CN112966320A - Method for calculating loess unloading collapsibility - Google Patents

Method for calculating loess unloading collapsibility Download PDF

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CN112966320A
CN112966320A CN202110095299.3A CN202110095299A CN112966320A CN 112966320 A CN112966320 A CN 112966320A CN 202110095299 A CN202110095299 A CN 202110095299A CN 112966320 A CN112966320 A CN 112966320A
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金鑫
王铁行
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Xian Technological University
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Abstract

The invention discloses a method for calculating loess unloading collapsibility, which comprises the following steps: step 1: calculating to obtain a collapsible completion ratio eta reflecting the extent of the loess completely collapsible when unloading occurs1Calculating to obtain an unloading stress ratio K reflecting the vertical pressure reduction amplitude when the unloading action occurs in the loess collapsible process, and step 2: using the collapsible completion ratio eta1And calculating the unloading wet collapse coefficient delta according to the unloading stress ratio KusAnd 3, step 3: by the unload coefficient of wet collapse deltausCalculating to obtain loess modulus reduction coefficient Z under unloading conditionuAnd 4, step 4: calculating the loess unloading collapse amount according to the loess modulus reduction coefficient under the unloading condition; the invention utilizes the modulus reduction method of the unloading effect, fully considers the actual stress change condition in the loess collapsibility process between piles, and determines the stress change condition through the simulationModulus reduction coefficient Z under the same unloading conditionuThe stress change in the loess collapsibility among the piles is enabled to accord with the actual working condition, the unloading collapsibility effect is successfully introduced into the loess collapsibility deformation calculation among the piles, the calculation process is simple, and the calculation result of the loess collapsibility deformation among the piles is reasonable.

Description

Method for calculating loess unloading collapsibility
Technical Field
The invention belongs to the field of loess unloading collapsibility calculation methods, and particularly relates to a loess unloading collapsibility calculation method.
Background
Under the positive influence of the policy of 'silk road economic zone' co-construction, engineering construction projects such as buildings, roads, municipal works, bank slopes, underground urban complexes and the like in loess areas are developed vigorously, but a large number of accidents such as foundation settlement, building inclination, structure cracking, ground subsidence, road surface damage and the like caused by settlement are frequently seen in engineering practice. Due to the complexity of the loess collapsibility problem, the existing loess collapsibility evaluation method is not suitable for the unloading collapsibility working condition, and the unloading collapsibility working condition refers in particular to the working condition with the unloading function in the loess collapsibility deformation process such as a test pit, a pipe trench, soil between piles and the like. Due to the deficiency of the evaluation research of the collapsibility of the loess under the working condition of unloading collapsibility, the quantitative analysis and prediction of the unloading collapsibility are difficult to carry out, the calculated value of the collapsibility obtained by simply applying the existing method for evaluating the collapsibility of the loess under the condition of constant load is greatly different from the measured value, so that the reliability of the calculation and analysis result of the collapsibility is poor, the engineering practice is difficult to guide, the engineering diseases are frequent, or the over-conservative engineering treatment method is adopted under the cautious principle, and the great waste is caused. Therefore, how to scientifically and quickly calculate and analyze the loess collapsibility is urgent for the unloading collapsibility condition.
At present, loess collapsibility calculation methods include a calculation analysis method and a field pit test immersion test method. The calculation analysis method calculates the loess collapsibility based on the constant pressure collapsibility coefficient measured by the indoor test. The field pit test immersion test method actually measures loess collapsibility through excavation of immersion test pits, but the field pit test immersion test is high in cost and long in period, and loess collapsibility evaluation is difficult to adopt in large quantities.
Disclosure of Invention
The invention aims to provide a method for calculating loess unloading collapsibility, which aims to solve the problems that the existing calculating method is high in cost and the calculated value is larger due to neglect of the influence of unloading action on loess collapsibility process.
The invention adopts the following technical scheme: a method for calculating loess unloading collapsible quantity comprises the following steps:
step 1: calculating to obtain a collapsible completion ratio eta reflecting the extent of the loess completely collapsible when unloading occurs1，
Calculating to obtain an unloading stress ratio K reflecting the reduction amplitude of the vertical pressure when the unloading action occurs in the loess collapsibility process,
step 2: using the collapsible completion ratio eta1And calculating the unloading wet collapse coefficient delta according to the unloading stress ratio Kus，
And step 3: by the unload coefficient of wet collapse deltausCalculating to obtain loess modulus reduction coefficient Z under unloading conditionuWherein Z is calculateduThe formula of (1) is:
Zu＝0.001p1-0.512δus-0.012，
in the formula: p is a radical of1Initial pressure (kPa);
and 4, step 4: and calculating the loess unloading collapse amount according to the loess modulus reduction coefficient under the unloading condition.
Further, η is calculated in step 11The formula of (1) is:
Figure BDA0002913868210000021
in the formula: s1Sample at pressure p before unloading takes place1The amount of wet sinking (mm) that has been completed under the action; s is the pressure p of the sample1Total amount of wet collapse (mm) under action.
Further, the formula for calculating K in step 1 is,
Figure BDA0002913868210000022
in the formula: p is a radical of1Initial pressure (kPa); Δ p is the vertical pressure (kPa) removed when unloading occurs during the collapse of the sample; p is a radical ofrThe vertical pressure (kPa) remaining after unloading the sample during the collapse process.
Further, δ is calculated in step 2usThe formula of (1) is:
δus＝δs[1-(1-η1)(1-1.067K1.695)]，
in the formula: deltasIs the collapsible coefficient of undisturbed loess.
Further, the loess unloading collapsibility amount delta is calculated in the step 4usThe formula of (1) is:
Figure BDA0002913868210000023
in the formula,. DELTA.piIncreasing the average additional stress generated in the ith layer of soil by the volume weight of the loess body in the loess collapsible process; alpha is a coefficient for correcting the collapsible deformation modulus, and is 1.1-1.5; e0iThe deformation modulus (MPa) of the i-th layer of collapsible loess before immersion and collapse; hiIs the thickness of the i-th layer collapsible loess.
