Assessing frost heave susceptibility of gravelly soils based on multivariate adaptive regression splines model

Highlights

• A multivariate adaptive regression splines-based model was developed to predict frost heave ratio of gravelly soils.

• The general and coupling effects of four influential factors on frost heave susceptibility of coarse fills were examined.

• Difference of frost heave response between closed and open systems was investigated.

Abstract

Frost heave of railway roadbed leads to track geometry degradation during the cold season, seriously threatening the safety of high-speed trains. An accurate estimation of freezing-induced deformation in subgrade aggregates is thus critical to construction and maintenance of transportation infrastructure in seasonally frozen regions. This paper proposes a practical approach to assessing the frost heave susceptibility of gravelly soils under unidirectional freezing conditions. Typical frost heave tests are first performed on gravel columns in closed and open systems. The multivariate adaptive regression splines algorithm is subsequently applied to develop a predictive model for the normalized heave of a specimen. Experimental data of freezing tests were collected from this study and available literature to compile a dataset. A randomly selected subset is used for training, while the complement of the subset is intended for testing. Relative importance analysis and analysis of variance are finally performed to examine the general and coupling effects of initial moisture content, fines, relative compaction, and stress level on the frost heave susceptibility of compacted soil. Hopefully, the developed model and comprehensive analysis of coarse fills could assist railway agencies in understanding the appropriate characterization of frost heave and provide an evaluation guideline for optimized railway roadbed.

Introduction

Significant frost heave is observed in embankments of high-speed rails (HSR) constructed on seasonally frozen ground, posing a severe threat to railway trains. Field investigations of Harbin-Dalian HSR suggested that the frost heave of subgrade surface contributed substantially to the total deformation (Luo et al., 2019). Since coarse fills (e.g., well-graded gravels) used for constructing roadbed (i.e., subgrade surface) were universally recognized as insensitive to frost action, attempts were made to elucidate the potential frost heave mechanism in HSR embankments. To date, the scientific community primarily attributes the frost-related issues to the moisture accumulation, excessive fines in coarse fills, or the combination of both (Zhang et al., 2015). Field observations confirmed unexpected moisture accumulation phenomena in some HSR foundations, and thus Niu et al. (2020) proved that the frost heave performance of track foundation would be significantly enhanced. Sheng et al. (2015) indicated that the cyclic train loads would cause the accumulation of excess pore water pressure in the subgrade, and hence facilitating moisture migration toward the freezing front and feeding ice formation. In recent years, researchers have developed a new concept that the moisture transfer could occur through coupled liquid and vapor migration (Bai et al., 2018; Gao et al., 2018; Zhang et al., 2016). To this end, Zhang et al. (2019a) and Wang et al. (2019b) applied a fluorescein tracer in one-dimensional freezing tests to investigate the liquid and vapor migration in gravelly soils under open-system conditions. Results indicated that the contribution of vapor migration is non-negligible regarding HSR frost heave issues. In the case of Lanzhou-Xinjiang HSR embankments that were constructed in arid regions, delamination of frost heave still takes place in railway roadbed (Lin et al., 2018; Wu et al., 2018). To sum up, the hydraulic condition and moisture redistribution should be carefully accounted for concerning gravelly soil in earthwork construction.

Meanwhile, a strong correlation was found between the frost heave susceptibility of fill material and its fines content (grain size threshold may vary between cases, e.g., 0.25 mm and 0.075 mm). She et al. (2019) demonstrated the clustering effect of fines in saturated coarse fills upon freezing with X-ray computed tomography technique and proposed an indicator known as clustering ratio for a quantitative assessment of fines distribution. To reveal the effect of fines and other influential factors on the frost heave susceptibility of coarse fills, laboratory unidirectional freezing tests were extensively performed on compacted gravel columns for obtaining the frost heave ratios (FHRs). Wang et al. (2016) and Luo et al. (2019) examined four factors, namely fines content, moisture content, compaction degree, and freezing temperature, showing that fines exerted a major influence on frost heave while the temperature gradient is weakly related. Wang et al. (2014) and Long et al. (2018) further considered the impact of overburden pressure, finding that the applied vertical loads could considerably mitigate the ultimate frost heave with and without water intake. Other studies (Konrad and Lemieux, 2005; Konrad, 2008; Li et al., 2017; Liu et al., 2020; Vinson et al., 1986; Zhang et al., 2019a, Zhang et al., 2019b, Zhang et al., 2019c) investigated the effects of repeated freeze-thaw cycles, compaction energy, segregation potential and constant head (i.e., open/closed system) on frost heave susceptibility of fill material used in HSR embankments. In brief, frost heave of gravelly soil is profoundly affected by the presence of excessive fines; laboratory freezing test has been proven a competent measurement method, which could provide useful information on frost heave of graded gravels under the impact of not only fines content, but also some other fundamental factors. Nevertheless, an appropriate characterization of frost heave and developing a practical guideline in field require an in-depth insight into influential factors interaction and establishing feasible prediction models of soil frost susceptibility from a quantitative point of view.

Multivariate Adaptive Regression Splines (MARS) is a nonlinear and nonparametric method for flexible regression of high dimensional data (Friedman, 1991). It can reflect the underlying functional relationships between predictor and response variables without knowing any assumptions before model training. The model shares its ability to capture optimal variable transformations and high order interactions. The method has been widely reported in the geotechnical literature, such as estimating the liquefaction-induced settlement of shallow foundations (Zheng et al., 2020b), the earthquake-induced uplift displacement of tunnels (Adoko et al., 2013; Zheng et al., 2020a), the undrained shear strength of clay (Samui, 2008; Samui and Kurup, 2012), the shaft resistance of piles (Lashkari, 2013; Zhang et al., 2019a, Zhang et al., 2019b, Zhang et al., 2019c), and the slope stability analysis (Wang et al., 2019a, Wang et al., 2019b; Wang et al., 2020). Therefore, the MARS algorithm is adopted in this study to make a connection between laboratory test data and predictive models and to facilitate field operation.

The paper is organized as follows. Typical unidirectional freezing tests of gravelly soils focusing on high levels of compaction are first presented. The methodology of multivariate adaptive regression splines (MARS) is introduced, and two MARS models for FHRs prediction are then developed based on laboratory freezing dataset from this study and previous literature. The proposed models are validated by a randomly chosen subset that is not used and assessed in terms of statistical performance, relative error, and cumulative probability. The general and coupling effects of four influential factors (predictors) on the FHR (response variable) are finally discussed in conjunction with a relative importance analysis.