresponding eta at different initial pressures 2 /(1-η 1 ) The curve form of the value of the ratio is quite similar with the change of the unloading stress ratio, and eta is reduced with the reduction of the unloading stress ratio 2 /(1-η 1 ) The value of (2) is obviously reduced, which means that the collapsibility of the undisturbed loess after unloading is reduced along with the increase of the vertical unloading amount.
(2) When the initial pressure is not more than 250kPa, eta 2 /(1-η 1 ) The curve decreasing relation is presented along with the decrease of the unloading stress ratio, the slope of the curve is gradually decreased along with the decrease of the unloading stress ratio, and when the unloading stress ratio is smaller than 0.5, the change of the slope of the curve tends to be stable. Description when vertical unloading webWhen the degree reaches more than 50%, the influence of the unloading effect on collapsibility of loess after unloading is weakened. When the initial pressure is greater than 250kPa, eta 2 /(1-η 1 ) And the linear decreasing relation is shown with the decrease of the unloading stress ratio. η (eta) 2 /(1-η 1 ) The change form of the relationship curve between the original loess and the unloading stress ratio reflects that if the original loess is collapsed to a certain extent under a larger initial pressure, the contact relationship of macroporous skeleton particles in the soil is destroyed to a higher extent, and the relationship between the collapse deformation and the unloading amount of the soil sample after unloading tends to be linear.
(3) η under the same unloading stress ratio 2 /(1-η 1 ) Decreasing with increasing completion ratio of collapse and η in case of substantial unloading 2 /(1-η 1 ) Is smaller than the amplitude of the decrease under small relief. Because the larger the degree of completion of the collapse of the undisturbed loess is when the unloading effect occurs, the higher the degree of formation of a new compacted structure after the soil particles are rearranged, the collapse deformation after the unloading will tend to be reduced, and this feature is more remarkable in the case of a smaller unloading amount.
(4) In the unloading and collapsing process, the unloading stress ratio causes eta 2 /(1-η 1 ) The reduction amplitude of the method is larger than that caused by the completion ratio of the collapsible, namely the collapse deformation of the undisturbed loess after unloading has higher sensitivity to the change of vertical pressure.
5.5 off-load collapse coefficient delta us Determination of the expression
f(K,η 1 ,p 1 ) Determination of the expression
As can be seen from FIG. 4, η 2 /(1-η 1 ) Although the overall change rule of the K curve is consistent, eta 2 /(1-η 1 ) The value of (1) is related to p 1 And eta 1 Variations of (c) are still present in small areas. To determine K, eta 1 And p 1 The influence degree of the loess unloading collapse deformation is that K, eta 1 And p 1 As an influence eta 2 /(1-η 1 ) The evaluation factors of the values are shown in Table 4, and a multi-factor orthogonal test is designed.
TABLE 4 factors and levels of orthogonal test designs
The method is characterized in that the orthogonal test results are subjected to range analysis, the range reflects the influence of different level changes of the factors on indexes, the range greatly indicates that the difference generated by different levels of the factors is large, the factors are important factors, the influence on the test results is remarkable, the factors with the range small are secondary factors, and the level change of the factors has no obvious influence on the test results. Influence η in orthogonal experiments 2 /(1-η 1 ) The analysis of the difference in the values of the factors is shown in Table 5.
TABLE 5 multiple factor orthogonal test range analysis
Note that: k (K) m The sum of statistical indexes corresponding to the levels of all factors m; k (k) m For K m Average value of (2); r is the very bad of each factor.
As can be seen from table 5, the order of primary and secondary effects of each factor on the test results is: k- & gteta 1 →p 1 Description of unloading stress alignment eta 2 /(1-η 1 ) The value of (2) plays a control role, and the initial pressure has the smallest influence on the collapsible deformation of loess after unloading. Each factor pair eta 2 /(1-η 1 ) Visual analysis of the effect of the value is shown in figure 7.
