Effect of Vehicle Cyclic Loading on the Failure of Canal Embankment on Soft Clay Deposit

Abstract

Road embankments along irrigation canals, constructed on soft Bangkok clay, have always been unstable. Numerous studies have shown that rapid drawdown of water level may be one of the main causes, while vehicle cyclic loading may also contribute to embankment failure. This study aims to investigate the impact of vehicle loading on the failure of embankments built on Bangkok soft clay. The behavior of soft Bangkok clay under vehicle load has been investigated by employing conventional and dynamic triaxial techniques, and finite element method (FEM). This study also examined the effects of soft clay thickness and cyclic loading with different magnitudes and frequencies. The laboratory testing results indicate that the threshold stress of the soft clay is estimated to be approximately three-fourths of the undrained shear strength of the soil. The reduction in effective stress in the soft clay is caused by varied frequencies and thicknesses of the clay. Based on the analysis results, it has been proven that the cyclic loads exerted by vehicles solely are insufficient to cause the embankment to collapse. Nevertheless, the repetitive loading of vehicles may result in a one-quarter decrease in the embankment’s factor of safety.

1. Introduction

In the past three centuries, numerous irrigation canals and embankments have been proposed as means to utilize a variety of water for agricultural, industrial, domestic, and drainage purposes, especially in the Lower Chao Phraya plain area in Bangkok, Thailand. Pavement structures have been implemented in several nations to renovate the surfaces of these embankments in order to accommodate the increased transportation demands caused by urbanization. It is observed that the number of embankment failure cases has been increasing in the past few decades. Examples of the embankment failure along irrigation canals in Bangkok, Thailand, are shown in Figure 1. Numerous scholarly works have investigated and determined the cause of the embankment’s instability problems. Certain sources disclose that the primary cause of embankment failure may be the abrupt decline in water level in canals [1,2]. However, some scholars concluded that potential failure causes may include a mix of factors, including the volume of traffic loading and dredging, as well as the summertime decline of the canal’s water level [3,4].

Studies have been performed to investigate the effect of traffic loading on the instability of the canal embankments. When evaluating the embankment instability due to traffic loading, researchers commonly utilize the finite element method (FEM), limit equilibrium method (LEM), and probabilistic method to examine the changes in stress–strain soil behavior and their resulting implications. Nanthannanthan (1998, 2005) [3,4] examined several cases of the aforementioned factors through analysis using the limit equilibrium method (LEM). However, in their study, traffic loading was assumed to be surcharge loading, and the water level difference was considered to be able to trigger a half reduction in the factor of safety. Wilson and Greenwood (1974) [5] conducted an investigation on lacustrine clay subjected to repetitive loading. Wilson and Greenwood (1974) [5] indicated that if the number of repetitive loads falls below the strength of the soil, axial strain and excess pore water pressure will be generated sharply in the initial stage, followed by the establishment of equilibrium without failure. In addition to this, the soil exhibits the same behavior as stated previously when subjected to cyclic stresses; subsequently, eventual failure will occur [5].

Progressive shear failure, known as a common subgrade failure in the Bangkok area, is also one of the potential modes of embankment failure caused by repetitive vehicle axle loading. The failure mechanism may arise due to the significant magnitude of the cyclic axle loading, which can squeeze the soft soil foundation layer laterally and cause it to lose its bearing capacity [6,7]. Li and Selig (1996) [8] proposed an empirical method for determining total axial strain, from which various dynamic triaxial test results with a given cyclic stress ratio (CSR) and frequency could be extracted in order to calculate the regression equation [6]. Li and Selig (1996) [8] utilized the two-dimensional (2D) finite element method (FEM) to analyze the short-term deformation and plastic zones of the railway embankment subjected to the train axle load. They indicated that the modified Cam Clay (MCC) soil and the Hardening soil model is capable of simulating the unloading-reloading behavior of soft Bangkok clay within plastic yield surface and concluded that train axle loading could potentially lead to a decrease in the factor of safety [9,10].

