Method for determining a permissible value of a bottom heave deformation

Abstract

A pit bottom uplift deformation allowable value determination method belongs to the technical field of foundation pit excavation engineering construction safety evaluation and disaster prevention, and comprises the following steps: step 1, a foundation pit excavation model is established, and the anti-uplift stability safety factor of the foundation pit is calculated; step 2, a foundation pit excavation mathematical model is established in the PLAXIS 2D finite element calculation software, the uplift deformation value d of the monitoring point is calculated, and the point with the maximum uplift deformation value is selected as a characteristic point; step 3, finally, the failure probability under a certain anti-uplift stability safety factor limit value is used to determine the pit bottom uplift deformation allowable value under the same failure probability. The anti-uplift stability safety factor and the pit bottom uplift deformation value are combined, and the pit bottom uplift deformation allowable value under different conditions is determined according to different regional specifications and different projects.

Description

Technical Field

[0001] This invention belongs to the field of construction safety assessment and disaster prevention technology for foundation pit excavation projects, and specifically relates to a method for determining the allowable value of pit bottom heave deformation. Background Technology

[0002] Foundation pit instability is a significant risk factor affecting safe construction, with bottom heave failure being a major contributing factor to such accidents. Therefore, accurately evaluating bottom heave stability is crucial for foundation pit engineering safety. Current research primarily uses two indicators to assess bottom heave stability: the heave stability safety factor and the bottom heave deformation value. Currently, the standard values ​​for the heave stability safety factor (as specified in the "Code for Design of Building Foundations" GB 50007-2011) and the bottom heave deformation monitoring alarm values ​​(as specified in the "Technical Code for Monitoring Foundation Pit Engineering" GB 50497-2009) are used as limits to determine whether heave instability has occurred. However, the standard values ​​for the heave stability safety factor vary across regions due to factors such as geological environment, soil quality, and the impact of foundation pit excavation on the surrounding environment. Furthermore, there are no precise regulations regarding bottom heave deformation values ​​for different situations. Therefore, a precise method is needed to determine the allowable bottom heave deformation values ​​under different conditions based on regional standards and specific engineering projects. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, this invention discloses a method for determining the allowable value of pit bottom heave deformation. This method combines the anti-heave stability safety factor and the pit bottom heave deformation value, and takes into account different regional specifications and different projects to determine the allowable value of pit bottom heave deformation under different conditions.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A method for determining the allowable value of pit bottom heave deformation includes the following steps:

[0006] Step 1: Establish a foundation pit excavation model. Based on the soil layer parameter samples of the foundation pit, write a program in MATLAB to calculate the safety factor of the foundation pit's heave stability using the circular arc sliding method.

[0007] Step 2: In PLAXIS 2D finite element calculation software, establish a mathematical model of the foundation pit excavation. According to the monitoring point layout scheme specified in "Technical Specification for Monitoring of Building Foundation Pit Engineering GB 50497-2009", set up a series of monitoring points at the bottom of the foundation pit, calculate the heave deformation value d of the monitoring points, and select the point with the largest heave deformation value as the feature point.

[0008] Step 3: Use the Monte Carlo sampling method to obtain random variable samples of different soil parameters. Samples with a heave stability safety factor less than the limit of the heave stability safety factor and samples with a characteristic point heave deformation value greater than the allowable value of the heave deformation at the bottom of the pit are taken as failure samples. Calculate the failure probability for each sample. Finally, based on the failure probability under a certain heave stability safety factor limit, determine the allowable value of the heave deformation at the bottom of the pit under the same failure probability.

[0009] Preferably, step 1 includes the following specific steps:

[0010] (A) Establish a mathematical model for foundation pit excavation, determine the geometric dimensions and parameter probability distribution types of the foundation pit, and generate N soil layer parameter samples X1, X2, ..., X using a random method based on the statistical measures of soil uncertainty parameters. N ; Calculate X1, X2, ..., X using formula (1) N The corresponding heave stability safety factor K D1 K D2 ... K DN ;

[0011]

[0012] In equation (1): K D R is the stability safety factor against uplift; R is the sliding radius (m); c j , The values ​​are the cohesion (kPa) and internal friction angle (°) of the j-th soil strip at the slip surface, respectively; j Let q be the slip arc length (m) of the j-th soil strip; j Let be the standard value (kPa) of the vertical pressure on the top surface of the j-th soil strip; b j Let θ be the width (m) of the j-th soil strip; j Let ΔG be the angle (°) between the normal at the midpoint of the slip surface of the j-th soil strip and the vertical plane; j Let j be the self-weight of the j-th soil strip (kN);

[0013] (B) To limit the safety factor for resistance to uplift, if These are called failed samples. This process is repeated until the number of failed samples, m, is counted.

