# Investigating the Shear Strength of Granitic Gneiss Residual Soil Based on Response Surface Methodology

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{2}of the area [1].

#### 2.1.1. Overview of the Sampled Colluvial Landslides

#### 2.1.2. Composition and Structure of GGRS

_{u}, and curvature coefficient, C

_{c}, of the soil samples were determined from the particle gradation curves, and it was indicated that C

_{u}> 5 and C

_{c}= 1~3 for all samples, indicating that the GGRS specimens are well graded.

#### 2.1.3. Parameters Considered for RSM Experimental Design

_{b}, is the dry weight of the solid per unit volume of the solid, representing the density of the soil when there is no water in the pores at all. Similar to the porosity ratio, it reflects the degree of compactness of the soil. The particle fractal dimension, D, is the most significant index to quantify the complexity and irregularity of an object or fractal body, and is a parameter to quantitatively depict the degree of fractal self-similarity, which is generally defined by Equation (1).

_{i}is the cumulative mass fraction of particles smaller than d

_{i}, d

_{max}is the largest dimension of the particles. The D value herein was calculated and averaged according to the contents of gravel grains (>2 mm), sand grains (0.075~2 mm), silt grains (0.002~0.075 mm), and clay grains (<0.002 mm) presented in Table 2, according to Equation (2):

_{0}is the total weight of each soil grain; M(<d) is the accumulated weight of soil with grain size less than d; d

_{max}is the average diameter of the largest particle size; d is the grain size of soil. The larger the value of D, the larger the content of fine particles, and the lower the content of coarse particles in the soil.

#### 2.2. Methods

#### 2.2.1. Direct Shear Tests

#### 2.2.2. RSM Method

_{0}, β

_{i}, β

_{i}

_{i}, and β

_{ij}are the regression coefficients, the first is a constant, and the following three denote the linear, quadratic and interactive coefficients, respectively. X

_{i}and X

_{j}are the independent influencing variables, represented by moisture content, bulk density, and fractional dimension in this study. X

_{i}

^{2}and X

_{ij}denote the secondary and interactive effects of the independent variables.

#### 2.2.3. Analysis of Variance (ANOVA)

## 3. Results

#### 3.1. Experimental Data

#### 3.2. Modeling Shear Strength Parameters

_{b}), and fraction dimension ($D$), as well as their impact on the response shear strength parameters, involving cohesion (c) and fractional angle (φ), as presented in Equations (4) and (5).

^{2}is employed to reflect the quality of the model. The predicted shear strength parameters versus the actual values obtained from the direct shear tests are plotted in Figure 6. It depicts a great agreement of the datum, with the R

^{2}of 0.9226 and 0.9271 for c and φ values, respectively. It provides the further proves for the accuracy of the response model. As depicted in Figure 6, all the c and φ data points fall into the 95% prediction band, 53.3% of the c data points are within the 95% confidence band and 46.6% of the φ data points are within the 95% confidence band, indicating that the regression equations have a significant prediction effect.

_{b}(0.0011) is the least and the p-value for ω (0.0403) is relatively large, indicating that they both have significant effects, and the influence of ρ

_{d}is much larger than that of ω. In contrast, the third variable, fractal dimension D, the interactive coefficients (ω × ρ

_{b}, ω × D, and ρ

_{b}× D), and the quadratic coefficients (ω

^{2}, ρ

_{b}

^{2}, and D

^{2}) have p-values greater than 0.05, indicating that the impact is insignificant. With regard to the responding model of φ values, Table 7 indicates that the independent variables (ρ

_{d}and ω) and the quadratic coefficient of ρ

_{b}

^{2}all have significant effects due to the low p-values, which is different from that of the c value. A closer inspection of the p-values shows that ρ

_{b}has the most pronounced influence, followed by ω and ρ

_{b}

^{2}. Besides, the rest of the coefficients have insignificant effects.

#### 3.3. The Effect of Independent Variable and Their Interaction on the Shear Strength

^{−3}), and the interaction of the two variables is insignificant. On the contrary, Line CD indicating the effect at low bulk density takes a large deflection and has an angle of 7.8° to the X-axis. It indicates that a low bulk density (1.20~1.45 g∙cm

^{−3}) may weaken its effect, and the effect of moisture content becomes dominant with negligible interactive impact of the two variables.

