A better knowledge of the subground state is beneficial in the sustainable design and development of the infrastructures’ foundations. Cone penetration test (CPT) is a fast, repeatable, economical site investigation test in geotechnical engineering that provides almost continuous measurements in depth [
37,
46]. Hence, its popularity is still growing among engineers. The continuous measurements of cone tip and sleeve frictional resistances in depth make it a promising method for subground stratification and soil behavior type (SBT) classification [
8], although an appropriate interpretation may provide further engineering information [
20,
37,
44,
48,
54,
64]. Meanwhile, the ranges of CPT measurements and the involved fluctuations for different SBTs are always influenced by several factors, such as the spatial variability of soils, cone size, and sensors’ precision of measurements [
2,
5,
28,
35,
37,
43]. They bring about both complexity and uncertainty in CPT-based soil stratification. Therefore, subground stratification has often been performed by the CPT experts. However, in the past 2 decades, numerous studies have tried to bridge the gap between mathematical and geotechnical knowledge for stratifying subsurface soils using CPT measurements.
To overcome the complexities and uncertainties of the measurements in stratification, vast research is performed on the determination of the CPT measurements ranges for different soils and SBT classes, as well as the development of the computational processing models to recognize the soil layers from measurements. Since the invention of CPT, SBT classification based on the measurements has been investigated numerously and some charts are proposed for this purpose [
4,
6,
7,
19,
21,
22,
29,
43,
45,
47,
49,
51,
53,
58]. However, as a problem, the existence of uncertainties and probably outliers in CPT measurements is almost inevitable. The outlier identification in time series and the procedures to approximate them mathematically have been targeted in numerous studies since many years [
1,
9,
10,
36,
57]. Some studies used the geotechnical principles and statistical methods simultaneously to detect and remove the outliers [
12,
20]. In the meantime, especially in the past 2 decades, engineers have sought computational methods to facilitate identifying subground layers and to substitute the required experts’ knowledge. Zhang and Tumay [
66] suggested the statistical and fuzzy sublayer identification approaches using the soil types almost similar to the ones in the unified soil classification system (USCS). The CPT tests conducted at the National Geotechnical Experimentation site (NGES) at Texas A&M University [
56] were used to show their method’s applicability. Hegazy and Mayne [
25] presented the improvement of clustering methods over the previous statistical ones for the CPT-based soil classification. They showed that clustering could detect major changes within the stratigraphy, which might not be apparently visible. A probabilistic approach was developed by Jung et al. [
30] to modify the soil identification charts based on the CPT data. Das and Basudhar [
17] proposed self-organizing maps and fuzzy clustering techniques for identification of different layers. The estimated results were comparable with those of obtained from the cone classification chart, hierarchical and K-mean clustering techniques. Wang et al. [
63] modelled the uncertainty in the CPT-based soil stratification and classification by means of the Bayesian approach and using the Robertson chart proposed in 1990 [
45]. The proposed model was evaluated based on some real CPT data. Ching et al. [
13] used the SBT index,
\(I_{\mathrm{c}}\), in their proposed stratigraphic profiling approach. The layer boundaries were recognized at the relatively large change points in the
\(I_{\mathrm{c}}\) profile. They utilized the wavelet transform modulus maxima (WTMM) method, and 50 real CPT-based stratification profiles provided by experts to determine the layer change point criterion. Cao et al. [
8] developed a Bayesian framework based on the SBT index,
\(I_{\mathrm{c}}\), for the probabilistic soil stratification. The number and thickness of layers, and also their associated identification uncertainty were estimated. Wang et al. [
62] proposed a semi-supervised clustering method built on a hidden Markov random field framework using boreholes and CPT sounding logs. Wang et al. [
59] suggested an unsupervised Bayesian inferential framework integrated with the Robertson chart [
45] to determine the strata and the corresponding SBTs. In brief, the literature indicates that the computational CPT-based subground stratification models were built on two general approaches. In the first approach, the consistency among the sequential CPT data points has been employed to find the thick layers, such as in the Bayesian theory and clustering models. On the other hand, in the second approach, the boundaries between the soil layers are determined based on the change points and especially sudden fluctuations detections in CPT results, such as in the wavelet model proposed by Ching et al. [
13]. There are still some deficiencies with the existing methods, although great progress has been made so far in stratification models. Some proposed methods are time-consuming, and investigation is still being performed to reduce their computation time. Almost all proposed models concentrated on seeking the strata featuring the high consistency of the corresponding measurements. But the transition layers between them are neglected or finding them may require longer computation time. In almost all methods, it has been tried to find the layer boundaries deterministically even though probabilistic methods were employed. However, due to some intrinsic uncertainties in CPT soundings which were not targeted focally in the proposed models, reporting the layers change boundaries and SBTs deterministically may be still a bit risky.
Hence, in this paper, integrating geotechnical knowledge with time series/signal smoothing, game theory, and optimization models, a totally different and novel model is proposed for identifying the strata depths and their SBTs. As the advantages of the proposed model, it runs rapidly, finds both the thick layers and the transition layers in between, and provides the possibility to tune the precision of stratification-SBT classification profile. The precision regulating parameter is implemented in the model to avoid deterministic presentation of the subground stratification and to provide the engineer the possibility to make their own judgement if required. In the proposed model, first, a local regression smoothing method is utilized to reduce the outliers’ and uncertainties’ impact within the CPT measurements. Then integrating the Nash–Harsanyi (N–H) model, as a game theory model, grey wolf optimizer (GWO), as an optimization model, and Robertson soil classification chart (1990), a model is proposed to identify the transition and then the thick layers in between, as well as their corresponding SBTs. Although the focus and novelty of the present study has been the developed model itself, after describing the model, the practicality of the model is verified based on training the model using only one CPT-based stratification profile provided by experts and comparing the results with two other published stratification models for other three testing CPT soundings.