Analysis and Optimization of Soil Nail Parameters in a Deep Foundation Pit of Silty Clay Based on Response Surface Methodology

doi:10.11988/ckyyb.20231429

Abstract

Abstract:

The aim of this research is to reveal the influence of spatial form parameters and other factors in soil nail design on the three-dimensional stability of deep foundation pits in silty clay. A deep foundation pit in a silty clay area in Hebei was taken as the engineering background. Based on the response surface method, Plackett-Burman and Box-Behnken experiments were designed. MIDAS-GTS and Design-Expert were used to establish experimental models. The influence of various parameters on the safety of soil nail support in deep foundation pits of silty clay and the applicability of optimization schemes were analyzed through numerical simulation and monitoring data. Results show that the impact of each parameter on the safety of the pit in the silty clay area, in descending order of significance, is as follows: soil nail length, slope angle of excavation, soil nail spacing, soil nail inclination, and soil nail diameter. In the combined effect of support parameters, the soil nail length and spacing have the greatest impact on the safety factor. The predictive model established by the response surface method can provide the best optimization scheme. The optimization scheme shifts the soil slip surface backward, reducing the maximum horizontal displacement of the foundation pit from 9.33 mm to 5.42 mm and the maximum vertical settlement from 16.9 mm to 11.8 mm, providing a reference for the design of soil nail support for this type of foundation pit.

Key words: foundation pit, soil nail support, response surface methodology, MIDAS-GTS, optimization design

CLC Number:

TU473.2

Cite this article

FAN Cheng, WANG Zi-yuan, QI Peng-fei, ZHANG Hong-bin, ZHANG Tiao-tiao. Analysis and Optimization of Soil Nail Parameters in a Deep Foundation Pit of Silty Clay Based on Response Surface Methodology[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 142-148.

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URL: http://ckyyb.crsri.cn/EN/10.11988/ckyyb.20231429

http://ckyyb.crsri.cn/EN/Y2025/V42/I4/142

Figures/Tables 17

Table 1 Physical and mechanical parameters of rock mass

土层	岩土名称	重度/ (kN·m^-3)	黏聚力/ kPa	内摩擦角/(°)	压缩模量/MPa
1	黄土状粉质黏土	19.5	17	22.4	6.5
2	杂填土	18.0	8	10.0	—
3	细砂	18.5	0	28.0	10.0
4	细砂②	18.5	0	30.0	12.0
5	粉质黏土	19.9	22	21.4	9.3

Table 1 Physical and mechanical parameters of rock mass

土层	岩土名称	重度/ (kN·m^-3)	黏聚力/ kPa	内摩擦角/(°)	压缩模量/MPa
1	黄土状粉质黏土	19.5	17	22.4	6.5
2	杂填土	18.0	8	10.0	—
3	细砂	18.5	0	28.0	10.0
4	细砂②	18.5	0	30.0	12.0
5	粉质黏土	19.9	22	21.4	9.3

Fig.1 Dimensions of support structure

Table 2 Experimental factor design

影响因素	代号	水平
影响因素	代号	1	2	3
放坡坡角/(°)	A	55	65	75
土钉长度/m	B	4.8	6.8	8.8
土钉直径/mm	C	16	—	32
土钉倾角/(°)	D	0	—	20
土钉间距/m	E	1	1.5	2

Table 2 Experimental factor design

影响因素	代号	水平
影响因素	代号	1	2	3
放坡坡角/(°)	A	55	65	75
土钉长度/m	B	4.8	6.8	8.8
土钉直径/mm	C	16	—	32
土钉倾角/(°)	D	0	—	20
土钉间距/m	E	1	1.5	2

Table 3 ANOVA results in PB

来源	平方和	自由度	均方差	F值	P值
模型	10.270 0	10	1.030 0	308.09	0.044 3
A	0.412 1	1	0.412 1	123.62	0.057 1
B	0.334 4	1	0.334 4	100.32	0.063 3
C	0.017 5	1	0.017 5	5.26	0.261 7
D	0.049 8	1	0.049 8	14.94	0.161 2
E	0.090 6	1	0.090 6	27.17	0.120 7

Table 3 ANOVA results in PB

来源	平方和	自由度	均方差	F值	P值
模型	10.270 0	10	1.030 0	308.09	0.044 3
A	0.412 1	1	0.412 1	123.62	0.057 1
B	0.334 4	1	0.334 4	100.32	0.063 3
C	0.017 5	1	0.017 5	5.26	0.261 7
D	0.049 8	1	0.049 8	14.94	0.161 2
E	0.090 6	1	0.090 6	27.17	0.120 7