^{−3}), and the interactive effect is non-significant herein. Whereas a low bulk density (1.20~1.45 g∙cm

^{−3}) may weaken the effect of bulk density and the effect of moisture content becomes dominant since Line KL deflects greatly towards the X-axis, with an angle of 6.3° to the X-axis, indicating that the interactive effect of the two variables become significant.

#### 3.4. Validation of the Regression Model

^{2}of 0.9471 and 0.9535, for cohesion and internal friction angle, respectively. As depicted in Figure 13, all the c and φ data points fall into the 95% prediction band, 77.8% of the c and φ data points fall into the 95% confidence band. These observations indicated that the proposed strength model is significantly effective and applicable for the GGRS distributed in the study area.

## 4. Discussion

_{s}is the specific gravity, which is associated with the mineral composition and particle gradation; and e is the porosity.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, P.; Li, M.J. Report on Feasibility Study on Potential Geological Hazards and Risks of Cutting Slopes for Rural Housing Construction in Huanggang City, Hubei Province; Report of Investigation; The 3rd Geological Department of Hubei Provincial Geological Bureau: Huanggang, China, 2020. (In Chinese)
- Xu, Q.; Wang, W.; Li, L.; Cao, Y. Failure Mechanism of Gently Inclined Shallow Landslides Along the Soil-bedrock Interface on Ring Shear Tests. Bull. Eng. Geol. Environ.
**2021**, 80, 3733–3746. [Google Scholar] [CrossRef] - Guo, H.; Xiao, Y.; Xu, L.; Sun, H.; Huang, J.; Hou, Z. Origin of allanite in gneiss and granite in the Dabie orogenic belt, Central East China. J. Asian Earth Sci.
**2017**, 135, 243–256. [Google Scholar] [CrossRef] - Liu, X.; Zhang, X.; Kong, L.; Chen, C.; Wang, G. Mechanical Response of Granite Residual Soil Subjected to Impact Loading. Int. J. Geomech.
**2021**, 21, 04021092. [Google Scholar] [CrossRef] - An, R.; Kong, L.; Zhang, X.; Li, C. Effects of Dry-Wet Cycles on Three-Dimensional Pore Structure and Permeability Characteristics of Granite Residual Soil Using X-Ray Micro Computed Tomography. J. Rock. Mech. Geotech.
**2022**, 14, 851–860. [Google Scholar] [CrossRef] - Ye, W.J.; Li, C.Q. The consequences of changes in the structure of loess as a result of cyclic freezing and thawing. Bull. Eng. Geol. Environ.
**2019**, 78, 2125–2138. [Google Scholar] [CrossRef] - An, R.; Zhang, X.; Kong, L.; Liu, X.; Chen, C. Drying-Wetting Impacts on Granite Residual Soil: A Multi-Scale Study from Macroscopic to Microscopic Investigations. Bull. Eng. Geol. Environ.
**2022**, 81, 447. [Google Scholar] [CrossRef] - Moon, S.W.; Hayashi, K.; Ku, T. Estimating Spatial Variations in Bedrock Depth and Weathering Degree in Decomposed Granite from Surface Waves. J. Geotech. Geoenviron. Eng.
**2017**, 143, 04017020. [Google Scholar] [CrossRef] - Zhang, S.; Tang, H. Experimental Study of Disintegration Mechanism for Unsaturated Granite Residual Soil. Rock Soil Mech.
**2013**, 34, 1668–1674. (In Chinese) [Google Scholar] - Zhao, J.J.; Wang, S.J.; Shang, Y.J.; Yue, Z.Q. Control factors on shear strength of completely decomposed granite. Rock Soil Mech.
**2005**, 26, 624–628. (In Chinese) [Google Scholar] [CrossRef] - Wu, D.; Liu, H.; Wang, C.; Xu, X.; Liu, X.; Wang, Q. The Interaction Effect of Particle Composition and Matric Suction on the Shear Strength Parameters of Unsaturated Granite Residual Soil. Arab. J. Sci. Eng.
**2022**, 47, 12453–12467. [Google Scholar] [CrossRef] - Wei, Y.; Wu, X.; Xia, J.; Miller, G.A.; Cai, C.; Guo, Z.; Hassanikhah, A. The Effect of Water Content on the Shear Strength Characteristics of Granitic Soils in South China. Soil Till Res.
**2019**, 187, 50–59. [Google Scholar] [CrossRef] - Hoyos, L.R.; Velosa, C.L.; Puppala, A.J. Residual Shear Strength of Unsaturated Soils via Suction-Controlled Ring Shear Testing. Eng. Geol.
**2014**, 172, 1–11. [Google Scholar] [CrossRef] - Al-Shayea, N.A. The Combined Effect of Clay and Moisture Content on the Behavior of Remolded Unsaturated Soils. Eng. Geol.
**2001**, 62, 319–342. [Google Scholar] [CrossRef] - Hossain, M.A.; Yin, J.-H. Behavior of a Compacted Completely Decomposed Granite Soil from Suction Controlled Direct Shear Tests. J. Geotech. Geoenviron.
**2010**, 136, 189–198. [Google Scholar] [CrossRef] - Amiri Khaboushan, E.; Emami, H.; Mosaddeghi, M.R.; Astaraei, A.R. Estimation of Unsaturated Shear Strength Parameters Using Easily-Available Soil Properties. Soil Till Res.
