1. Introduction
Landslides are the major type of geohazards affecting the living environment of the residents in the Huanggang area, China. By the end of 2021, a total of 585 landslides have been recognized in the Huanggang area, which severely threaten human life and property safety [
1]. The gneiss in the area has two main types, granitic gneiss and hornblende feldspar gneiss. In particular, landslides with bedrock of granitic gneiss account for 30%, and that of hornblende feldspar gneiss account for 25%, as shown in
Figure 1. Upon field investigation, these colluvial landslides are predominantly minor or medium-sized, and primarily slide along the contact zone between weathered residual soil and bedrock [
2]. Therefore, the shear strength of gneiss residual soils and its influencing factors are particularly essential for studying the stability of colluvial landslides in the Huanggang area.
Granite gneisses are formed by the recrystallization of minerals from granite under long-term ground stress, and their lithology and mineral composition are comparable to that of granite [
3]. Being derived from the in-situ weathering and decomposition of granite gneisses, it is identified that the properties of granite gneisses residual soil (GGRS) are dominated by the parent rock [
4], and hence the findings on the mechanical properties of granite residual soils (GRS) can be directly applied to the study of GGRS, thus the following text would employ the word residual soil to collectively describe these two kinds of soil. As a remark of commonality, the intrinsic microstructure, i.e., primary pores and fractures, as well as the unique grain distribution from clay to gravel, pose a significant challenge to sophisticatedly capturing the physical, hydraulic, and mechanical behaviors of residual soil [
5,
6,
7,
8,
9].
The acquisition of the shear strength of the residual soil, of the mechanical properties, is of the most significance in the evaluation of colluvial landslide stability. The studies associated with the predominant factors governing the shear strength are thus of particular importance. Zhao et al. analyzed the strength of GRS by triaxial tests and direct shear tests, and found that the GRS have the characteristics of shear dilation and shrink, and concluded the effects of different particle compositions on shear strength [
10]. Wu et al. identified the interaction effect of particle composition and matrix suction on the shear strength of GRS through laboratory experiments [
11]. Wei et al. examined the shear strength properties of GRS based on the study of GRS in Southern China and indicated that the moisture content has a significant effect on their shear strength [
12]. Meanwhile, a considerable number of studies on colluvial landslides in the Huanggang area also demonstrated that the reduced shear strength caused by the increasing moisture content of GGRS under heavy rainfall acts is the dominant factor for the instability [
13]. Combined with related research results of other soil types, it revealed that the shear strength of GGRS is highly associated with its moisture content [
12,
14,
15], compactness state [
16], and particle composition [
14,
16,
17,
18]. However, the contribution of these factors and their interactions has been insufficiently studied.
To evaluate the correlation of shear strength of geo-materials and the related indices, the orthogonal experimental design method has been employed by the present studies. For instance, Zhou et al. studied the shear strength of soil-rock mixture under the freeze–thaw cycle environment considering five factors, including rock content, compaction degree, moisture content, number of freeze–thaw cycles and freezing temperature at four experimental levels, respectively according to the orthogonal experimental design method [
19]. Ren et al. performed a series of multi-factor orthogonal softening experiments on gypsum rock from Lower Triassic Jialing River Formation [
20]. However, the orthogonal test has the drawback of incapability of identifying the interaction of the different factors. Therefore, the interaction of the factors has not been identified.
Given this shortcoming, the response surface methodology (RSM), a mathematical and statistical technique that optimizes the experimental results by approximately developing a explicit polynomial expression, provides a corresponding strategy that enables the complicated connection between the required response and input factors to be ascertained [
21]. Moreover, it allows a minimization of the number of experiments and the level of independent variables, and offers internal error estimates [
22]. It has been extensively applied in the food industry, chemical industry, etc., for optimization design [
23]. Recently, a couple of studies have introduced it into the geotechnical engineering field for estimating the mechanical properties of geo-material and building materials. Asadizadeh et al. assessed the individual and interactive weighting contributions of the parameters (e.g., bridge length, bridge step angle, Joint Roughness Coefficient, etc.) on the shear and uniaxial compression strengths of jointed rocks through RSM [
24]. Soltani et al. applied RSM to investigate the influence of cement content, water–cement ratio, and aggregate size on the compressive strength, permeability, and porosity of pavement concrete [
25]. A recent study has also investigated the shear strength of paddy soil and its influencing factors by RSM method [
17]. However, the application of RSM to the study of strength parameters of residual soils from colluvial landslides has not been reported yet.