As can be seen from FIG. 7, the initial pressure p 1 And the completion ratio of the collapse eta 1 The limit values of the (B) are similar, the limit value of the unloading stress ratio K is the largest in sensitivity analysis, and the fact that K is the main factor influencing the test result and p 1 And eta 1 Then to index eta 2 /(1-η 1 ) The effect of (2) is not significant. Because the extremely poor analysis cannot accurately estimate the influence degree of each factor on the test result, the multi-factor analysis of variance is carried out on the test result to make up for the deficiency.
According to the analysis of variance results of Table 6, the initial pressure was related to the loess unloading collapsible deformation propertyThe degree of relatedness of the products, correlation of collapse completion ratio with loess unloading collapse deformation property, < >> Indicating p 1 And eta 1 The impact on loess unloading collapsible deformation property does not reach a significant level, but F K =33.633>F 0.01 >F 0.05 Indicating that eta is affected 2 /(1-η 1 ) Among the 3 factors, the unloading stress ratio K has the most obvious influence on the collapse deformation of the sample after unloading.
TABLE 6 analysis of influence factor variance of test
Based on the analysis result of the multi-factor orthogonal test, the method determines f (K, eta 1 ,p 1 ) K is taken as the primary consideration in fitting the expression of (c). By multiple pairs of functions K and eta 2 /(1-η 1 ) The correlation can be approximately represented by a power function, and the expression is that
f(K)=aK b (18)
Wherein: a, b are regression parameters. By carrying out regression analysis on unloading collapsibility test data, different p's are determined 1 And eta 1 Regression parameters under the conditions are shown in Table 7.
As can be seen from Table 7, at different p 1 η 1 Under the condition of K and eta 2 /(1-η 1 ) The correlation coefficient of (2) is above 0.9. From the nature of the function itself, the power function can also qualitatively represent the unloading amountThe change rule of the collapse deformation after loess unloading is that the collapse deformation after loess unloading is reduced along with the increase of unloading load, and the values of a and b are subjected to p 1 And eta 1 Is less influential, consistent with the analysis of variance results described above. Due to the parameters a, b at different p 1 And eta 1 The values under the condition are close, and the average value of a and b can be adopted to further simplify the expression of f (K). 5.6 delta us Expression of (c) and verification thereof
Substituting the average value of the parameters a and b into f (K) to obtain an unloading collapse coefficient expression considering unloading effect in the loess collapse process:
δ us =δ s [1-(1-η 1 )(1-1.067K 1.695 )] (19)
delta is converted into delta by the method (19) us Performing correlation analysis on the calculated result and the measured result to obtain a variation coefficient C between the calculated result and the measured result v And partial comparison curves are shown in table 8 and fig. 8, respectively.
TABLE 7 eta 2 /(1-η 1 ) Parameters of the-K relationship
TABLE 8 delta us Calculated value and test value C v
As can be seen from fig. 8 and table 8, the test value and the calculated value are well matched, the overall rule is consistent, and the variation coefficient between the test value and the calculated value is smaller than 0.15. Described in regression f (K, eta 1 ,p 1 ) The factor p is ignored when the expression of (2) is expressed 1 And eta 1 It is reasonable to influence and simplify the parameters in f (K). Explaining loess unloading calculated according to formula (19)The collapsible deformation result has certain reliability, and the loess collapsible deformation under different initial pressures, different unloading and collapse completion degrees can be calculated by using the method, so that the collapsible property of loess under the influence of the unloading effect is scientifically evaluated.
6. Modulus reduction coefficient under constant load wet collapse condition
Deformation modulus E of the undisturbed loess after soaking and collapsing 0 Both the shear strength and the shear strength c,the method is mainly used for stability analysis of slope and foundation pit engineering, and deformation modulus E 0 Is mainly used for calculating the deformation of the foundation and coping with the deformation modulus E of the loess for calculating the collapsible deformation of the loess 0 And carrying out reduction. Performing indoor compression test on undisturbed loess from Cuchuan to obtain different initial pressures p 1 Compression modulus E at S By E 0 And E is connected with S The correlation of the loess in the original state is obtained at different p 1 E under conditions of 0 As shown in table 9.