There has been limited research specifically focused on the instability of canal embankments on the Bangkok soft clay under traffic loading. Furthermore, there is disagreement among a number of researchers about the notion that soft clays and peats with an undrained shear strength ranging from 60% to 91% might cause failure. In this study, the impact of vehicle loading on the failure of an embankment found on the Bangkok soft clay along an irrigation canal was evaluated. The embankment is located between Sta. 16 + 100 and Sta. 17 + 600 on rural road No. PT-5021 in Pathum Thani province, Thailand. A section of the embankment between stations 17 + 475 and 17 + 525 along the canal failed in 2013. Field vane shear testing was conducted between stations 16 + 100 and 17 + 730 following the failure incidence.

There have been no studies conducted on the distribution of vehicle cyclic stress on road embankments along the irrigation canals over the soft Bangkok clay. This study utilized extensive laboratory programs, which involved dynamic triaxial and conventional experiments. These experiments were combined with a two-dimensional finite element method (FEM) that relied on the modified Cam Clay (MCC) soil model, the Hardening soil model (HSM), and the Li and Selig empirical approach. The objective was to investigate and evaluate the behavior of soft clay in terms of stress–strain relationships and excess pore water pressure relationships. This article is divided into five sections. Following Section 1—Introduction, Section 2 reviews relevant prior research on the failure of embankments on the Bangkok soft clay deposit. The research methodology used in this study is provided in Section 3. Section 4 analyzes the impact of vehicle loading on embankment instability. The Section 5 presents the conclusions and recommendations derived from this study.

2. Previous Studies Related to Embankment Failure on Bangkok Soft Clay Due to Vehicle Loading

2.1. Geotechnical Characteristics of Bangkok Soft Clay

The fluctuation of sea level over the Holocene geologic era (5000 to 3000 years ago) has periodically impacted the deposition of the Bangkok soft clay in the lower Chao Phraya plain area; the height of the plain ranges from 0.00 to 2.00 m above mean sea level [11,12,13]. Between the middle and late Holocene, the Coriolis force caused the Bangkok soft clay to vary in thickness from 0 to 20 m. The border and classification map of the different thicknesses of the Bangkok soft clay is illustrated in Figure 2. According to Amornkul (2010) [14], the soil may be divided into six distinct zones. The Zone A to Zone D soft clay thickness is less than 15 m. In addition to that, zones E and F, situated on the eastern and western peripheries near the Gulf of Thailand, have the greatest thickness at over 15 m. The thickness of the soft clay obtained from this study, as presented in Section 4 of the paper, is consistent with that shown in the thickness zonation map.

2.2. Shear Strength Characteristics of Bangkok Soft Clay

Various methods exist for estimating the undrained shear strength of clay ($S_u$) under static loading conditions. Among these, the field vane shear strength test (FVT), unconfined compressive strength (UCS), direct shear test (DSS), and triaxial test are the most often used techniques. The initial pioneering investigation to examine the shear strength properties of the Bangkok soft clay from the Rangsit region using the consolidated undrained (CU) triaxial test was conducted by Moh et al. (1969) [15]. The present investigation identifies four primary strata comprising the soft profile: the weather crust zone (OCR = 5–15), soft clay (OCR = 1), stiff clay (OCR = 2–5), and the sand and gravel layers, in that order. The hardening response of the soft clay is evident in the stress and strain relationship during all test periods; the strain at failure is between 4 and 6 percent of the axial strain, and the Bangkok soft clay under triaxial environment test demonstrated no cohesion ($C^{\prime }$) and total and effective frictional angles (${\varnothing }^{\prime }$) of 20°–26° [15,16]. The shear strength parameters of the Bangkok soft clay obtained from previous studies were used to support the laboratory test data obtained in this study.

Notwithstanding the existence of numerous publications detailing the monotonic shear strength properties of soft clay, it is imperative not to overlook the behavior of soft clay when subjected to cyclic loading. Matasovic and Vucetic (1992) [17] simulated dynamic loading on a variety of clay samples with OCR ranging from one to four and examined the observed behavior of the NC and OC clay samples. In the case of the NC clay, it is evident that the soil exhibits contractionary behavior across the entire period, leading to an increase in positive surplus pore water pressure [6,17,18,19,20,21,22]. On the contrary, soil that has undergone substantial over-consolidation (OCR ≥ 4) experiences dilation during many cycles, indicating negative pore water pressure formation. The Bangkok soft clay was determined to be NC or lightly over-consolidated clay. Thus, the NC clay behavior was expected to be observed during the dynamic test program for the Bangkok soft clay.