**2018**, 184, 118–127. [Google Scholar] [CrossRef] - Jiang, Q.; Cao, M.; Wang, Y.; Wang, J.; He, Z. Estimation of Soil Shear Strength Indicators Using Soil Physical Properties of Paddy Soils in the Plastic State. Appl. Sci.
**2021**, 11, 5609. [Google Scholar] [CrossRef] - Wei, Y.; Wu, X.; Cai, C. Splash Erosion of Clay–Sand Mixtures and Its Relationship with Soil Physical Properties: The Effects of Particle Size Distribution on Soil Structure. CATENA
**2015**, 135, 254–262. [Google Scholar] [CrossRef] - Zhou, Z.; Li, F.; Yang, H.; Gao, W.; Miao, L. Orthogonal Experimental Study of Soil–Rock Mixtures under the Freeze–Thaw Cycle Environment. Int. J. Pavement Eng.
**2021**, 22, 1376–1388. [Google Scholar] [CrossRef] - Ren, S.; Li, Z.Y.; Deng, G.L.; Liu, W.; Pu, W.P. Softening characteristic of gypsum rock under the action of multi-factors. Rock Soil Mech. 2018; 39, 789–796. (In Chinese) [Google Scholar]
- Lu, Y.; Cai, G.; Zhao, C. The Shear Strength of Granite Weathered Soil Under Different Hydraulic Paths. Appl. Sci.
**2020**, 10, 6615. [Google Scholar] [CrossRef] - Li, J.; Zhang, P.; Hu, J.; Zhang, Y. Study of the Synergistic Effect of Induction Heating Parameters on Heating Efficiency Using Taguchi Method and Response Surface Method. Appl. Sci.
**2023**, 13, 555. [Google Scholar] [CrossRef] - Myers, R.H.; Montgomery, D.C.; Vining, G.G.; Borror, C.M.; Kowalski, S.M. Response Surface Methodology: A Retrospective and Literature Survey. J. Qual. Technol.
**2004**, 36, 53–77. [Google Scholar] [CrossRef] - Asadizadeh, M.; Masoumi, H.; Roshan, H.; Hedayat, A. Coupling Taguchi and Response Surface Methodologies for the Efficient Characterization of Jointed Rocks’ Mechanical Properties. Rock Mech. Rock Eng.
**2019**, 52, 4807–4819. [Google Scholar] [CrossRef] - Soltani, M.; Moayedfar, R.; Vun, C.V. Using Response Surface Methodology to Assess the Performance of the Pervious Concrete Pavement. Int. J. Pavement Res. Technol.
**2022**, 16, 576–591. [Google Scholar] [CrossRef] - Wang, J.; Wang, Y.; Li, S.; Yang, L. Strength Softening Characteristics of Shale Clay Mineral Expansion. Chem. Technol. Fuels Oils
**2020**, 56, 300–311. [Google Scholar] [CrossRef] - Zhang, S.; Tang, H.; Zhan, H.; Lei, G.; Cheng, H. Investigation of Scale Effect of Numerical Unconfined Compression Strengths of Virtual Colluvial–Deluvial Soil–Rock Mixture. Int. J. Rock. Mech. Min.
**2015**, 77, 208–219. [Google Scholar] [CrossRef] - Lu, H.; Zhang, L.; Xi, X.; Nie, Z. Optimization of pulse bi-directional electrolysis in-situ synthesis of tungsten carbide by response surface methodology. Int. J. Refract. Met. Hard Mater.
**2023**, 111, 106063. [Google Scholar] [CrossRef] - Babanouri, N.; Asadizadeh, M.; Hasan-Alizade, Z. Modeling Shear Behavior of Rock Joints: A Focus on Interaction of Influencing Parameters. Int. J. Rock Mech. Min.
**2020**, 134, 104449. [Google Scholar] [CrossRef] - Sellke, T.; Bayarri, M.J.; Berger, J.O. Calibration of p values for testing precise null hypotheses. Am. Stat.
**2001**, 55, 62–71. [Google Scholar] [CrossRef] - Ng, C.W.W.; Chiu, A.C.F. Laboratory Study of Loose Saturated and Unsaturated Decomposed Granitic Soil. J. Geotech. Geoenviron
**2003**, 129, 550–559. [Google Scholar] [CrossRef] - Li, C.; Kong, L.; An, R. Evolution of cracks in the shear bands of granite residual soil. J. Rock Mech. Geotech. Eng.
**2022**, 14, 1956–1966. [Google Scholar] [CrossRef] - Kaliakin, V.N. Chapter 1—Example Problems Involving Phase Relations for Soils. In Soil Mechanics; Kaliakin, V.N., Ed.; Butterworth-Heinemann: Oxford, UK, 2017; pp. 1–50. ISBN 978-0-12-804491-9. [Google Scholar]
- Rahai, A.; Dolati, A.; Kamel, M.E.; Babaizadeh, H. Studying the Effect of Various Parameters on Mechanical Properties of Lightweight Aggregate Concrete Using MANOVA. Mater. Struct.
**2015**, 48, 2353–2365. [Google Scholar] [CrossRef] - Dong, Y.; Liao, Z.; Wang, J.; Liu, Q.; Cui, L. Potential Failure Patterns of a Large Landslide Complex in the Three Gorges Reservoir Area. Bull. Eng. Geol. Environ.
**2023**, 82, 41. [Google Scholar] [CrossRef] - Zou, Z.; Luo, T.; Zhang, S.; Duan, H.; Li, S.; Wang, J.; Deng, Y.; Wang, J. A Novel Method to Evaluate the Time-Dependent Stability of Reservoir Landslides: Exemplified by Outang Landslide in the Three Gorges Reservoir. Landslides
**2023**. [Google Scholar] [CrossRef]