Fig.2 Three-dimensional numerical model

Table 4 ANOVA results in BBD

来源	平方和	自由度	均方差	F值	P值
模型	0.803 3	9	0.089 3	11.99	0.001 8
A	0.137 0	1	0.137 1	18.41	0.003 6
B	0.162 5	1	0.162 5	21.83	0.002 3
E	0.062 1	1	0.062 1	8.34	0.023 4
AB	0.002 5	1	0.002 5	0.33	0.580 4
AE	0.003 1	1	0.003 1	0.41	0.539 2
BE	0.006 4	1	0.006 4	0.86	0.384 6
A²	0.177 0	1	0.177 2	23.78	0.001 8
B²	0.076 9	1	0.076 9	10.33	0.014 8
E²	0.012 2	1	0.012 2	1.64	0.240 8

Table 4 ANOVA results in BBD

来源	平方和	自由度	均方差	F值	P值
模型	0.803 3	9	0.089 3	11.99	0.001 8
A	0.137 0	1	0.137 1	18.41	0.003 6
B	0.162 5	1	0.162 5	21.83	0.002 3
E	0.062 1	1	0.062 1	8.34	0.023 4
AB	0.002 5	1	0.002 5	0.33	0.580 4
AE	0.003 1	1	0.003 1	0.41	0.539 2
BE	0.006 4	1	0.006 4	0.86	0.384 6
A²	0.177 0	1	0.177 2	23.78	0.001 8
B²	0.076 9	1	0.076 9	10.33	0.014 8
E²	0.012 2	1	0.012 2	1.64	0.240 8

Table 5 BBD experiment design

试验方案	放坡坡角/(°)	土钉长度/m	土钉间距/m	F_s
1	65	6.8	1.5	1.51
2	65	6.8	1.0	1.54
3	75	4.8	1.5	0.91
4	65	4.8	1.0	1.12
5	75	8.8	1.5	1.11
6	75	6.8	2.0	0.95
7	65	4.8	2.0	1.08
8	55	8.8	1.5	1.31
9	75	6.8	1.0	1.12
10	65	8.8	1.0	1.62
11	55	6.8	1.0	1.57
12	65	6.8	2.0	1.36
13	55	4.8	1.5	1.21
14	65	6.8	1.5	1.51
15	65	8.8	2.0	1.42
16	65	6.8	1.5	1.51
17	65	6.8	1.5	1.51

Table 5 BBD experiment design

试验方案	放坡坡角/(°)	土钉长度/m	土钉间距/m	F_s
1	65	6.8	1.5	1.51
2	65	6.8	1.0	1.54
3	75	4.8	1.5	0.91
4	65	4.8	1.0	1.12
5	75	8.8	1.5	1.11
6	75	6.8	2.0	0.95
7	65	4.8	2.0	1.08
8	55	8.8	1.5	1.31
9	75	6.8	1.0	1.12
10	65	8.8	1.0	1.62
11	55	6.8	1.0	1.57
12	65	6.8	2.0	1.36
13	55	4.8	1.5	1.21
14	65	6.8	1.5	1.51
15	65	8.8	2.0	1.42
16	65	6.8	1.5	1.51
17	65	6.8	1.5	1.51

Fig.3 Fitting result between BBD test results and prediction results

Fig.4 Synergistic effects between soil nail spacing and soil nail length,soil nail length and slope excavation angle, soil nail spacing and slope excavation angle

Fig.5 Optimization design of response surface

Table 6 Original support design scheme

坡角/(°)	土钉道数	土钉倾角/(°)	水平间距/m	土钉长度/m
65	4	15	1.5	6.8
		15	1.5	6.8
		15	1.2	6.8
		15	1.2	4.3

Table 6 Original support design scheme

坡角/(°)	土钉道数	土钉倾角/(°)	水平间距/m	土钉长度/m
65	4	15	1.5	6.8
		15	1.5	6.8
		15	1.2	6.8
		15	1.2	4.3

Table 7 Optimized design scheme

坡角/(°)	土钉道数	土钉倾角/(°)	水平间距/m	土钉长度/m
60	4	15	1.5	6.8
		15	1	8
		15	1	8
		15	1.2	4.3

Table 7 Optimized design scheme

坡角/(°)	土钉道数	土钉倾角/(°)	水平间距/m	土钉长度/m
60	4	15	1.5	6.8
		15	1	8
		15	1	8
		15	1.2	4.3

Fig.6 Comparison of horizontal displacement between original scheme and optimized scheme

Fig.7 Comparison of axial force of soil nailing between original scheme and optimized scheme

Fig.8 Comparison of the optimization effect of soil nail parameters

Fig.9 Location of monitoring points

Fig.10 Comparison between simulated values and monitored values at monitoring point 8

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