2.3. Conventional and Dynamic Triaxial Approaches

2.3.1. Consolidated Undrained (CU) Triaxial Test

The consolidated undrained (CU) triaxial test is commonly executed using a framework consisting of three primary stages: saturation, consolidation, and shearing [23,24,25]. During the stage of soil sample saturation, numerous options for soil saturation are feasible. The back pressure method is the prevailing and customary approach for achieving complete saturation of clay specimens. One crucial approach for monitoring the level of saturation is B-checking, which is performed using the coefficient B of Skempton’s equation [26]. In addition, the average B-values for soft and medium clay are near one (B$\ge$0.95), and the maximum B-value for stiff clay is approximately 0.91 [24].

Following the completion of the saturation phase, the consolidation stage ensues in order to minimize the effects of soil sample dilatation. At this point, the confined pressure is often applied using either the Shansep or recompression techniques. Bjerrum (1973) [27] introduced the recompression technique, which eliminates the expansion effect of soil by applying pressure corresponding to the overburden pressure carried by the soil in situ. In contrast, the Shansep technique was suggested for clay, which demonstrated normalized behavior; the consolidation pressure applied is between 1.50 and 4 times the maximum past pressure (${\sigma \prime }_p$) [24,28]. Subsequent to that, Seah and Lai (2003) [29] found that the recompression technique resulted in an undrained shear strength of the Bangkok soft clay that was approximately 30 percent greater than that of the Shansep technique. In addition, the volumetric strain (%) and the square root consolidation time ($\sqrt{t}$) can then be obtained and plotted at specific times, which correspond to 50% ($t_{50}$)and 100% ($t_{100}$) of the primary degree of consolidation, respectively, in order to assess the rate of shearing in the subsequent phase [30]. It can be seen that the Shansep technique is more suitable to be applied in the CU test for the Bangkok soft clay. Thus, the Shansep technique was used in the study.

The soil specimen is subjected to shear loading as the final step. The strain rate, which could significantly influence the pore water pressure, is the most critical control factor for acquiring a reliable result. The utilization of a rapid strain rate to apply force to the specimen may impede the dispersion of excess pore water pressure throughout the specimen, hence potentially compromising the reliability of the obtained result. In order to ascertain the dependable shearing rate, the strain at failure percentage (${\epsilon }_f$) has been specified. However, several recommendations exist on the typical values of strain at failure. Head (1998) [23] suggests that the strain for typically consolidated undisturbed clay (NC clay) falls within the range of 15 to 20 percent (CU test). Furthermore, the magic number for the loading rate is around 0.0166 percent per minute (1%/hour) [30], while the essential results of the CU test consist of the stress–strain response, strain–excess pore water pressure relationship, Mohr-circle diagram, and stress path. The basics and fundamentals of these diagrams can be followed in [31,32]. Therefore, the CU tests performed for the Bangkok soft clay in this study followed the strain and the rate of shearing recommended by Head (1998) [23].

2.3.2. Dynamic Undrained (DU) Triaxial Test

The essential protocols for this examination are identical to those outlined in Section 2.3.1 regarding the CU examination. Nevertheless, the vylastic sleeve modifies the contraction between the extension top cap and the specimen top cap to let the soil specimen be subjected to the entire dynamic stress [33]. The magnitude and number of cycles of the cyclic loading delivered during the shearing stage have been predetermined prior to conducting the test. As previously stated, the cyclic load pattern is often represented as the sinusoidal functions and is presented in Figure 3. Numerous researchers have investigated the amount of cyclic load. The distribution of stress on the subgrade was examined by Owende et al. (2001) [34]. The tire pressures applied by the truck exhibited a range of 350 kPa to 770 kPa. The subgrade is subject to forces ranging from 20 to 40 kPa. While Lu et al. (2018) [35] argued that dynamic stress distribution on subgrade is approximately 10–25% of stress value [34]. The load frequency can be ascertained by examining the ratio between the length of the vehicle and its velocity (Kph) [6,21,36,37]. Therefore, the stress distribution of the subgrade obtained from Owende et al. (2001) [34] in the field test was utilized in this research.

