A method for predicting horizontal displacement of deep and narrow foundation pit supporting structure

Abstract

This invention relates to the field of construction and discloses a method for predicting the horizontal displacement of support structures in deep and narrow foundation pits. The method predicts the maximum horizontal displacement of these structures by incorporating the pit width and embedment depth into the Clough system stiffness formula. This prediction method, by introducing the pit width, uses fewer parameters to predict the maximum horizontal displacement of deep and narrow foundation pits, making it more accurate than Clough predictions for such cases. The method requires fewer parameters, is easy to operate, and can be widely applied in engineering design.

Description

Technical Field

[0001] This invention relates to the field of construction, and in particular to a method for predicting the horizontal displacement of support structures in deep and narrow foundation pits. Background Technology

[0002] The horizontal displacement of the foundation pit support structure is an important indicator for evaluating the stability of the foundation pit. Clough first proposed the concept of system stiffness prediction, and Clough's system stiffness prediction formula is as follows:

[0003] (1-1)

[0004] Where: EI is the horizontal bending stiffness of the support structure, γ w S represents the specific gravity of water. v The average vertical spacing for support.

[0005] The relationship between the system stiffness K and the maximum relative horizontal displacement δ of the support structure was established. hm The trend curve for / H can be seen in... Figure 1 δ hm The maximum horizontal displacement is given by H, and the depth of the foundation pit is given by H. The system stiffness K is calculated, and... Figure 1 The curve search and calculation yielded the system stiffness corresponding to δ hm Since the depth H of the foundation pit is a known constant, the maximum horizontal displacement δ can be calculated. hm This forecasting method is simple and practical, and easy for frontline practitioners to quickly master. Currently, it is also a widely used forecasting method among frontline practitioners.

[0006] However, in recent years, numerous deep and narrow foundation pits have been created in projects such as integrated utility tunnels, underground pipeline renovations, and cable burials. Clough's maximum displacement prediction method does not consider the impact of changes in pit width on the maximum horizontal displacement of the support structure. This results in the foundation pit support structure established using Clough's displacement prediction method having a stiffness far greater than the actual support stiffness required for deep and narrow foundation pits, leading to waste of support structure materials and increased support costs.

[0007] Although some scholars have improved Clough's prediction method, they all suffer from problems such as introducing too many parameters and having overly complicated calculation principles and processes, making it difficult to promote and apply among practitioners.

[0008] In addition, the finite element simulation method can also obtain relatively accurate results of the maximum horizontal displacement of the support structure. However, each calculation requires consideration of many issues such as structural modeling, the applicability of the constitutive model, and the accuracy of soil parameter selection. The finite element modeling and solution process is complex and time-consuming. It requires highly skilled professionals with extensive engineering and finite element analysis experience to master it well, and it cannot be widely applied among a large number of front-line practitioners.

[0009] To address the aforementioned shortcomings, it is an urgent technical problem to provide a simple, practical, and easy-to-use method for predicting the horizontal displacement of deep and narrow foundation pit support structures that is convenient for frontline engineering professionals. Summary of the Invention

[0010] The technical problem to be solved by this invention is to provide a simple and easy-to-use method for predicting the horizontal displacement of support structures for deep and narrow foundation pits. By introducing the width of the foundation pit and the embedment depth, it requires few parameters and has a relatively simple calculation process. It correlates the maximum horizontal displacement with the width of the foundation pit and the embedment depth, making it suitable for the design of support structures for deep and narrow foundation pits. It saves materials and reduces support costs. Moreover, the prediction method of this invention is economical and practical, and is worthy of widespread application.