**Figure 3.**SEM images of GGRS specimens: (

**a**) flake-like silicate minerals in specimens obtained from PLL; (

**b**) intergranular voids observed in specimens obtained from PLL.

**Figure 5.**Direct shear test: (

**a**) tetragenous strain-controlled direct shear apparatus (TT-ADS4D); (

**b**) GGRS specimen in the shearing box after shear test; (

**c**) representative stress-displacement curves, the colored lines and the adjacent pressure values represents the stress-displacement curves at diverse normal stress.

**Figure 6.**Predicted shear strength parameters versus actual values obtained from direct shear tests: (

**a**) predicted c values versus measured c values; (

**b**) predicted φ values versus measured φ values.

**Figure 7.**3D and 2D response surface plots of the interactive effect of moisture content and bulk density on cohesion: (

**a**) 3D plot; (

**b**) 2D plot.

**Figure 8.**3D and 2D response surface plots of the interactive effect of bulk density and fractal dimension on cohesion: (

**a**) 3D plot; (

**b**) 2D plot.

**Figure 9.**3D and 2D response surface plots of the interactive effect of moisture content and fractal dimension on cohesion: (

**a**) 3D plot; (

**b**) 2D plot.

**Figure 10.**3D and 2D response surface plots of the interactive effect of bulk density and moisture content on internal friction angle: (