Based on the traffic loading characteristics, it is possible to hypothesize that the position of the wheel load determines the direction of the maximum principal stress in the soil, and that the direction of the greatest principal stress is influenced by the location of the wheel load [20]. As previously stated, the highest limit of the stress–strain response under repeated loading is the threshold stress of the soil. The threshold stress can be determined using a cyclic stress path diagram (P’-q diagram) by the intersection point between the cyclic path and critical state line (CSL) [6,7,21]. The behavior of soft soil subjected to cyclic loading while remaining below the threshold stress can be readily categorized into two typical soil responses, as described in references [5,22,38,39]. The initial finding of the cyclic triaxial test was the presence of plastic non-recoverable strain (${∆\epsilon }_p$), the test result indicates the resilient strain (${∆\epsilon }_r$) where the increased pore water pressure created in the soil exhibits identical behavior to the strain response, and the parameters in their entirety are illustrated in Figure 4. The mode of the failure can be discussed in Indraratna et al. (2020) [22] namely shear failure, liquefaction, and flow deformation via the typical methods, i.e., the plots between axial strain and the number of cycles. These strain responses, excess pore water pressures, threshold stresses, and failure behaviors were expected to be observed during the DU tests. By using the cumulative strain empirical model (power model), which was introduced by Li and Selig (1996) [8], one may analyse the strain and cycle count in accordance with the equation provided (1). Regression is the foundation of the practical analysis method.

$${\epsilon }_p=\mathrm{a} {\mathrm{N}}^{\mathrm{b}}{\left[\frac{{\sigma }_d}{{\sigma }_s}\right]}^{\mathrm{m}}$$

(1)

where ${\epsilon }_p$ is the cumulative plastic strain,

N is the number of repetitive loads,

a, b, and m result from the regression analysis,

${\sigma }_d$ and ${\sigma }_s$ are cyclic stress and monotonic stress, respectively.

Figure 4. The strain response of soft soil underneath traffic loading.

Figure 4. The strain response of soft soil underneath traffic loading.

2.4. Previous Study for Embankment Failure Due to Vehicle Loading

The mode of embankment slope failure could be categorized as local failure, surficial failure, general slope failure, and deep seat failure [40,41]. In regard to the failure mode under repetitive loading, Loh (2011) [7] and Selig and Waters (1994) [42] discovered that progressive shear failure can occur in embankments. This occurs due to the fact that additional pore pressures accumulate during each loading cycle and cannot be completely recouped after each unloading. As a result, the shear resistance of the soil is diminished. One of the most effective approaches for assessing the effects of vehicle repeated loads on an embankment situated on a soft clay base is the utilization of the finite element method (FEM). According to Eberhardt (2021) [43], Essat (2021) [44], and Potts and Zdravković (2001) [45], the approach utilized in soil and rock mechanics problems is founded on continuum mechanics and can be likened to a computational method. The underlying principle of this approach is the material’s discretization into minute, surface-connected components.

The Mohr–Coulomb soil constitutive model (MCM) is one of the simplest soil constitutive models; it shows completely plastic behavior (bilinear stress–strain curve), and its yield surface is a three-dimensional hexagonal surface; further information is available in [44,45]. But in addition to being a widely used constitutive model for soil, the MCM has been criticized in numerous works due to its inability to reproduce stiffness at low strain concentrations, leading to an underestimation of the strain [46,47]. One potential soil constitutive model that may yield more dependable outcomes is the Hardening soil model (HSM), which works with the strength reduction technique to determine the stability status of an embankment. According to a study by Obrzud and Truty (2018) [47], the soil model is expected to exhibit perfect elasticity under low-pressure conditions. Within this strain range, soil may demonstrate a nonlinear connection between strain and stress.