The invention has the beneficial effects that: the invention utilizes the modulus reduction method of the unloading effect, fully considers the actual stress change condition in the loess collapsibility process between piles, and designs the modulus reduction coefficient Z under different unloading conditionsuThe stress change in the loess collapsibility among the piles is enabled to accord with the actual working condition, the unloading collapsibility effect is successfully introduced into the loess collapsibility deformation calculation among the piles, the calculation process is simple, and the calculation result of the loess collapsibility deformation among the piles is reasonable.
Drawings
FIG. 1 is a schematic view of the loess pit soaking unloading collapsible working condition of the present invention;
FIG. 2 is a schematic view of the loess unloading collapsible condition between piles according to the present invention;
FIG. 3 is a comparison of the amount of collapsibility of the soil between piles calculated by the method for calculating the amount of collapsibility of different loess according to the present invention;
FIG. 4 is a schematic view of the present invention showing unloading and wet collapse;
FIG. 5 is a schematic view of an unloading and wet-out test process according to the present invention;
FIG. 6 shows η of the present invention2/(1-η1) Curve with K;
FIG. 7 is a graph illustrating the trend of the test influencer index in accordance with the present invention;
FIG. 8Is delta according to the inventionusCalculating a comparison curve with the test result;
FIG. 9 is a method for calculating the amount of undisturbed loess collapsibility by modulus reduction according to the present invention;
FIG. 10 shows the present invention deltasSchematic diagram of relation with Z;
FIG. 11 is a comparison between calculated values and measured values of loess unloading collapsibility in accordance with the present invention;
FIG. 12 is a loess deformation modulus reduction coefficient determination method under the unloading collapsible condition according to the present invention;
FIG. 13 is a loess collapsibility degradation verification result calculated by modulus reduction method according to the present invention;
FIG. 14 is a comparison between calculated values and measured values of side frictional resistance of loess-unloading collapsible piles among ZH4 piles in accordance with the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a method for calculating loess unloading collapsibility, which comprises the following steps:
step 1: calculating to obtain a collapsible completion ratio eta reflecting the extent of the loess completely collapsible when unloading occurs1Calculating eta1The formula of (1) is:
Figure BDA0002913868210000031
in the formula: s1Sample at pressure p before unloading takes place1The amount of wet sinking (mm) that has been completed under the action; s is the pressure p of the sample1Total amount of wet collapse (mm) under action.
Calculating to obtain an unloading stress ratio K reflecting the reduction amplitude of the vertical pressure when the unloading action occurs in the loess collapsibility process, wherein the formula for calculating K is as follows,
Figure BDA0002913868210000032
in the formula: p is a radical of1Initial pressure (kPa); Δ p is the sample during the collapse processVertical pressure (kPa) to unload when unloading occurs; p is a radical ofrThe vertical pressure (kPa) remaining after unloading the sample during the collapse process.
Step 2: using the collapsible completion ratio eta1And calculating the unloading wet collapse coefficient delta according to the unloading stress ratio KusCalculating deltausThe formula of (1) is:
δus＝δs[1-(1-η1)(1-1.067K1.695)]
in the formula: deltasIs the collapsible coefficient of undisturbed loess.
And step 3: by the unload coefficient of wet collapse deltausCalculating to obtain loess modulus reduction coefficient Z under unloading conditionuCalculating ZuThe formula of (1) is:
Zu＝0.001p1-0.512δus-0.012
in the formula: p is a radical of1Initial pressure (kPa).
And 4, step 4: calculating loess unloading settlement according to loess modulus reduction coefficient under unloading condition, and calculating loess unloading settlement deltausThe formula of (1) is:
Figure BDA0002913868210000033
in the formula,. DELTA.piIncreasing the average additional stress generated in the ith layer of soil by the volume weight of the loess body in the loess collapsible process; esiThe compressive modulus of the i-th layer collapsible loess; hiIs the thickness of the i-th layer collapsible loess.
Wherein:
Esi＝αE’0
wherein alpha is a coefficient for correcting the modulus of deformation due to collapse, and is 1.1 to 1.5.
Figure BDA0002913868210000034
In the formula, E0Deformation modulus (MPa) of loess before immersion and collapse; e0Is prepared by soaking in waterDeformation modulus (MPa) of the collapsed loess; zuThe modulus reduction coefficient of loess under an unloading condition,
according to
Zu＝0.001p1-0.512δus-0.012
The formula for calculating the loess unloading collapse amount by the loess modulus reduction coefficient is obtained as follows:
Figure BDA0002913868210000041
namely:
Figure BDA0002913868210000042
in the formula, alpha is a coefficient for correcting the modulus of deformation due to collapse, and is 1.1-1.5; e0iThe deformation modulus (MPa) of the i-th layer before the collapsible loess is soaked in water and collapsed.
The reason and the verification test that the loess is unloaded and collapsed under the current working condition and the unloading effect of the loess collapsing process are considered are stated below.
1. Loess unloading and collapsible working condition
As shown in fig. 1, in the loess test pit soaking test, affected by the seepage funnel, the collapsible soil distribution and the boundary effect, the soil layers from the center of the test pit to the outer edge form a wrong platform due to uneven development of collapsible deformation, when the self-weight stress of the soaked loess soil layer can not overcome the perimeter resistance, the soil layers at the periphery of the test pit are not completely collapsed or even not collapsed, the relative displacement of the unevenly collapsed soil body can cause frictional resistance, and the effect can inhibit the development of the collapsible deformation of loess due to soaking.