[0014] (C) Change The number of failure samples m under different limits was obtained. j Formula (2) is used to calculate the failure probability p of the pit bottom anti-heave stability safety factor under different limits. f1j :

[0015] P f =m / N (2)

[0016] In equation (2): Pf denoted as , where m is the failure probability; m is the number of failure samples; and N is the total number of samples.

[0017] Preferably, step 2 includes the following specific steps: calculating d for N soil parameter samples. i ;d max Let d be the allowable value for the heave deformation at the bottom of the pit. i >d max This is called a failed sample. Repeating this process yields the number of failed samples, m. Changing d... max The number of failure samples m under different limits was obtained. j Based on formula (2), the failure probability p of the pit bottom heave deformation value exceeding the limit under different limits is calculated. f2j .

[0018] Preferably, step 3 includes the following specific steps: drawing a graph with failure probability p f1j p f2j A line graph with different anti-heave stability safety factor limits and different pit bottom heave deformation allowable values ​​on the x-axis is used to obtain the pit bottom heave deformation allowable value with the same failure probability as the required anti-heave stability safety factor limit.

[0019] The beneficial effects of the method for determining the allowable value of pit bottom heave deformation of the present invention are as follows: The present invention combines the anti-heave stability safety factor and the pit bottom heave deformation value. Considering that the standard limit value of the anti-heave stability safety factor is different in different regions, the allowable value of pit bottom heave deformation is determined according to the principle of equal failure probability. In this way, the allowable value of pit bottom heave deformation under the standard limit value of the anti-heave stability safety factor can be obtained, thereby achieving the effect of determining the allowable value of pit bottom heave deformation under different conditions according to the standards of different regions and different projects. Attached Figure Description

[0020] Figure 1 The flowchart of this invention;

[0021] Figure 2 Diagram illustrating the verification of the circular arc sliding mode for resisting pit bottom heave;

[0022] Figure 3 PLAXIS 2D foundation pit excavation mathematical model and monitoring point layout diagram;

[0023] Figure 4 Illustrations of uplift deformation values ​​at each monitoring point;

[0024] Figure 5 Failure probability p under different limits f1j p f2j . Detailed Implementation

[0025] The following description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0026] Example 1:

[0027] A method for determining the allowable value of pit bottom heave deformation, such as Figure 1 As shown, it includes the following steps:

[0028] Step 1: Establish a foundation pit excavation model. Based on the soil layer parameter samples of the foundation pit, write a program in MATLAB to calculate the safety factor of the foundation pit's heave stability using the circular arc sliding method.

[0029] Step 2: In PLAXIS 2D finite element calculation software, establish a mathematical model of the foundation pit excavation. According to the monitoring point layout scheme specified in "Technical Specification for Monitoring of Building Foundation Pit Engineering GB 50497-2009", set up a series of monitoring points at the bottom of the foundation pit, calculate the heave deformation value d of the monitoring points, and select the point with the largest heave deformation value as the feature point.

[0030] Step 3: Use the Monte Carlo sampling method to obtain random variable samples of different soil parameters. Samples with a heave stability safety factor less than the limit of the heave stability safety factor and samples with a characteristic point heave deformation value greater than the allowable value of the heave deformation at the bottom of the pit are taken as failure samples. Calculate the failure probability for each sample. Finally, based on the failure probability under a certain heave stability safety factor limit, determine the allowable value of the heave deformation at the bottom of the pit under the same failure probability.

[0031] Example 2:

[0032] Based on Example 1, this example discloses:

[0033] like Figure 1 As shown, step 1 includes the following specific steps:

[0034] (A) Establish a mathematical model for foundation pit excavation, determine the geometric dimensions and parameter probability distribution types of the foundation pit, and generate N soil layer parameter samples X1, X2, ..., X using a random method based on the statistical quantities of soil uncertainty parameters (such as mean and standard deviation). N ; Calculate X1, X2, ..., X using formula (1) N The corresponding heave stability safety factor K D1 K D2 ... K DN ;

[0035]

[0036] In equation (1): KD R is the stability safety factor against uplift; R is the sliding radius (m); c j , The values ​​are the cohesion (kPa) and internal friction angle (°) of the j-th soil strip at the slip surface, respectively; j Let q be the slip arc length (m) of the j-th soil strip; j Let be the standard value (kPa) of the vertical pressure on the top surface of the j-th soil strip; b j Let θ be the width (m) of the j-th soil strip; j Let ΔG be the angle (°) between the normal at the midpoint of the slip surface of the j-th soil strip and the vertical plane; j Let j be the self-weight of the j-th soil strip (kN);

[0037] (B) To limit the safety factor for resistance to uplift, if These are called failed samples. This process is repeated until the number of failed samples, m, is counted.