Additionally, the modified Cam Clay soil model (MCC), currently the most robust model based on the critical state theory, is an additional dependable soil constitutive model. The modified Cam Clay model utilizes this critical state line (CSL) as a failure line, given that it is similarly influenced by the mean effective primary stress. Furthermore, the parameter M determines the shape of the ellipse; specifically, the value of the coefficient of lateral earth pressure (${K_o}^{NC}$) under normal consolidated one-dimensional compression conditions is dependent on the height of the ellipse. A measure of the pre-consolidation pressure ($P_p$) establishes the breadth of the ellipse, and an estimation of the MCC model parameters $\kappa$, $\lambda$, and M can be found in the Plaxis manual (2020) [46]. Balasubramaniam and Chaudry (1978) [16] and Wijeyakulasuriya and Balasubramaniam (2015) [10] compared the stress–strain relationship observed in the triaxial experiments and discussed the application of the MCC model for the Bangkok soft clay. They indicated that the MCC model is capable of effectively predicting the behavior of the Bangkok soft clay.

To ensure the reliability of the analysis result can be trusted, the soil parameters must be calibrated during the numerical simulation process. Surarak et al. (2012) [48] and Obrzud and Truty (2018) [47] conducted the calibration of the HSM, based on the single element technique and then made comparisons between the relationship of stress–strain, excess pore water pressure–strain, and stress path from finite element software (Plaxis 2D V.20.02 software) and actual laboratory results. Moreover, there are several publications publishing the Bangkok soft clay parameters with various soil constitutive models [48,49,50,51,52,53,54]. The parameters for flexible pavement components were proposed by Mulungye et al. (2007), Leonardi et al. (2017), and Karatağ et al. (2018) [55,56,57]. The pavement layer parameters that were implemented in this study have been taken from Leonardi et al. (2017) and Karatağ et al. (2018) [56,57]. Likitlersuang et al. (2018) [9] indicated that the strength reduction algorithm can be utilized to analyze the train traffic loading on the railway embankment on the Bangkok soft clay. Consequently, the single-element technique was employed in this study to calibrate the soil parameters in the numerical modeling, as presented in Section 4.3 of the paper.

3. Methodology Used in This Study

Figure 5 illustrates a flow chart of the methodology adopted for this study, which commences with the examination of pre-existing construction and survey data, as well as other relevant material. If the available data are adequate for assessing the impact of vehicle loads on the embankment, the finite element method (FEM) study can be conducted using the Plaxis 2D V.20.02 software. This study proposes the deployment of additional boreholes to collect soil samples from areas near the failure zones (Sta.17 + 535 and Sta.17 + 642.50). These samples were used to conduct both consolidated undrained (CU) and dynamic undrained (DU) triaxial tests in the laboratory. The aim is to observe the stress–strain behavior, excess pore water pressure–strain relationship, σ-τ diagram, and stress path relationship for the CU test. Meanwhile, the DU test focused on measuring both plastic and resilient strain, as well as excess pore water pressure, under various numbers of cycles (50,000 cycles). Subsequently, the soil parameters of MCM, HSM, and MCC were analyzed by considering the results of the CU tests. These parameters were calibrated using the single-element technique, as indicated in the preceding section.

Instead of illuminating the FEM analysis for the embankment, the clarification of the DU test results analysis was investigated. The association between strain and the number of cycles was examined using the Li and Selig empirical model with the regression technique. This analysis was conducted to generate empirical models that can predict the strain of the Bangkok soft clay based on the total cyclic strain. The criterion deemed appropriate for this study is $R^2$ $\ge$ 0.90, which signifies a strong correlation between empirical and experimental data. Once the soil constitutive parameters calibration had been successfully performed, the input parameters were used to create a geometric embankment model in Plaxis software. Notwithstanding the restrictions of the MCC in determining the factor of safety (FS), the HSM was employed to assess this measure of safety. Therefore, this study introduces the concepts of the MCC and HSM soil models as methods to demonstrate soil behavior. Next, the numerical modeling was conducted with sinusoidal functions to simulate varying load frequencies in vehicle loading applications. The numerical models were validated using the results of the laboratory tests. Additionally, the empirical approach proposed by Li and Selig (1996) [8] was evaluated in this study to provide our opinions regarding the application of the Li and Selig empirical approach for the Bangkok soft clay under cyclic loading.