The soil layer is subjected to an initial stress p1The soil body in the pit sinks due to water immersion, and the vertical stress on the soil body is p in the process of sinking due to the difference of the amount of the sinking and the friction resistance tau of the surrounding soil body1Is reduced to prThe larger the amplitude of the collapsible deformation is, the larger the amplitude of the reduction of the vertical stress is. The phenomenon is similar to the dragging action of loess in the vertical direction in the process of subsidence of the collapsible container, and the soil body is vertical in the process of subsidenceThe reduction of the stress can be called as an unloading effect, and the soil stress is influenced by the unloading effect in the process of the collapse to generate redistribution.
For another example, the composite foundation of the self-weight collapsible loess field plain concrete pile has the stress distribution different from that of a common soil layer and the accompanying process of unloading and collapse due to the fact that the stress state and the collapse characteristics of loess among piles in the process of soaking and collapsing are different from those of a natural field and the pile distance of the loess composite foundation is small, and loess among piles (shown in figure 2) is influenced by the sharing effect of the piles and the negative friction resistance of the pile side in the process of bearing load and submerging.
2. The reason for considering the unloading effect in the loess collapsible process
According to the test data of the immersion load of the non-compaction pile composite foundation in the self-weight collapsible loess field in different loess areas, the test result of the non-compaction pile side negative friction resistance field is obtained and is shown in the table 1.
TABLE 1 dead weight collapsible loess field non-compaction pile negative friction resistance field test
Figure BDA0002913868210000043
Figure BDA0002913868210000051
The change condition of the vertical stress of the soil between piles in the process of soaking and loading is considered, and the characteristic of the associated unloading and collapsibility in the loess collapsibility process is combined, so that the unloading collapsibility coefficient delta is providedusCalculating the collapse amount of loess among piles as follows:
Figure BDA0002913868210000052
in the formula, alpha and beta are respectively the water immersion probability and the correction coefficients of factors such as soil texture, foundation stress state, area and the like. DeltausThe calculation method of (2) is shown as the following equation:
δus＝δs[1-(1-η1)(1-0.7K1.5)] (2)
in the formula: deltausIs the unloading wet-fall coefficient; deltasTaking an initial pressure p1The corresponding coefficient of wet sinking; eta1Is the collapsible completion ratio; k is the unloading stress ratio, and since the unloading effect and the collapsible deformation occur simultaneously, eta is10. And taking the average value of the pile side negative friction resistance in the unloading amount delta p in the unloading stress ratio K calculation.
TABLE 2 physical Properties of collapsible loess in various regions
Figure BDA0002913868210000053
To illustrate the necessity of considering the unloading effect when calculating the loess collapsibility, the loess collapsibility between piles in the dead-weight collapsible loess field was calculated by calculating the unloading collapsibility of loess between piles in different loess areas (table 2) by using formula (1) and comparing the calculated loess collapsibility with the loess norm and the loess collapsibility calculation method recommended by the literature (see table 3), and the result is shown in fig. 3.
TABLE 3 loess collapsibility calculation expression based on different correction methods
Figure BDA0002913868210000061
As can be seen from fig. 3:
(1)04 loess standard when calculating the collapsible volume of loess between the stake, owing to do not consider the actual stress variation condition of loess collapsible in-process between the stake, tightly carry out mechanical stack with the collapsible volume, neglected the influence of off-load effect to the loess collapsible process, make its calculated value bigger than normal.
(2) In order to make up for the defect that only the soil quality difference is corrected in the calculation of 04 loess standard collapsibility, 18 loess standard introduces foundation soil soaking probability coefficient alpha to reduce loess calculated collapsibility, and Zheng construction countries and the like and Huangxue peaks and the like respectively consider the nonuniformity of collapsibility loess distribution and the lower limit depth of collapsibility, and further use a collapsibility discontinuous distribution coefficient k and a collapsibility lower limit depth evaluation coefficient
Figure BDA0002913868210000062
The loess collapsibility is again reduced in order to make the calculated collapsibility closer to the actual value.
(3) In the calculation of loess collapsibility among the piles in the three regions, for the case that the collapsible soil layers have the same thickness, if the machine is according to the method in table 3, the collapsible coefficient delta under the constant-load working condition is usedsThe calculated values of the amount of wet fall are the same. If the method is blindly applied to the unloading working condition of loess collapsibility between piles, the reliability of the method is greatly questioned.
For example, under the condition that the depth of a neutral point and the thickness of a collapsible soil layer are the same at measuring points H4 and H7 in Binxian province, the collapsible volume calculated by the prior method is the same, but when the collapsible volume is calculated according to the formula (1), because the unloading collapsible coefficient delta is calculatedusThe calculation follows the actual change characteristics of the soil body stress in the loess collapsible process, and the difference of the negative frictional resistance is introduced into delta through the unloading stress ratio KusThe calculation fully reflects the influence of the unloading action on the collapsible deformation in the loess collapsible process, the pile side negative friction resistance of the H7 measuring point is larger than that of the H4 measuring point, the unloading action on the loess among the piles is more severe, and the collapsible deformation of the soil among the piles at the H7 under the influence of the stronger unloading action is smaller. The difference of the collapsible amount of two measuring points at the pile side is the best embodiment of considering the unloading effect in the loess collapsible process.
The general trend of the existing loess collapsibility calculation development is that each angle performs moderate reduction on the collapsibility macroscopically, but in the face of unloading collapsibility working conditions, the concrete influence of unloading action on loess collapsibility deformation in the collapsibility process can not be quantified by adjusting according to various empirical coefficients, and the limitation of the existing adjusting means in the process of dealing with the general phenomenon of stress change in the loess collapsibility process is exposed. Therefore, it is necessary to utilize the unload wet trap coefficient δusAnd obtaining a modulus reduction method for calculating the loess unloading collapse quantity, and exploring a rapid calculation and analysis method for the loess unloading collapse quantity, so that the calculation of the loess collapse quantity under the influence of the unloading action is legal and well documented.
3. Factor of unloading action
According to the operating mode of loess field off-load collapsible, the loess collapsible process under the influence of off-load effect mainly considers the factor in two aspects: the completion degree of loess collapsibility when unloading occurs; the magnitude of the unloading amount during unloading. Therefore, to clarify the unloading process, the following relevant parameters are defined.