TABLE 9 undisturbed loess at different p 1 E under conditions of 0
According to Table 9, take different p 1 Lower undisturbed loess E 0 Is 24.5MPa. To determine the deformation modulus E after the wet collapse of the undisturbed loess 0 ' the room collapsibility test is now simulated by means of flexural modulus subtraction.
Calculating the difference p of the raw loess by modulus folding method 1 The lower collapsible deformation, the deformation modulus of which was differently reduced when the undisturbed loess was collapsible in water, was calculated as shown in fig. 9 and table 10.
Table 10 calculation of percentage error in the collapsible deformation of undisturbed loess by modulus reduction at different levels
When the deformation modulus E of the undisturbed loess is taken respectively 0 1/13 to 1/15 of the modulus E after immersion 0 In the' case, the measured value of the loess collapse amount is close to the calculated value, and the modulus reduction ratio is in the range of E after the loess collapse with the large amount of loess collapse load test in the literature 0 ' is before-collapse E 0 The results of 1/20 to 1/10 of the above were matched, and it was confirmed that it was reasonable to calculate the collapsible deformation of the raw loess by modulus folding method.
In order to quantify the extent of the flexural modulus decrease before and after loess collapse so as to realize accurate calculation of the loess collapse shape, a modulus decrease coefficient Z under constant load condition is now defined to reflect the relationship between the flexural modulus after loess collapse and the initial modulus:
wherein E is 0 Deformation modulus (MPa) of the clay before wet sinking; e (E) 0 ' is the deformation modulus of the bentonite after wet collapse.
To further establish the relationship between the deformation modulus and the collapsible deformation after the collapse of the undisturbed loess, the initial pressures p are obtained 1 Modulus reduction coefficient and sag coefficient delta under the condition s The correlation of (2) is shown in FIG. 10.
According to FIG. 10, at the same p 1 Delta under the condition s The relation with Z is basically linear, and delta is further obtained s The correlation with Z is shown in Table 11.
TABLE 11 delta under different parameters s Correlation with Z
As can be seen from Table 11, the value of parameter a in f (Z) varies with the initial pressure p 1 The fluctuation range of the change is smaller, and the value of the parameter b follows p 1 The variation of (2) is shown in the following formula:
b=0.001p 1 -0.023 (21)
to simplify the expression of f (Z), taking the mean of a and substituting formula (4) into the expression of f (Z) yields:
δ S =-1.952Z+0.001p 1 -0.023 (22)
obtaining modulus reduction coefficient Z and collapse coefficient delta under constant load according to (22) s Is the relation of:
Z=0.001p 1 -0.512δ S -0.012 (23)
the different initial pressures p can be calculated according to equation (23) 1 Under the condition, the modulus reduction coefficient Z of the immersed and collapsed original loess can calculate the deformation modulus E of the immersed and collapsed original loess 0 ' thereby calculating loess collapsible deformation using a modulus folding and subtracting method.
7. Modulus reduction coefficient under load and collapse conditions
To verify the reliability of the modulus folding and subtracting method to calculate the collapse deformation under load taking the load action into account, different p's are calculated by equation (19) 1 η 1 The results of the indoor loess multiple unload wet collapse test under the condition are shown in FIG. 11.
According to FIG. 11, the loess collapsible deformation calculated by the modulus reduction method taking the collapse effect into consideration substantially coincides with the indoor loess collapse test value and the average relative error (MAPE) is less than 5%, illustrating that the loess modulus reduction coefficient Z under the collapse condition is obtained by the equation (7) u It is reasonable to calculate the loess collapse deformation, and therefore, in order to calculate the loess collapse deformation more accurately, the modulus-decreasing coefficient Z under the condition of collapse is proposed u The determination method of (2) is shown in fig. 12.