[0011] To address the aforementioned technical problems, this invention provides a method for predicting the horizontal displacement of support structures in deep and narrow foundation pits, comprising the following steps:

[0012] Step 1: Select a typical geological section from the actual project and introduce the parameter B / h, which characterizes the width of the foundation pit. q By selecting support structures with different pit widths, different bending stiffnesses, and different support spacings, corresponding finite element models were established, and the maximum horizontal displacement of each support structure combination was calculated; where B is the pit width, h q The embedding depth;

[0013] Step 2: Based on the maximum horizontal displacement calculation results in Step 1, evaluate the pit width and S... v The degree of influence of EI on system stiffness;

[0014] Step 3: Find δ using different values ​​of n hm / h q With EI / (γ) w S v n The correlation of ) ; where n is the S v The exponent of the parameter;

[0015] Step 4: Use the δ obtained in Step 3 hm / h q With EI / (γ) w S v n The correlation formula is used to introduce the parameter B / h through curve fitting. q Establish a formula for predicting the maximum horizontal displacement suitable for narrow foundation pits.

[0016] Preferably, in step 1, the section containing a thick layer of raw or mixed fill soil should be avoided when selecting typical strata.

[0017] Preferably, in step 1, δ hm / h q Characterizes the maximum horizontal displacement.

[0018] Preferably, in step 2, based on the maximum horizontal displacement result from step 1, different support conditions and δ are considered. hm / h q The relationship between the system stiffness and δ hm / h q With B / h q Relationship diagram, evaluation of S v EI, B / h q The degree of influence on the system stiffness.

[0019] Preferably, in step 3, the range of the exponent n is set, within different B / h values. q Under different n values, δ is fitted using a power function. hm / h q With EI / (γ) w S v n The relationship between ) determines the R-squared of the fitted function. 2 The value of n corresponding to ≥0.95.

[0020] Preferably, in step 3, under different B / hq conditions, δ hm / h q With EI / (γ) w S v n (R²) Relationship diagram, where n is the R² of the fitted function. 2 The value corresponding to ≥0.95; according to δ hm / h q With EI / (γ) w S v n Relationship diagram, seeking δ hm / h q With EI / (γ) w S v n The correlation between them.

[0021] Preferably, in step 3, δ hm / h q With EI / (γ) w S v n The correlation formula between them can be expressed as a power function:

[0022] (2-1)

[0023] Where a and b are the fitting parameters, and n is the R-squared value of the fitting function.2 S corresponding to ≥0.95 v The exponential value of the parameter.

[0024] Preferably, in step 4, different B / h values ​​are determined based on different fitting equations. q The curves of the fitting parameters a and b are plotted to determine the relationship between the fitting parameters a and b and B / h. q The relevant formulas.

[0025] Preferably, the prediction formula applicable to northern regions is:

[0026] (2-9)

[0027] Where, δ hm h represents the maximum horizontal displacement of the support structure. q Where B is the embedment depth, B is the pit width, EI is the horizontal bending stiffness of the support structure, and S is the depth of embedment. v For the average vertical spacing of the supports, γ w It is the density of water.

[0028] The method for predicting horizontal displacement of deep and narrow foundation pit support structures of the present invention has the following advantages compared with the prior art:

[0029] 1) It provides a prediction method specifically for the maximum horizontal displacement of deep and narrow foundation pits, which improves the prediction accuracy.

[0030] The method of this invention introduces the pit width and embedment depth into the Clough system stiffness formula, and directly obtains the maximum horizontal displacement result of deep and narrow pits using fewer parameters. This makes the predicted maximum horizontal displacement result more accurate than the Clough system stiffness prediction method for the maximum displacement of deep and narrow pits. Under the premise of ensuring the stiffness of the support structure, the stiffness of the support structure is reduced, the material used in the support structure is reduced, and the cost of the support structure is reduced.

[0031] 2) It requires few parameters and is simple to use.

[0032] Only the pit width B and embedment depth h are introduced. q Both parameters are directly related to the width of the foundation pit, and their values ​​can be directly obtained from the engineering data. They can be directly substituted into formula (2-1) to solve the problem.

[0033] 3) It does not require prior finite element modeling, the introduction of too many parameters, and the calculation principles and tedious calculation processes.

[0034] 4) The principle of this invention is simple and easy to operate, and it can be promoted and applied among front-line engineering practitioners. Attached Figure Description

[0035] Figure 1 This is a graph of the Clough system stiffness prediction method.

[0036] Figure 2 It is a geological and load model (B / h) q =1.5, 1st support level).