(1) Collapsible completion ratio eta1
Definition eta1To reflect the degree of complete collapse of loess when unloading occurs.
Figure BDA0002913868210000071
In the formula: s1Sample at pressure p before unloading takes place1The amount of wet sinking (mm) that has been completed under the action; s is the pressure p of the sample1Total amount of wet collapse (mm) under action.
(2) Unload stress ratio K
K is defined to reflect the magnitude of the decrease in vertical pressure when unloading occurs during loess collapsibility.
Figure BDA0002913868210000072
In the formula: p is a radical of1Initial pressure (kPa); Δ p is the vertical pressure (kPa) removed when unloading occurs during the collapse of the sample; p is a radical ofrThe vertical pressure (kPa) remaining after unloading the sample during the collapse process.
(3) Unload wet trap ratio eta2
Definition eta2To reflect the size of the sample collapsibility after unloading.
Figure BDA0002913868210000073
In the formula: s2For the sample after unloading at a pressure prThe amount of collapse (mm) achieved under the action.
(4) Loess unloading to reduce collapse coefficient deltar
Due to the loess inThe reduction of the vertical pressure in the unloading and collapsible process is that the collapsible deformation of the unloading and collapsible process is smaller than that of the unloading and collapsible process under the constant pressure. The unfinished collapsible amount S is expressed by the size of unfinished collapsible amount of undisturbed loess under the effect of unloadingrAnd an initial height h0Is defined as the loess unloading decreasing collapse coefficient deltar：
Figure BDA0002913868210000074
In the formula: srThe unfinished collapsibility (mm) of the undisturbed loess sample under the influence of unloading; h is0The initial height (mm) of the undisturbed loess sample.
The unloading and collapsing process is shown in fig. 4. In the figure, the line bf shows the sample at p1The amount of collapse when fully collapsed under the action of the force. In the whole process of the wet trap, the product of the wet trap amount and the vertical pressure is A1Then, then
A1＝p1S (5)
Line bc indicates that the sample is at p1Partial collapse quantity S is completed under the action of1At this point the vertical load Δ p is immediately discharged, and the sample is subsequently at prBy the action of (2)2The change in the height of the sample is indicated by the line de. Let the product of the amount of collapse and the vertical stress be A2And then:
A2＝p1S1+prS2(S1≤S,S2≤S) (6)
because the vertical unloading is carried out in the process of the collapsible, the following steps are carried out:
A1＞A2 (7)
namely, it is
p1S＞p1S1+prS2 (8)
The formula (8) can be represented as
Figure BDA0002913868210000081
And because of pr≤p1And then:
S＞S1+S2 (10)
as can be seen from the formula (10), in comparison with the amount of the collapsible caused by the constant pressure, the loess has a part of the amount of the collapsible which is not generated in the unloading collapsible process, and the part of the amount of the collapsible can be unloaded to reduce the collapsible coefficient deltarAnd (4) showing.
Reduction of the coefficient of collapsibility delta for unequivocal unloadingrCoefficient of wet trap deltasBy substituting the formulae (1) and (3) for the formula (4)
Figure BDA0002913868210000082
According to the norm to deltasCan be written as
δr＝δs(1-η1-η2) (12)
The formula (12) can be represented as
Figure BDA0002913868210000083
Wherein:
Figure BDA0002913868210000084
in the formula (14), S2/(S-S1) The values of (a) relate to 3 deflection: sample at initial pressure p1Total amount of wet collapse under influence S; before the unloading takes place, the sample is at a pressure p1The amount of wet sinking S that has been completed by the action1(ii) a After the unloading has taken place, the sample is at pressure prAmount of affected collapsible S2. According to the definition of each influencing factor in the unloading and collapsible process, K and eta can be used1And p1The magnitude of the above 3 deformation quantities is described, which is equal to S2/(S-S1) The correlation between them can be represented by the following formula:
Figure BDA0002913868210000085
4. loess unloading collapse coefficient deltaus
Based on the physical significance of each influence factor in the loess unloading and collapsible process. To show the magnitude of the collapsibility of the loess under the influence of the unloading effect, the unloading collapsibility coefficient deltausCan be defined as
δus＝δs-δr (16)
By substituting formulae (13) to (15) for formula (16)
δus＝δs[1-(1-η1)(1-f(K,η1,P1)] (17)
The formula (17) establishes the loess unloading collapsibility coefficient delta in the loess collapsibility process by comprehensively considering the unloading effectusIs described in (1). It can be seen thatusIs to deltasThe reduction is carried out to a certain degree, and 3 influencing factors in the unloading and collapsible process are mainly considered during the reduction: initial pressure p to which the sample is subjected at the onset of collapse1The size of (d); the completion degree of loess collapsibility before unloading, i.e. collapsibility completion ratio eta1(ii) a The magnitude of the unloading amount when the unloading action occurs is the unloading stress ratio K.
Delta derived for verification during loess unloading and collapseusThe reasonability of the method needs to be tested by the unloading collapsibility, and the law of loess collapsibility deformation under the influence of unloading is explored, so that f (K, eta) is determined1，p1) Is given by the expression of (D), to obtainusThe calculation formula of (2).
5. Loess unload collapsible test
5.1 test procedure
To determine deltausThe invention firstly carries out a conventional wet-fall test and then carries out an unloading wet-fall test. In the unloading and wet-fall test, different initial pressures p are determined1And collapsible completion ratio eta1Under the condition, the unloading stress ratio K and the unloading collapsible deformation S2The correlation between them.
First, the sample is measured inDifferent p1Coefficient of wet collapse of the following. Determination of undisturbed loess sample p by using double-line method1The coefficient of wet collapse delta is respectively 200, 250, 300, 350 and 400kPas。(p1The value range of (1) is the common vertical stress range in the loess foundation of the multi-storey and high-rise building in the loess region at present, and the corresponding deltasReflecting the size of the collapsibility of the loess under a certain pressure).