According to the calculation process of fig. 12, a method for determining the modulus reduction coefficient Z under the unloading condition is obtained:
(1) Firstly, according to the indoor unloading collapsibility test result and combining with modulus folding and subtracting method, under the unloading condition, the modulus folding and subtracting coefficient Z reflecting the relation between the deformation modulus and the initial modulus after loess collapsibility is calculated ui . Then calculating loess collapse amount delta 'considering unloading effect according to the relationship between deformation modulus and collapsible deformation after the original loess is collapsed' ui 。
(2) Will be delta' ui And the measured collapse delta of the unloading collapse test ui Comparing, if the percentage error is less than 5%, determining a modulus reduction coefficient Z considering unloading effect ui . The above procedure was repeated to determine Z for different unload wet collapse test conditions ui Further according to Z ui Loess collapsible deformation in consideration of unloading effect is calculated. If delta' ui And delta ui If the percentage error is greater than 5%, Z is to be re-formulated ui And performing iterative calculation until the two meet the error requirement.
(3) According to Z meeting the error requirement u Let Δp=0 during loess collapse, calculate loess collapse amount under constant load collapse condition, and compare with indoor conventional loess collapsibility test result to further verify Z u Reliability of (3).
8 method verification
Indoor degradation verification
To verify the loess unloading collapse coefficient delta under the established unloading condition us Modulus reduction coefficient Z u And the corresponding relation between the two under the condition of constant load collapsible is utilized when the unloading amount is zero (delta p=0), the degradation verification is carried out on the loess, the undisturbed collapsible loess in different areas is taken, and according to the formula (19), the calculated value and the measured value of the loess collapsible amount calculated by the modulus folding and subtracting method are compared, and the degradation verification result is shown in fig. 13.
As can be seen from fig. 13, the initial pressures p are different 1 Under the condition, the loess unloading collapsible amount calculated values under different unloading states are calculated by using a deformation modulus folding and subtracting method and are consistent with the actual unloading collapsible deformation rule, and the Nash coefficients (NSE) of the loess unloading collapsible amount calculated values and the actual unloading collapsible deformation rule are both larger than 0.9, which indicates that the influence of the unloading amount on the loess unloading collapsible deformation can be well reflected by using the modulus folding and subtracting method to fully follow the actual stress change condition in the loess collapsible process. To further verify modulus reduction coefficient Z u With the unloading amount Δp=0, the loess collapse amount under constant load collapse condition was calculated using the formula (19), and found at different initial pressures p 1 Under the condition, the loess collapse amount degradation verification value is flat with three groups of indoor actual measurement valuesThe relative errors are less than 5%, which indicates that the loess unloading collapse deformation calculated by modulus folding and subtracting method is reasonable and has higher precision.
4.2 engineering instance verification
To verify the rationality of the calculation of loess collapsible deformation by modulus folding and subtracting method taking the unloading effect into consideration, the present test of ZH4 cast-in-place pile load bearing property and negative frictional resistance based on yellow snow peak and the like carried out on the dead weight collapsible loess field in Ningxia region is compared with the result of the on-site pile foundation soaking test by calculating the soil collapsible deformation between piles by modulus folding and subtracting method taking the unloading effect, and the result is shown in fig. 14 (b).
As can be seen from fig. 14:
(1) With the further reduction of loess modulus among piles, the soil among piles is collapsible and deformed, the positive stress of the upper soil layer is reduced, and the soil is gradually converted into negative frictional resistance, so that a pull-down load is formed.
(2) The neutral point position and the negative friction resistance evolution characteristic in the calculated result are basically consistent with the actual measurement trend, and the neutral point position gradually moves upwards along with the increase of pile top load, namely positive friction resistance is increased, and negative friction resistance is reduced.
(3) The depth change range of the limit position of the neutral point of the pile foundation is basically consistent with the thickness of the actual collapsible soil layer on site, and the actual measurement value of the negative frictional resistance and the calculated value of the calculated value are respectively larger than 0.9 under different pile top loads, so that the prediction by using modulus folding subtraction and the calculation of the loess unloading collapsible shape are reasonable.