[0037] Figure 3 It is δ hm / h q A partial relationship diagram between the system stiffness K and the system stiffness.

[0038] Figure 4 B / hq and δ under different support structures hm / h q Relationship diagram.

[0039] Figure 5 It is δ hm / h q With EI / (γ) w S v 3 Relationship diagram.

[0040] Figure 6 This is a graph showing the relationship between parameter a and B / hq.

[0041] Figure 7 This is a graph showing the relationship between parameter b and B / hq. Detailed Implementation

[0042] Regarding the above technical solutions, preferred embodiments are now described in detail with reference to the figures.

[0043] In the following embodiments, Plaxis2D finite element software and Hardening-Soil model (HS model for short) were used for simulation calculations.

[0044] The present invention provides a method for predicting the horizontal displacement of support structures in deep and narrow foundation pits, comprising the following steps:

[0045] Step 1: Perform finite element modeling and calculate the maximum horizontal displacement:

[0046] First, a stormwater pipe gallery project in Xi'an was selected, and its geological conditions (depth and physical and mechanical parameters of each soil layer, etc.) and support design scheme were extracted. The parameters of each soil layer are shown in Table 1. It should be noted that, in order to ensure the generality and representativeness of the research results, sections containing thick layers of plain or miscellaneous fill soil should be avoided. A calculation model was established, and step-by-step simulations were performed according to the construction conditions.

[0047] Table 1. Parameter values ​​for each soil layer

[0048]

[0049] Taking into account the width of the foundation pit, the embedment depth h is selected. q The ratio of B / h to the pit width B is used to characterize the pit width factor, and B / h is used to represent the pit width factor. q Defined as embedment ratio, nine different B / h values ​​were selected. q 9 different B / h q Five different combinations of support structures with bending stiffnesses (0.5, 0.75, 1, 1.5, 2, 3, 5, 10, 15) were selected, as shown in Table 2.

[0050] Table 2 Bending stiffness EI of different support structures

[0051]

[0052] Two different support spacing options were selected: one-support and two-support. Each B / h... q It can accommodate 10 different support structure combinations with varying stiffness, and a total of 90 numerical models have been established. (See attached image) Figure 2 The maximum horizontal displacement δ was obtained through finite element simulation. hm For ease of comparison, δ is used. hm / h q Characterized by the maximum horizontal displacement. δ hm / h q The calculation results are shown in Table 3.

[0053] Table 3 δ hm / h q Calculation results

[0054]

[0055] Step 2: Based on the calculation results in Table 3 and the engineering monitoring results in Step 1, make partial δ calculations. hm / h q The relationship between the system stiffness K and the design of the foundation pit support structure is shown in the diagram. Since the system stiffness value remains constant once the design is determined, the system stiffness is calculated using the Clough system stiffness calculation formula. The accuracy of the finite element simulation is verified. (See attached diagram.) Figure 3 .

[0056] At the same time, according to Table 3, δ hm / h q With B / h q Relationship diagram, see Figure 4 Theoretically, similar system stiffness K should correspond to similar δ. hm / h q However, by Figure 3 It can be seen that for similar systems, the stiffness K differs due to B / h. q The difference, δ hm / h qThe distribution of δ is highly discrete, especially when the system stiffness K is less than 100. For example, a support system of type IV sheet piles with two supports has a similar K value to a support system of diaphragm wall with one support, but the latter has a corresponding δ hm / h q However, it is much smaller than the former, which indicates that for deep and narrow foundation pits, S v 4 Unlike EI, which has an inconsistent effect on system stiffness, S v The impact on system stiffness has been overestimated and needs to be reassessed.

[0057] Depend on Figure 4 It can be seen that for the same system with different stiffness B / h q The foundation pit, δ hm / h q With B / h q The increase is due to the increase in B / h q It has a significant impact on the system stiffness K; however, B / h q The effect of the system stiffness K gradually weakens as its value increases (i.e., the width of the foundation pit increases). When B / hq ≤ 2, the impact of the foundation pit width on δ hm / h q The impact is obvious.