Next, an unloading and collapsible test was performed. At p1Under the action of the air, the sample is firstly compressed and stabilized under natural humidity. The sample after the pressure sinking stabilization is subjected to the wet deformation under the saturated state, and when the sample is subjected to different wet amounts S1During the test, vertical unloading is carried out to different degrees, after the unloading, the sample is attached to sink stably, the test is terminated, and the collapse deformation S of the sample after the unloading is measured2(the rebound phenomenon which is worth considering does not appear in the unloading and wet-fall test, and the unloading rebound deformation can be ignored). Vertical initial pressure p borne by the sample during the unloading and wet-fall test1The values are 200, 250, 300, 350 and 400kPa respectively. Eta1The samples were unloaded immediately after the completion of the initial amount of the total amount of the wet load, which was taken into account by 20%, 40%, 60% and 80% of the total amount of the wet load under the initial pressure of the sample. In the process of collapsible, the method for determining the vertical stress after unloading comprises the following steps: when p1200kPa and 250kPa, respectively, the unloading amounts Δ p are 25, 50, 75, 100, 125, 150 and 175kPa, respectively; when p1At 300, 400kPa, respectively, the unloading amount Δ p is 50, 75, 100, 125, 150, 175, 200, 225, 250kPa, respectively. The unload slump test protocol is shown in table 1.
TABLE 1 unload Wet trap test protocol
Figure BDA0002913868210000091
The unloading slump test procedure is shown in figure 5. Fig. 5(a) shows a conventional collapsing process. I.e. the sample is at a constant initial pressure p1Under the action, the collapsible deformation S is completed; FIG. 5(b) shows the unloading collapse process. The sample is first at an initial pressure p1Partial collapse deformation S is completed under the action of1(S1<S), the vertical load Δ p is immediately removed, and the sample is subsequently pressed vertically (p)1- Δ p) to accomplish the collapsing deformation S2. In this example, the emphasis is on the measurement of p1And eta1Under the condition, the collapse deformation S of the sample after unloading2Law of variation with K and K, eta1And η2/(1-η1) The correlation between them.
5.2 preparation of test samples and measurement of physical indices
The undisturbed loess sample for the test is taken from a certain building construction foundation pit in cuphua of Shaanxi, the soil taking depth is 5.0-8.5 m, the sample is in a brown yellow and hard plastic state, and the physical properties are shown in Table 2.
TABLE 2 physical Properties of undisturbed loess sample for testing
Figure BDA0002913868210000101
5.3 different initial pressures p1Corresponding loess collapsibility coefficient deltas
The experiment shows that different p1Collapse coefficient delta of undisturbed loess under actionsThe results are shown in Table 3. When p is1In the range of 0-200 kPa, the initial collapse pressure of the undisturbed loess sample for the test was measured to be 75kPa, and the saturation density of the soil covering over the sample was obtained as rho according to Table 2s＝1.67g/cm3. When the soil sampling depth is 5m, the saturated self-weight stress of the upper covering soil is 83.5kPa, which is greater than the initial collapse pressure, so when the soil sampling depth is 5-8.5 m, the sampled soil is self-weight collapsible loess, p is1At 200kPa, δs>0.07, judging that the soil sample has strong collapsibility according to the standard.
TABLE 3 delta for different initial pressures for the sampless
Figure BDA0002913868210000102
5.4 unload Wet trap test results and analysis
To determine f (K, eta)1P1) was first determined at different p1 and η1Under the condition, the unloading and collapsing deformation of the sample is S2, and is further determined according to S2/(S-S1) and eta2/(1-η1) To obtain η2/(1-η1) The relationship of-K, as shown in FIG. 6.
As can be seen from fig. 6:
(1) corresponding η at different initial pressures2/(1-η1) The values of the stress ratio are very similar to the curve forms of the stress ratio change along with the unloading, and eta is reduced along with the unloading stress ratio2/(1-η1) The value of (A) is obviously reduced, which shows 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, eta2/(1-η1) The curve descending relation is presented along with the reduction of the unloading stress ratio, the slope of the curve is gradually reduced along with the reduction of the unloading stress ratio, and when the unloading stress ratio is less than 0.5, the change of the slope of the curve tends to be stable. It is shown that when the vertical unloading amplitude reaches more than 50%, the influence of the unloading effect on the collapsibility of the loess after unloading is weakened. Eta when the initial pressure is greater than 250kPa2/(1-η1) The linear decreasing relation is presented along with the reduction of the unloading stress ratio. Eta2/(1-η1) The change form of the curve of the unloading stress ratio reflects that if the original loess is subjected to a certain degree of collapsibility under a larger initial pressure, the contact relation of macroporous skeleton particles in the soil is damaged to a higher degree, and the relation between the collapsibility deformation of the soil sample after unloading and the unloading amount tends to be linear.
(3) At the same unload stress ratio, eta2/(1-η1) Decreases with increasing wet end ratio and, with large unloading, η2/(1-η1) Is smaller than the magnitude of the reduction under small-amplitude unloading. Since the greater the completion of the collapsibility of the undisturbed loess at the time of the unloading action, the greater the formation of a new compacted structure after the rearrangement of the soil particles, the more the collapsibility deformation after the unloading will tend to be reduced, and this characteristic will be more pronounced with a smaller amount of unloading.
(4) In the process of unloading and wet-falling,η caused by unload stress ratio2/(1-η1) The reduction amplitude of the pressure relief valve is larger than that caused by the completion ratio of the collapse, namely, the deformation of the original loess after unloading has higher sensitivity to the change of the vertical pressure.
5.5 unload Wet coefficient δusDetermination of expressions
f(K，η1，p1) Determination of expressions
As can be seen from FIG. 4,. eta.2/(1-η1) The overall change rule of the-K curve is consistent, but eta2/(1-η1) Is taken as p1And η1There is still a difference in variation of (a) within a small range. To determine K, eta1And p1Influence degree on loess unloading collapse deformation, and K, eta1And p1As a function of η2/(1-η1) And (3) taking values to examine factors, and designing a multi-factor orthogonal test, wherein the levels of all factors are shown in a table 4.