There are two primary aims of this study: (1). To investigate the contribution of physical indices, in terms of moisture, dense state and grain size gradation, to the shear strength of GGRS; (2). To facilitate the empirical estimation model of shear strength of GGRS in a more effective way. In this sense, this study employed RSM to examine the individual and interacting effects of the factors. Moreover, the non-linear regression relationships were developed and verified to estimate the shear strength parameters via Analysis of Variance (ANOVA). The attempt of this application provides a prerequisite for the estimation of landslide stability in the study area, thus promoting the evaluation of landslide stability, and allows the extension of this research framework to other regions with similar geo-material.
4. Discussion
The current study found that although there are slight differences in the degree of variation, the effect of the individual factors and their interactions on the cohesion and internal friction angle share a very similar pattern. Of these, bulk density has the greatest effect, followed by moisture content, while the effect of the fractal dimension of grain size has the least. One unanticipated finding was that the increasing moisture content has a considerable weakening effect on both cohesion and internal friction angle. This finding is contrary to previous studies which have suggested that the moisture only affects the cohesion, whereas it has an insignificant effect on the internal friction angle [
31]. A possible explanation for this might be stated as follows. Owing to the larger moisture content, the orientation of fine particles during the shearing process is more pronounced, and leads to the weakening of interparticle bonding, and the reduction in larger pores between the agglomerates and the growth of smaller pores. Combined with the lubricating effect of free water, it leads to the reduction in both cohesion and internal friction angle as two inseparable components of the shear strength [
32]. Moreover, the discrepancy could be attributed to the different fine grain content of the studied fine samples. The high content of fines results in more significant bond weakening effect and lubrication effect by free water, which in turn affects the interparticle friction and manifests in the reduction in the internal friction angle component.
Meanwhile, contrary to expectations from the ANOVA that there is no significant interaction of the variables, the further analysis of the responses surface indicated that the interaction between bulk density and fractal dimension is more considerable, and bulk density has a certain interaction with moisture content, while the interactive action between moisture content and fractal dimension is negligible. This might be related to the definition of bulk density, which corresponds to the density of a soil when it is completely waterless in its pores. Its conversion relationship with other variables is [
33]
where
ρ is the natural density;
Gs is the specific gravity, which is associated with the mineral composition and particle gradation; and
e is the porosity.
It is noticeable that bulk density is naturally dependent on the moisture content and particle gradation (fractal dimension in the current study), and therefore coincides with the results of the above analysis. Thereby, it is further demonstrated that relying on ANOVA solely fails to yield robust findings, and the response surface model successfully captures this interactive effect, even if it is not significant in terms of manifesting in p-values. This finding, while preliminary, suggests that the interaction of the key factors is necessary, and the proposed response surface model provides an effective solution for shear strength estimation.
Future studies on the current topic are therefore recommended. Firstly, as noted above, this study regarded the shear strength indices as unrelated dependent variables and performed univariate multivariable regression analysis. The multivariate regression analysis may be facilitated in the further study considering the covariance matrix analysis among the dependent variables; and the other multivariate analysis, such as principal component analysis, cluster analysis, and MANOVA may be adopted to capture more fresh results [
34]. Secondly, due to the drawbacks of the direct shear test, the further study may be implemented by the triaxial compression or ring shear apparatus, with emphasis on observing the change in stress-strain during the test, as well as stiffness and residual shear strength. Moreover, the shear strength of the geomaterials in the study area can be estimated based on the estimation model so that stability analysis can be launched to analyze the spatial-temporal landslide hazard [
35,
36].
5. Conclusions
This study performed a series of laboratory experiments to investigate the main contribution of individual physical variables, moisture content, bulk density, and fractal dimension of grain size, and their interaction to the shear strength parameters of GGRS of colluvial landslides in the Huanggang area, China. The conclusions can be drawn as follows.
Firstly, employing RSM approach and ANOVA analysis, a prediction model for the shear strength parameters of GGRS is proposed based on the factorial model of multiple quadratic regression equations considering the individual and interacting effects of the considered three variables, moisture content, bulk density, and fractal dimension of grain size. With regard to either cohesion or internal friction angle, bulk density has the greatest effect, followed by moisture content, while the effect of the fractal dimension of grain size is the least. Combined with the response surface plots, other than the interaction of bulk density and fractal dimension of grain size, the interaction of other variables is insignificant.
Secondly, the prediction model for the GGRS is validated by performing laboratory experiments to the GGRS sampled from other colluvial landslides with the same parent rock, as well as the collected data. The model is proved to be significant and applicable to the same kind of GGRS of the area.
This statistical analysis explored the variables at three separate levels and assess the efficacy of each parameter and the interactive coefficients comprehensively. The further study may extend the experimental design method to CCD to explore the possibility of extreme value. Moreover, the statistical method can be applied to more influencing variables and more objective properties, e.g., the permeability and compression index, to obtain more sophisticated observations. Besides, the proposed prediction model for GGRS can be applied to assess the regional landslide stability considering the infiltration process of the rainfall on the surface.