The modulus reduction method taking unloading effect into consideration fully considers the actual stress change condition in the loess collapse process between piles, and by constructing modulus reduction coefficients Z under different unloading conditions u The stress change in the loess collapsible sinking between piles is caused to be consistent with the actual working condition, the unloading collapsible effect is successfully introduced into the loess collapsible deformation calculation between piles, the calculation flow is simple, and the loess collapsible deformation calculation result between piles is reasonable.
Aiming at unloading working conditions such as test pit soaking, soil soaking and collapsible among piles and the like, the loess is subjected to collapsible sinking after soaking, the vertical stress is influenced by the sharing effect and negative frictional resistance of the piles, the vertical pressure is reduced in the loess collapsible process, and the effect of unloading and collapsible is one of the important reasons for causing the difference between a calculated value and an actual measured value of the collapsible.
In the loess unloading and collapsing process, the vertical stress is reduced, the collapsing deformation and collapsing types obtained by the existing method (considered according to the natural loess field) are changed, and various macroscopic experience adjustment coefficients are not suitable for blind machines in the face of unloading and collapsing working conditions. It is necessary to consider the influence of the collapse of the unloading in the loess collapse amount calculation.
The calculated value of the unloading collapsible quantity is smaller than the standard value, the influence of pile side friction resistance on collapsible deformation can be reflected through the unloading collapsible coefficient in the calculation of loess collapsible quantity among piles, and the larger the negative friction resistance is, the more obvious the unloading collapsible effect is.
The loess collapsible deformation is reasonably calculated by adopting a deformation modulus folding method. Through iterative calculation, when the calculated value of the unloading collapse amount and the calculated value are smaller than 5%, the modulus reduction coefficient Z under the unloading condition can be established u . It is necessary to utilize means for reducing the deformation modulus to pass the unloading wet-out action through Z u And delta us The loess collapsible amount calculation is scientifically introduced.
Claims (1)
1. The loess unloading collapse amount calculating method is characterized by comprising the following steps of:
step 1: calculating to obtain a collapsible completion ratio eta reflecting the degree of collapse of loess when unloading occurs 1 ,
Calculating to obtain unloading stress ratio K reflecting the reduction amplitude of vertical pressure when unloading action occurs in loess collapse process,
step 2: by applying the wet-out completion ratio eta 1 The unloading stress ratio K calculates the unloading collapse coefficient delta us ,
Step 3: by unloading the coefficient of collapse delta us Calculating loess modulus reduction coefficient Z under unloading condition u ,
Step 4: calculating loess unloading collapse amount according to the loess modulus reduction coefficient under the unloading condition;
wherein in step 1Calculating eta 1 The formula of (2) is:
wherein: s is S 1 For the sample before unloading takes place at pressure p 1 The completed collapse amount is mm; s is the pressure p of the sample 1 The total collapse under action is mm;
wherein, the formula for calculating K in the step 1 is as follows,
wherein: p is p 1 Is the initial pressure kPa; Δp is the vertical pressure kPa that the sample is unloaded when unloading occurs during the collapse process; p is p r The method is characterized in that the vertical pressure kPa remaining after unloading of the sample in the wet sinking process is used;
wherein, in step 2, delta is calculated us The formula of (2) is:
δ us =δ s [1-(1-η 1 )(1-1.067K 1.695 )],
wherein: delta s Is the collapsible coefficient of the undisturbed loess;
wherein Z is calculated u The formula of (2) is:
Z u =0.001p 1 -0.512δ us -0.012,
wherein: p is p 1 Is the initial pressure kPa;
wherein, in the step 4, loess unloading collapse amount delta is calculated us The formula of (2) is:
wherein Δp i Adding average additional stress generated by volume weight in the ith layer of soil to the yellow soil body in the loess collapse process; alpha is a correction coefficient of the collapsible deformation modulus, and 1.1 to 1.5 is taken; e (E) 0i Is the ithThe deformation modulus of the layer collapsible loess before soaking and collapsing is MPa; h i Is the thickness of the i-th layer collapsible loess.
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