TABLE 4 factors and levels of orthogonal experimental design
Figure BDA0002913868210000111
And (3) performing range analysis on the orthogonal test result, wherein the range reflects the influence of the variation of different levels of the factor on the index, the large range indicates that the difference generated by different levels of the factor is large, the factor is an important factor and has obvious influence on the test result, the small range factor is a secondary factor, and the change of the level has no obvious influence on the test result. Influence of eta in orthogonal experiments2/(1-η1) The analysis of the values of the various factors is shown in Table 5.
TABLE 5 pole difference analysis of multifactor orthogonal experiments
Figure BDA0002913868210000112
Figure BDA0002913868210000121
Note: kmIs the sum of the statistical indexes corresponding to the level of each factor m; k is a radical ofmIs KmAverage value of (d); r is the extreme difference of each factor.
From table 5, the primary and secondary order of the effect of each factor on the test results is: k → eta1→p1The unload stress ratio eta is illustrated2/(1-η1) The value of (2) plays a control role, and the initial pressure has the minimum influence on the collapsed deformation of the loess after unloading. Each factor pair eta2/(1-η1) A visual analysis of the value impact is shown in fig. 7.
As can be seen from FIG. 7, the initial pressure p1And collapsible completion ratio eta1The extreme difference value of (A) is close, the unloading stress ratio K is the maximum in the extreme difference value in the sensitivity analysis, which shows that K is a main factor influencing the test result, p1And η1Then to the index eta2/(1-η1) The effect of (a) was not significant. Because the influence degree of each factor on the test result cannot be accurately estimated by the range analysis, the test result is subjected to multi-factor variance analysis to make up for the deficiency.
According to the results of the analysis of variance in Table 6, the correlation between the initial pressure and the properties of loess-unloading collapsibility,
Figure BDA0002913868210000123
the correlation between the completion ratio of collapsibility and the deformation property of loess unloading collapsibility,
Figure BDA0002913868210000124
Figure BDA0002913868210000125
indicates p1And η1The influence on the loess unloading collapsible deformation property does not reach a remarkable level, and FK＝33.633>F0.01>F0.05Showing that the influence is on2/(1-η1) Among the 3 factors of the values, the unloading stress ratio K has the most obvious influence on the collapsible deformation of the sample after unloading.
TABLE 6 analysis of variance of the test influencing factors
Figure BDA0002913868210000122
According to the analysis result of the multi-factor orthogonal test, f (K, eta) is determined1，p1) K is taken as a main consideration in fitting analysis. By a plurality of functions to K and eta2/(1-η1) The correlation can be approximately expressed by a power function, and the expression is
f(K)＝aKb (18)
In the formula: and a and b are regression parameters. Determining different p by carrying out regression analysis on unloading and wet-fall test data1And η1The regression parameters under the conditions are shown in table 7.
As can be seen from Table 7, at different p1And eta1Under the condition of K and eta2/(1-η1) The correlation coefficients of (A) are all above 0.9. From the property of the function, the power function can also qualitatively reflect the change rule of the unloading amount and the collapse deformation after loess unloading, namely the collapse deformation after loess unloading is reduced along with the increase of the unloading amount, and the values of a and b are influenced by p1And η1Is less, consistent with the analysis of variance results described previously. Since the parameters a, b are different at p1And η1Values under the condition are close, and the expression of the mean value of a and b to f (K) can be further simplified.
5.6δusExpression of (2) and verification thereof
Substituting the average value of the parameters a and b into f (K) to obtain an unloading collapsible coefficient expression taking the unloading action into consideration in the loess collapsible process:
δus＝δs[1-(1-η1)(1-1.067K1.695)] (19)
by the formula (19) tousThe calculated result and the measured result are subjected to correlation analysis to obtain a variation coefficient C between the calculated result and the measured resultvAnd part of the comparison curves are shown in table 8 and fig. 8, respectively.
TABLE 7 η2/(1-η1) -K relation curveParameter (d) of
Figure BDA0002913868210000131
TABLE 8. deltausC of calculated and test valuesv
Figure BDA0002913868210000132
Figure BDA0002913868210000141
As can be seen from fig. 8 and table 8, the experimental values and the calculated values are well matched, the overall regularity is consistent, and the variation coefficient between the two values is less than 0.15. Described in regression f (K, eta)1，p1) When expressing (2), neglecting the factor p1And η1Is reasonable and simplifies the parameters in f (K). The loess unloading collapsible deformation result obtained by calculation according to the formula (19) has certain reliability, and can be used for calculating loess collapsible deformation under different initial pressures, different unloading and collapsible completion degrees, so that the collapsible property of loess under the influence of unloading action can be scientifically evaluated.
6. Modulus reduction factor under constant load wet trap condition
Deformation modulus E of undisturbed loess after immersion and collapse0And shear strength, both reduced, shear strength c,
Figure BDA0002913868210000144
mainly used for stability analysis of slope and foundation pit engineering, deformation modulus E0Mainly used for deformation calculation of foundation, and the deformation modulus E of loess for calculating the collapsible deformation of loess0And (6) performing reduction. Performing indoor compression test on undisturbed loess from Cuchuan to obtain different initial pressures p1Compressive modulus of lower ESBy using E0And ESObtaining the undisturbed loess at different p1Under the condition of E0As shown in table 9.
TABLE 9 undisturbed loess at different p1Under the condition of E0
Figure BDA0002913868210000142
According to Table 9, take different p1Undisturbed loess E0Average value of 24.5 MPa. To determine the deformation modulus E of undisturbed loess after soaking and collapsing0' now, the modulus of deformation reduction method is used to simulate the indoor collapsible test.