[0038] (C) Change The number of failure samples m under different limits was obtained. j Formula (2) is used to calculate the failure probability p of the pit bottom anti-heave stability safety factor under different limits. f1j :

[0039] P f =m / N (2)

[0040] In equation (2): P f ρ is the failure probability; m is the number of failure samples; N is the total number of samples. This calculation process is implemented in MATLAB, and the simplified calculation diagram is shown below. Figure 2 As shown.

[0041] like Figure 1 As shown, step 2 includes the following specific steps: calculating d for N soil parameter samples. i ;d max Let d be the allowable value for the heave deformation at the bottom of the pit. i >d max This is called a failed sample. Repeating this process yields the number of failed samples, m. Changing d... max The number of failure samples m under different limits was obtained. j Based on formula (2), the failure probability p of the pit bottom heave deformation value exceeding the limit under different limits is calculated. f2j This calculation process is implemented in MATLAB.

[0042] like Figure 1 As shown, step 3 includes the following specific steps: plotting the failure probability p f1j p f2jA line graph with different anti-heave stability safety factor limits and different pit bottom heave deformation allowable values ​​on the x-axis is used to obtain the pit bottom heave deformation allowable value with the same failure probability as the required anti-heave stability safety factor limit.

[0043] Example 3:

[0044] Based on the above embodiments, this embodiment illustrates the following example:

[0045] Excavation pit: The excavation depth is 10m, the excavation width is 30m, the diaphragm wall is embedded to a depth of 6m and has a thickness of 0.8m, and internal supports are applied at excavation depths of 2m and 6m respectively. The soil layer of the excavation pit is silty clay, and there is a hard rock layer 22m below the excavation surface. The silty clay has a cohesion c of 15kPa, an internal friction angle φ of 25°, and a unit weight γ of 21kN / m³. 3 Unload and reload modulus E ur The value is 54.24 kPa.

[0046] Using the method of the present invention:

[0047] Considering the uncertainties in the parameters of silty clay, the cohesion c, internal friction angle φ, and unloading-reloading modulus E of silty clay are... ur Treating N as a log-normal random variable, use random methods to generate N=10 5 A sample of soil layer parameters.

[0048] Based on the dimensions of the foundation pit, the support structure, and the soil parameters, the corresponding N = 10 was calculated using the anti-heave stability safety factor calculation formula written in MATLAB using formula (1). 5 A safety factor for heave resistance. When N=10 5 In the anti-uplift stability safety factor, if Then X i These are called failure samples, and the number of failure samples is denoted as m. j ,in Starting from 1.8, the value increased in increments of 0.01 up to 3.0, for a total of 120 groups. Using formula (2) to obtain each The probability of failure of the anti-uplift stability p f1j (j = 1, 2, ..., 120).

[0049] According to the design plan, a foundation pit excavation model was established in PLAXIS 2D. Following the monitoring point layout scheme specified in the "Technical Specification for Monitoring of Building Foundation Pit Engineering GB 50497-2009", a series of monitoring points were set up at the bottom of the foundation pit, such as... Figure 3 As shown, calculate the uplift value at each monitoring point, as follows: Figure 4As shown, the bulge value is largest at the center point of the pit bottom. Using the center point as the feature point and repeating this step continuously, we obtain N = 10. 5 d i In N=10 5 Among the deformation values ​​of the bottom heave of the pit, if Then X i These are called failure samples, and the number of failure samples is denoted as m. j ,in Starting from 46mm, the thickness increases in increments of -0.1mm up to 34mm, for a total of 120 groups. Using formula (2) to obtain each The probability of failure due to excessive deformation value at the bottom of the pit (p) f2j (j = 1, 2, ..., 120).