**a**) 3D plot; (

**b**) 2D plot.

**Figure 11.**3D and 2D response surface plots of the interactive effect of bulk density and fractal dimension on internal friction angle: (

**a**) 3D plot; (

**b**) 2D plot.

**Figure 12.**3D and 2D response surface plots of the interactive effect of moisture content and fractal dimension on internal friction angle: (

**a**) 3D plot; (

**b**) 2D plot.

**Figure 13.**Predicted shear strength parameters versus actual values obtained from direct shear tests and collected data: (

**a**) predicted c values versus actual c values; (

**b**) predicted φ values versus actual φ values.

Sample No. | Percentage of Mineral Composition (%) | ||||||
---|---|---|---|---|---|---|---|

Montmorillonite | Rectorite | Illite | Tremolite | Quartz | Orthoclase | Albite | |

PLL | 37.74 | 23.54 | — | — | 21.12 | 5.75 | 11.85 |

GLX | 65.36 | 13.9 | — | 3.1 | 10.64 | — | 7.01 |

QLQ | 3.34 | — | 27.36 | — | 33.11 | — | 36.2 |

ZLM | 17.92 | 33.46 | — | 12.87 | 28.54 | — | 7.22 |

CLH | 13.64 | — | 16.15 | — | 31.79 | 10.66 | 27.76 |

Sample No. | Percentage Content of Each Grain Group (%) | C_{u} | C_{c} | |||
---|---|---|---|---|---|---|

>2 mm | 0.075–2 mm | 0.002–0.075 mm | <0.002 mm | |||

PLL | 31.49 | 58.97 | 8.99 | 0.55 | 21.822 | 1.146 |

GLX | 31.83 | 32.65 | 33.73 | 1.79 | 19.818 | 0.077 |

QLQ | 11.08 | 79.50 | 9.05 | 0.37 | 4.951 | 1.521 |

ZLM | 23.37 | 57.34 | 19.01 | 0.28 | 8.036 | 0.877 |

CLH | 22.21 | 68.66 | 8.64 | 0.49 | 6.868 | 2.594 |

Parameters | ω/% | ρ_{b}/g · cm^{−3} | D |
---|---|---|---|

Maximum | 26.28 | 1.53 | 2.76 |

Minimum | 23.27 | 1.20 | 2.37 |

Mean value | 24.92 | 1.37 | 2.55 |

Levels | ω/% | ρ/g · cm^{−3} | D |
---|---|---|---|

−1 | 18 | 1.2 | 2.4 |

0 | 24 | 1.4 | 2.55 |

1 | 30 | 1.6 | 2.7 |

Run | ω/% | ρ/g · cm^{−3} | D | Response | |
---|---|---|---|---|---|

c/kPa | φ/° | ||||

1 | 24 | 1.4 | 2.55 | 11.99 | 19.99 |

2 | 18 | 1.2 | 2.55 | 10.53 | 17.55 |

3 | 18 | 1.6 | 2.55 | 17.29 | 29.82 |

4 | 30 | 1.4 | 2.7 | 11.98 | 19.63 |

5 | 24 | 1.6 | 2.4 | 16.98 | 30.33 |

6 | 24 | 1.2 | 2.7 | 13.29 | 22.16 |

7 | 18 | 1.4 | 2.7 | 13.94 | 23.23 |

8 | 24 | 1.2 | 2.4 | 13.25 | 22.09 |

9 | 30 | 1.6 | 2.55 | 15.23 | 25.39 |

10 | 30 | 1.2 | 2.55 | 9.95 | 15.53 |

11 | 24 | 1.6 | 2.7 | 15.68 | 25.52 |

12 | 18 | 1.4 | 2.4 | 14.56 | 24.27 |

13 | 30 | 1.4 | 2.4 | 12.16 | 18.96 |

Source | Sum of Squares | Degree of Freedom | Mean Squares | F-Value | p-Value | Performance |
---|---|---|---|---|---|---|