Calculating undisturbed loess at different p by modulus reduction method1The deformation by collapse was performed by reducing the deformation modulus of the undisturbed loess in the form of collapse to different degrees, and the calculation results are shown in fig. 9 and table 10.
TABLE 10 calculation of percent errors of undisturbed loess collapsibility and deformation by modulus reduction at different degrees
Figure BDA0002913868210000143
Figure BDA0002913868210000151
When the original loess deformation modulus E is taken respectively01/13-1/15 as modulus E after immersion in water0In the case of the method, the measured value and the calculated value of the loess collapse amount are close to each other, and the modulus reduction ratio range is in the range of E after the loess-containing water collapse is tested by a large loess submerging load0Is before collapsible E0The results of 1/20-1/10 are matched, and it is reasonable to calculate the collapse deformation of the original loess by the modulus subtraction method.
For the deformation modulus reduction range before and after the quantification loess collapsibility to realize the accurate calculation to the loess collapsibility, the modulus reduction coefficient Z under the dead load condition is now defined in order to reflect the relation of deformation modulus and initial modulus after the loess collapsibility:
Figure BDA0002913868210000152
in the formula, E0Deformation modulus (MPa) of loess before immersion and collapse; e0' is the deformation modulus of loess after water immersion and collapse.
To further establish the relation between the deformation modulus and the collapse deformation of the undisturbed loess after collapse and obtain different initial pressures p1Modulus reduction coefficient and wet collapse coefficient delta under the conditionsThe correlation of (2) is shown in FIG. 10.
According to FIG. 10, at the same p1Under the condition of deltasThe relation with Z is basically linear, and further delta is obtainedsThe correlation with Z is shown in Table 11.
TABLE 11. delta. under different parameterssIn relation to Z
Figure BDA0002913868210000153
As can be seen from Table 11, the value of the parameter a in f (Z) is dependent on the initial pressure p1The fluctuation range of the change is small, and the value of the parameter b is changed along with the p1The change of (a) is shown by the following formula:
b＝0.001p1-0.023 (21)
to simplify the expression of f (Z), taking the mean value of a and substituting the formula (4) into the expression of f (Z) yields:
δS＝-1.952Z+0.001p1-0.023 (22)
obtaining the modulus reduction coefficient Z and the wet collapse coefficient delta under the condition of constant load according to the formula (22)sThe relationship of (1):
Z＝0.001p1-0.512δS-0.012 (23)
from equation (23) different initial pressures p can be calculated1Under the condition, the modulus reduction coefficient Z after the original loess is immersed in water and collapsed can be calculated through Z, and the deformation modulus E after the original loess is immersed in water can be calculated through Z0', to calculate the loess collapsibility deformation using a modulus reduction method.
7. Modulus reduction factor under unloading and wet collapse conditions
To verify the reliability of the calculation of the unloaded wet set deformation by the modulus reduction method taking account of the unloading effect, the equation (19) is used to calculate the difference p1And eta1The indoor loess under the condition was subjected to the unloading collapse test several times, and the results are shown in fig. 11.
According to the graph of FIG. 11, the loess collapsibility deformation calculated by the modulus reduction method considering the unloading collapsibility is basically consistent with the indoor loess unloading collapsibility test value, and the average relative error (MAPE) of the loess collapsibility deformation and the indoor loess unloading collapsibility test value is less than 5%, which shows that the loess modulus reduction coefficient Z under the unloading condition obtained by the formula (7)uIt is reasonable to calculate the loess unloading collapse deformation, therefore, in order to calculate the loess unloading collapse deformation more accurately, the modulus reduction coefficient Z under the unloading collapse condition is provideduFig. 12 shows a method of determining (c).
According to the calculation process of fig. 12, the determination method for obtaining the modulus reduction coefficient Z under the unloading condition:
(1) firstly, according to the indoor unloading collapsibility test result and combining with modulus reduction method, under the unloading condition, a modulus reduction coefficient Z reflecting the relationship between deformation modulus and initial modulus after loess collapsibility is drawnui. Then calculating the loess collapsibility delta 'considering the unloading effect according to the relation between the deformation modulus of the undisturbed loess after collapsibility and the collapsibility deformation'ui。
(2) Is delta'uiMeasured by unloading and wet-fall testuiComparing, if the percentage error is less than 5%, determining the modulus reduction coefficient Z considering the unloading actionui. Repeating the above process to determine Z for different unload wet trap test conditionsuiFurther according to ZuiAnd calculating the loess collapsibility deformation considering the unloading effect. If delta'uiAnd deltauiIf the percentage error is greater than 5%, Z needs to be newly determineduiAnd carrying out iterative calculation until the two meet the error requirement.
(3) According to Z meeting the error requirementuCalculating loess collapsibility under constant load collapsibility condition by making Δ p equal to 0 in loess collapsibility process, and comparing with indoor conventional loess collapsibility test result to further verify ZuThe reliability of (2).
8 method authentication
Indoor degradation verification
For verifying loess unloading collapse coefficient delta under established unloading conditionusCoefficient of reduction of modulus ZuThe correspondence relationship between the values is used to verify the degradation of the loess under the condition that the loess can degrade to the constant load collapsible condition when the unloading amount is zero (Δ p is 0), and the comparison between the calculated value of the loess collapsible amount calculated by the modulus reduction method and the actual measurement value and the degradation verification result according to the formula (19) are shown in fig. 13.
As can be seen from FIG. 13, the different initial pressures p1Under the condition, the calculated values of the loess unloading collapsible amount in different unloading states calculated by the modulus reduction method are consistent with the actually measured unloading collapsible deformation rule, and the NashNash coefficients (NSE) of the calculated values and the actually measured unloading collapsible deformation rule are both more than 0.9, which shows that the modulus reduction method can fully follow the actual stress change condition in the loess collapsible process and better reflect the influence of the unloading amount on the loess unloading collapsible deformation. To further verify the modulus reduction factor ZuThe loess collapsibility under the constant load collapsibility condition was calculated by the equation (19) with the load discharge amount Δ p being 0, and it was found that the loess collapsibility was obtained at different initial pressures p1Under the condition, the average relative errors of the loess collapsibility degradation verification value and the three groups of indoor measured values are less than 5%, which shows that the unloading collapsibility deformation of the loess calculated by the modulus reduction method is reasonable and the accuracy is high.