[0050] Plotting with failure probability p f1j p f2j A line graph with different anti-heave stability safety factor limits and different allowable values ​​for pit bottom heave deformation on the horizontal axis, as shown below. Figure 5 As shown, the allowable value for pit bottom heave deformation with the same failure probability as the required heave stability safety factor limit can be obtained. Taking a heave stability safety factor limit of 2.2 as an example, firstly... Figure 5 Draw a horizontal line with a heave stability safety factor limit of 2.2. The intersection of this line with the heave stability safety factor failure probability graph shows a failure probability of 27.80% when the heave stability safety factor limit is 2.2. Next, draw a vertical line with a failure probability of 27.80%. The intersection of this vertical line with the failure probability graph of pit bottom heave deformation exceeding the limit shows an allowable pit bottom heave deformation value of 39.3 mm when the failure probability is 27.80%. Therefore, when the heave stability safety factor is specified as 2.2, the corresponding allowable pit bottom heave deformation value is 39.3 mm.

[0051] Compared with previous studies, this invention combines the anti-heave stability safety factor and the pit bottom heave deformation value to propose a method for determining the allowable value of pit bottom heave deformation. Since the standard limit value of the anti-heave stability safety factor is different in different regions, the allowable value of pit bottom heave deformation is determined based on the principle of equal failure probability. In this way, the allowable value of pit bottom heave deformation under different standard limit values ​​of the anti-heave stability safety factor can be obtained. The effectiveness and practicality of this invention are analyzed through examples.

Claims

1. A method for determining the allowable value of pit bottom heave deformation, characterized in that, Includes the following steps: Step 1: Establish a foundation pit excavation model. Based on the foundation pit soil layer parameter samples, write a program in MATLAB to calculate the safety factor of the foundation pit's heave stability using the circular arc sliding method. Step 2: In PLAXIS 2D finite element calculation software, establish a mathematical model of the foundation pit excavation. According to the monitoring point layout scheme specified in "Technical Specification for Monitoring of Building Foundation Pit Engineering GB 50497-2009", set up a series of monitoring points at the bottom of the foundation pit, calculate the heave deformation value d of the monitoring points, and select the point with the largest heave deformation value as the feature point. Step 3: Use the Monte Carlo sampling method to obtain random variable samples of different soil parameters. Samples with a heave stability safety factor less than the limit of the heave stability safety factor and samples with a characteristic point heave deformation value greater than the allowable value of the heave deformation at the bottom of the pit are taken as failure samples. Calculate the failure probability for each sample. Finally, based on the failure probability under a certain heave stability safety factor limit, determine the allowable value of the heave deformation at the bottom of the pit under the same failure probability. Step 1 includes the following specific steps: (A) Establish a mathematical model for foundation pit excavation, determine the geometric dimensions and parameter probability distribution types of the foundation pit, and generate N soil layer parameter samples X1, X2, ..., X using a random method based on the statistical measures of the uncertain parameters of the soil. N ; Calculate X1, X2, ..., X using formula (1) N The corresponding heave stability safety factor K D1 K D2 ... K DN ; （1）； In equation (1): K D R is the safety factor for resistance to uplift; R is the sliding radius (m). These represent the cohesion (kPa) and internal friction angle (°) of the j-th soil strip at the slip surface, respectively; l j Let q be the slip arc length (m) of the j-th soil strip; j b is the standard value (kPa) of the vertical pressure on the top surface of the j-th soil strip; j θ is the width (m) of the j-th soil strip; j Let be the angle (°) between the normal at the midpoint of the j-th soil strip's sliding arc surface and the vertical plane. The weight of the j-th soil strip is (kN). (B) To determine the safety factor limit for resistance to uplift, if K Di < If the sample is a failure sample, then it is called a failed sample. This process is repeated to count the number of failed samples, m. (C) Change The number of failure samples m under different limits was obtained. j Formula (2) is used to calculate the failure probability p of the pit bottom anti-heave stability safety factor under different limits. f1j : P f =m / N(2); In equation (2): P f denoted as , where m is the failure probability; m is the number of failure samples; and N is the total number of samples.

2. The method for determining the allowable value of pit bottom heave deformation as described in claim 1, characterized in that, Step 2 includes the following specific steps: Calculate d for N soil parameter samples. i ;d max Let d be the allowable value for the heave deformation at the bottom of the pit. i >d max This is called a failed sample. Repeating this process yields the number of failed samples, m. Changing d... max The number of failure samples m under different limits was obtained. j Based on formula (2), the failure probability p of the pit bottom heave deformation value exceeding the limit under different limits is calculated. f2j .

3. The method for determining the allowable value of pit bottom heave deformation as described in claim 2, characterized in that, Step 3 includes the following specific steps: plotting the failure probability p f1j p f2j A line graph with different anti-heave stability safety factor limits and different pit bottom heave deformation allowable values ​​on the vertical axis is used to obtain the pit bottom heave deformation allowable value with the same failure probability as the required anti-heave stability safety factor limit.

Images