[0058] Step 3: Utilize different values ​​of n (n is S) v To seek δ (the index) hm / h q With EI / (γ) w S v n A better correlation between them.

[0059] Depend on Figure 3 and Figure 4 It can be seen that for deep and narrow foundation pits, S v The impact on system stiffness is overestimated. In the system stiffness formula, S... v The index is 4, therefore, during the reassessment, S is set to... v The exponent n = 2 - 4. A power function can be used to fit δ very well. hm / h q With EI / (γ) w S v n The relationship between ).

[0060] When n = 2-4, the R-value of the fitting function is... 2 The values ​​are shown in Table 4. From this table, it can be seen that when n=3, R... 2 Greater than 0.95, i.e., δ hm / h q With EI / (γ) w Sv 3 There is a better correlation between them.

[0061] Table 4 δ hm / h q With EI / (γ) w S v n Relationship

[0062]

[0063] Step 4, draw δ hm / h q With EI / (γ) w S v 3 Relationship diagram, see Figure 5 δ hm / h q With EI / (γ) w S v 3 This means that the system stiffness decreases monotonically with increasing B / hq (i.e., the pit width). The dispersion of the data increases with increasing B / hq. Referring to Table 4, when B / hq < 2, R... 2 Greater than 0.95. Therefore, for deep and narrow foundation pits, EI / (γ) can be used. w S v 3 ) instead of Clough's proposed EI / (γ w S v 4 To predict δ hm / h q That is, the maximum horizontal displacement.

[0064] Will Figure 5 δ hm / h q With EI / (γ) w S v 3 The relationship between them can be expressed as:

[0065] (2-1)

[0066] Where a and b are fitting parameters.

[0067] The analysis was performed using only data where B / hq ≤ 2, and the fitted equation is as follows:

[0068] (2-2)

[0069] (2-3)

[0070] (2-4)

[0071] (2-5)

[0072] (2-6)

[0073] Different B / h q The values ​​of a and b under the given conditions are as follows: Figure 6 and Figure 7 As shown.

[0074] according to Figure 6 and Figure 7 a and b can be defined as follows:

[0075] (2-7)

[0076] (2-8)

[0077] Substituting the obtained definitions a and b into formula (2-1), we get the prediction formula:

[0078] (2-9)

[0079] The prediction formula shows that the maximum horizontal displacement is related not only to the system stiffness, but also to the pit width and embedment depth.

[0080] In this embodiment, an actual project in Xi'an is used as a reference for explanation, and the prediction formula derived from this method is applicable to northern regions with similar land areas as Xi'an. For southern regions, an actual project in the south can be used as a reference to establish a prediction formula applicable to southern regions using the prediction method of this invention.

[0081] Therefore, the prediction method of the present invention can be applied to the prediction of the maximum horizontal displacement of deep and narrow foundation pit projects in various regions.

[0082] Validation of the prediction method of this invention

[0083] The relevant monitoring data from some deep and narrow foundation pit projects in Xi'an were used for verification. The stiffness prediction method of the Clough system and the prediction formula (2-9) in this paper were used to obtain δ respectively. hm / H and δ hm / h q The predicted value is then used to derive the predicted value δ of the horizontal displacement of the support structure. hm And compare it with the monitoring values ​​of the actual project.

[0084] For example, consider a deep and narrow foundation pit. The pit depth H = 27.1m, the embedment depth hq = 9m, the pit width B = 21m, and the support piles are Φ1200@1600 with an average vertical spacing S. v =5.18m. Table 5 shows the predicted maximum horizontal displacement and actual monitoring data using the Clough system stiffness prediction method and the prediction method of this invention, respectively.

[0085] Table 5

[0086]

[0087] A deep and narrow foundation pit (type II) has a depth H = 16.1m, an embedment depth hq = 6m, a width B = 18m, and is supported by Φ800@1200 retaining piles with an average vertical spacing S. v =4.93m. Table 6 shows the predicted maximum horizontal displacement and actual monitoring data using the Clough system stiffness prediction method and the prediction method of this invention, respectively.