4.2 engineering example validation
In order to verify the rationality of calculating loess collapsible deformation by a modulus reduction method considering an unloading effect, the load-bearing property and the negative frictional resistance test of the ZH4 cast-in-place pile carried out on a dead-weight collapsible loess field in Ningxia regions based on Huangxuefeng and the like are used, and the negative frictional resistance generated by calculating the soil collapsible deformation among the piles by the modulus reduction method considering the unloading effect is compared with the field pile foundation soaking test result, and the result is shown in fig. 14 (b).
As can be seen from fig. 14:
(1) along with further reduction of loess modulus between piles, the soil between piles is subjected to collapsible deformation, the positive stress of the upper soil layer is reduced, and the soil is gradually converted to negative frictional resistance to form a pull-down load.
(2) The neutral point position and the evolution characteristic of the negative friction resistance in the calculation result are basically consistent with the trend of the measured value, and the neutral point position gradually moves upwards along with the increase of the pile top load, namely the positive friction resistance is increased, and the 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 an actual collapsible soil layer on site, the measured values of the negative frictional resistance under different pile top loads and the calculated value Nash coefficient are respectively calculated to be more than 0.9, and the prediction and calculation of the loess unloading collapsible shape by the modulus reduction method are reasonable.
The modulus reduction method considering the unloading effect fully considers the actual stress change condition in the loess collapsibility process between piles, and the modulus reduction coefficient Z under different unloading conditions is drawn upuThe stress change in the loess collapsibility among the piles is enabled to accord with the actual working condition, the unloading collapsibility effect is successfully introduced into the loess collapsibility deformation calculation among the piles, the calculation process is simple, and the calculation result of the loess collapsibility deformation among the piles is reasonable.
Aiming at the unloading working conditions of pit immersion, pile inter-pile soil immersion, collapse and the like, the loess sinks after being immersed in water, the vertical stress of the loess sinks under the influence of the sharing effect and the negative frictional resistance of the piles, the vertical pressure is reduced along with the loess collapse process, and the unloading and collapse are associated with one of important reasons for causing the difference between the calculated value and the measured value of the collapse amount.
The vertical stress is reduced in the loess unloading and collapsible process, the collapsible deformation and the collapsible category 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 the unloading and collapsible working condition. It is necessary to consider the influence of the unloading collapsibility in the loess collapsibility calculation.
The calculated value of the unloading collapsible amount of the invention is smaller than the standard value, the influence of the pile side friction on the collapsible deformation can be reflected by the unloading collapsible coefficient in the calculation of the loess collapsible amount among the piles, and the unloading collapsible effect is more obvious when the negative friction is larger.
The method is reasonable in calculating the loess collapsible deformation by adopting the deformation modulus reduction methodIn (1). Through iterative calculation, when the calculated value and the calculated value of the unloading wet settlement are less than 5 percent, the modulus reduction coefficient Z under the unloading condition can be establishedu. It is necessary to use a means of flexural modulus reduction to pass the unload slump through ZuAnd deltausThe loess collapsibility calculation is scientifically introduced.

Claims (5)

1. A method for calculating loess unloading collapsible quantity is characterized by comprising the following steps:
step 1: calculating to obtain a collapsible completion ratio eta reflecting the extent of the loess completely collapsible when unloading occurs1，
Calculating to obtain an unloading stress ratio K reflecting the reduction amplitude of the vertical pressure when the unloading action occurs in the loess collapsibility process,
step 2: using the collapsible completion ratio eta1And calculating the unloading wet collapse coefficient delta according to the unloading stress ratio Kus，
And step 3: by the unload coefficient of wet collapse deltausCalculating to obtain loess modulus reduction coefficient Z under unloading conditionuWherein Z is calculateduThe formula of (1) is:
Zu＝0.001p1-0.512δus-0.012，
in the formula: p is a radical of1Initial pressure (kPa);
and 4, step 4: and calculating the loess unloading collapse amount according to the loess modulus reduction coefficient under the unloading condition.
2. The method for calculating an amount of loess-unloading collapsibility as claimed in claim 1, wherein η in the step 1 is calculated1The formula of (1) is:
Figure FDA0002913868200000011
in the formula: s1Sample at pressure p before unloading takes place1The amount of wet sinking (mm) that has been completed under the action; s is the pressure p of the sample1Total amount of wet collapse (mm) under action.
3. The method for calculating a loess unloading collapsibility according to claim 1, wherein the formula for calculating K in step 1 is,
Figure FDA0002913868200000012
in the formula: p is a radical of1Initial pressure (kPa); Δ p is the vertical pressure (kPa) removed when unloading occurs during the collapse of the sample; p is a radical ofrThe vertical pressure (kPa) remaining after unloading the sample during the collapse process.
4. The method for calculating an amount of loess unloading collapsibility according to any one of claims 1 to 3, wherein δ is calculated in step 2usThe formula of (1) is:
δus＝δs[1-(1-η1)(1-1.067K1.695)]，
in the formula: deltasIs the collapsible coefficient of undisturbed loess.
5. The method for calculating a loess unloading collapsibility as claimed in claim 4, wherein the loess unloading collapsibility Δ is calculated in step 4usThe formula of (1) is:
Figure FDA0002913868200000013
in the formula,. DELTA.piIncreasing the average additional stress generated in the ith layer of soil by the volume weight of the loess body in the loess collapsible process; alpha is a coefficient for correcting the collapsible deformation modulus, and is 1.1-1.5; e0iThe deformation modulus (MPa) of the i-th layer of collapsible loess before immersion and collapse; hiIs the thickness of the i-th layer collapsible loess.
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