Model | 61.79 | 9 | 6.87 | 6.62 | 0.0255 | significant |

A-w | 7.84 | 1 | 7.84 | 7.57 | 0.0403 | significant |

B-p_{b} | 46.34 | 1 | 46.34 | 44.71 | 0.0011 | significant |

C-D | 0.84 | 1 | 0.84 | 0.81 | 0.4103 | insignificant |

AB | 0.33 | 1 | 0.33 | 0.31 | 0.5993 | insignificant |

AC | 0.22 | 1 | 0.22 | 0.21 | 0.6640 | insignificant |

BC | 0.24 | 1 | 0.24 | 0.24 | 0.6475 | insignificant |

A^{2} | 8.459 × 10^{−3} | 1 | 8.459 × 10^{−3} | 8.161 × 10^{−3} | 0.9315 | insignificant |

B^{2} | 6.60 | 1 | 6.60 | 6.37 | 0.0529 | insignificant |

C^{2} | 5.87 | 1 | 5.87 | 5.67 | 0.0631 | insignificant |

Residual Error | 5.18 | 5 | 1.04 | |||

Total | 66.97 | 14 |

Source | Sum of Squares | Degree of Freedom | Mean Squares | F-Value | p-Value | Performance |
---|---|---|---|---|---|---|

Model | 228.63 | 9 | 25.40 | 7.07 | 0.0222 | significant |

A-w | 33.78 | 1 | 33.78 | 9.40 | 0.0279 | significant |

B-p_{b} | 167.30 | 1 | 167.30 | 46.53 | 0.0010 | significant |

C-D | 3.60 | 1 | 3.60 | 1.00 | 0.3628 | insignificant |

AB | 0.81 | 1 | 0.81 | 0.22 | 0.6558 | insignificant |

AC | 1.78 | 1 | 1.78 | 0.50 | 0.5131 | insignificant |

BC | 5.00 | 1 | 5.00 | 1.39 | 0.2914 | insignificant |

A^{2} | 0.59 | 1 | 0.59 | 0.17 | 0.7012 | insignificant |

B^{2} | 24.15 | 1 | 24.15 | 6.72 | 0.0487 | significant |

C^{2} | 16.17 | 1 | 16.17 | 4.50 | 0.0874 | insignificant |

Residual Error | 17.98 | 5 | 3.60 | |||

Total | 246.61 | 14 |

Test Group | w | ρ_{b} | D | Measured | Predicted | ||
---|---|---|---|---|---|---|---|

c | φ | c | φ | ||||

GLX | 24.7 | 1.322 | 2.66 | 12.13 | 20.76 | 11.72 | 19.43 |

QLQ | 13.1 | 1.617 | 2.74 | 21.25 | 29.13 | 19.26 | 30.83 |

ZLM | 30 | 1.157 | 2.64 | 13.67 | 19.45 | 11.41 | 18.70 |

CLH | 20.1 | 1.5 | 2.75 | 16.26 | 32.32 | 15.86 | 26.01 |

MLW | 35.7 | 1.047 | 2.77 | 15.13 | 27.17 | 15.82 | 26.62 |

JLM | 18.8 | 1.505 | 2.57 | 14.32 | 24.26 | 14.19 | 23.94 |

SLC | 27.4 | 1.463 | 2.54 | 12.81 | 20.44 | 12.06 | 19.97 |

MLK | 21.8 | 1.363 | 2.49 | 11.73 | 19.69 | 12.01 | 20.04 |

XLB | 26.1 | 1.456 | 2.70 | 13.84 | 22.98 | 13.43 | 22.14 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zou, H.; Zhang, S.; Zhao, J.; Qin, L.; Cheng, H.
Investigating the Shear Strength of Granitic Gneiss Residual Soil Based on Response Surface Methodology. *Sensors* **2023**, *23*, 4308.
https://doi.org/10.3390/s23094308

**AMA Style**

Zou H, Zhang S, Zhao J, Qin L, Cheng H.
Investigating the Shear Strength of Granitic Gneiss Residual Soil Based on Response Surface Methodology. *Sensors*. 2023; 23(9):4308.
https://doi.org/10.3390/s23094308

**Chicago/Turabian Style**

Zou, Hao, Shu Zhang, Jinqi Zhao, Liuzhi Qin, and Hao Cheng.
2023. "Investigating the Shear Strength of Granitic Gneiss Residual Soil Based on Response Surface Methodology" *Sensors* 23, no. 9: 4308.
https://doi.org/10.3390/s23094308