[0088] Table 6

[0089]

[0090] A deep and narrow foundation pit (number 3) has a depth H = 9m, an embedment depth hq = 4m, a width B = 7m, and 800mm diameter retaining piles at 1500mm intervals. The average vertical spacing of the supports is S. v =6.8m. Table 7 shows the predicted maximum horizontal displacement and actual monitoring data using the Clough system stiffness prediction method and the prediction method of this invention, respectively.

[0091] Table 7

[0092]

[0093] As shown in Tables 5, 6, and 7 above, in deep and narrow foundation pits, the maximum horizontal displacement predicted by the Clough system stiffness prediction method is much larger than the actual monitored value, while the maximum horizontal displacement predicted by the method of this invention is slightly larger than the actual monitored value, relatively close to the monitored value, and much smaller than the predicted value calculated using the Clough system stiffness prediction method. Therefore, it can be concluded that the stiffness of the support structure designed using the maximum horizontal displacement data obtained by the prediction formula of this invention fully meets the stiffness requirements of the support structure in actual engineering projects. Compared with the support structure designed based on the maximum horizontal displacement obtained by the Clough system stiffness prediction method, this method saves materials and reduces support costs.

Claims

1. A method for predicting the horizontal displacement of a support structure in a deep and narrow foundation pit, comprising the following steps: Step 1: Select a typical geological section from the actual project and introduce the parameter B / h, which characterizes the width of the foundation pit. q By selecting support structures with different pit widths, different bending stiffnesses, and different support spacings, corresponding finite element models were established, and the maximum horizontal displacement of each support structure combination was calculated; where B is the pit width, h q δ represents the embedment depth. hm The maximum horizontal displacement of the support structure is δ hm / h q Characterizes the maximum horizontal displacement; Step 2: Based on the maximum horizontal displacement calculation results in Step 1, calculate δ under different support conditions. hm / h q The relationship between the system stiffness and δ hm / h q With B / h q Relationship diagram, evaluating B / h q S v The influence of EI on the system stiffness, respectively; where EI is the horizontal bending stiffness of the support structure, and S... v The average vertical spacing for support; Step 3: Find δ using different values ​​of n hm / h q With EI / (γ) w S v n The correlation of ) is determined by setting the range of the index n, at different B / h. q Under different n values, δ is fitted using a power function. hm / h q With EI / (γ) w S v n The relationship between ) determines the R-squared of the fitted function. 2 The value of n corresponding to ≥0.95; where γ w Let S be the specific weight of water, and n be the weight of water. v The exponent of the parameter; Step 4: Use the δ obtained in Step 3 hm / h q With EI / (γ) w S v n By incorporating parameters a and b through curve fitting, a formula for predicting the maximum horizontal displacement of narrow foundation pits is established. ， Where a and b are the fitting parameters, and n is the R-squared value of the fitting function. 2 S corresponding to ≥0.95 v The exponential value of the parameter; Based on different fitting equations, determine different B / h ratios. q The curves of the fitting parameters a and b are used to determine the relationship between the fitting parameters a and b and B / h. q The relevant formulas.

2. The method for predicting horizontal displacement of support structures in deep and narrow foundation pits according to claim 1, characterized in that, In step 1, typical strata should avoid selecting sections containing thick layers of raw soil and miscellaneous fill.

3. The method for predicting horizontal displacement of support structures in deep and narrow foundation pits according to claim 1, characterized in that, In step 3, under different B / hq conditions, δ hm / h q With EI / (γ) w S v n (R²) Relationship diagram, where n is the R² of the fitted function. 2 The value corresponding to ≥0.95; according to δ hm / h q With EI / (γ) w S v n Relationship diagram, seeking δ hm / h q With EI / (γ) w S v n The correlation between them.

4. The method for predicting the horizontal displacement of a deep and narrow foundation pit support structure according to any one of claims 1 to 3, characterized in that, The forecasting formula applicable to northern regions is: ， Where, δ hm h represents the maximum horizontal displacement of the support structure. q Where B is the embedment depth, B is the pit width, EI is the horizontal bending stiffness of the support structure, and S is the depth of embedment. v The average vertical spacing for support. γ w It is the density of water.

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