4. Analyses of Traffic Loading on the Canal Embankment Failure

4.1. Site Information and Field Data Collection

The project site is located between Sta. 16 + 100 and Sta. 17 + 600 on rural road No. PT-5021 in Pathum Thani province, Thailand, as shown in Figure 6. The deep seat failure was witnessed between stations 17 + 475 and 17 + 525. Field vane shear testing was conducted between stations 16 + 100 and 17 + 730 following the failure incidence. Two extra soil boreholes have been excavated at Sta. 17 + 535 and Sta. 17 + 642.50 to examine soil layers and collect soil samples. The soil boring data and field vane shear test results were summarized and presented in Figure 7. It is observed that between stations 16 + 300 m and 17 + 500 m, the deepest layer of soft clay covers approximately 1 km. The maximum thickness of the soft layer is around 12 m, whereas the thickness of soft clay beyond station 17 + 500 m is less than 10 m. Zones from station 17 + 280 m to 17 + 357 m and from station 17 + 487 m to station 17 + 550 m experienced collapse in the shallow area. The failure zone occurred at the interface between the deep and shallow layers of soft clay.

4.2. Laboratory Testing

4.2.1. Conventional Consolidated Undrained (CU) Triaxial Tests

The conventional triaxial tests were conducted in accordance with the ASTM procedure of consolidated undrained triaxial test (CU) [25]. The initial stage of specimen preparation was conducted according to the method described in the literature [23,24,25]. The back pressure method was utilized to fully saturate the specimen, which can be verified by the B-value as per Skempton (1954) [26]. The Shansep technique [28,29] was employed to ensure the specimens followed the virgin compression line and to minimize any disturbances caused by the soil collection process. The last step involved subjecting the specimen to shear loading at a slow and suitable rate following the ASTM D4767 approach to determine the rate of loading corresponding to the recommended strain at failure. The specifics of the conventional triaxial test design for soft clay layers were outlined in

Table 1. Summary of consolidated undrained triaxial tests (CU) for weather crust and Bangkok soft clay.

Soil Type	Series	Test No.	Depth (m)	${{\mathit{\sigma }}_{\mathit{c}}}^{\mathit{\prime }}$ (kPa)	${{\mathit{\sigma }}_{\mathit{v}\mathit{o}}}^{\mathit{\prime }}$ (kPa)	${{\mathit{\sigma }}_{\mathit{c}}}^{\mathit{\prime }}$$/{{\mathit{\sigma }}_{\mathit{v}\mathit{o}}}^{\mathit{\prime }}$	Targeted OCR
Soft clay	CIU-I	CIU-1	5.50	80	50.50	1.58	1
		CIU-2	5.50	150	50.50	2.97	1
		CIU-3	5.25	300	50.50	6.15	1
		CIU-4	5.25	550	50.50	11.28	1

.

Figure 8 shows the results of the CU triaxial tests for the Bangkok soft clay samples tested. Figure 8a shows the deviatoric stress and axial strain diagram of the soft clay CU tests, indicating that the specimen experienced contraction throughout the test period. The strain at failure ranges from 2% to 4%, with excess pore water pressure increasing throughout the test, as depicted in Figure 8b. This increase in excess pore water pressure can lead to a decrease in the effective stress of the soil specimen until failure develops. The stress path diagram provides reinforced evidence supporting the soil’s contraction behavior. It is evident that the stress trajectory of the specimen does not go beyond the envelope line and tends to shift to the left side throughout the test, as shown in Figure 8c. The pore pressure at specimen failure can be calculated by measuring the distance between the total stress path (TSP) and the effective stress path (ESP), within the range of 50–250 kPa. The coefficient A for CIU-1 to CIU-4 exceeds 0.50, indicating normally consolidated clay behavior (NC). The Mohr–Coulomb model (MCM) parameters and additional information can be understood by referring to Figure 8d, and the summarized outcomes are included in

Table 2. Summary of the interpretation of MCM and other parameters of Bangkok soft clay.

Order	Lists of Parameters	Interpreted Results	Literature Results	Reference
1	Initial stiffness ($E^{\prime }$)	9000–13,333 (kPa)	7690–11,300	Viggiani, 2012 [51]
				Surarak et al., 2012 [48]
2	50% deviatoric stress stiffness ($E_{50}$)	10,000–15,000 (kPa)	4831–10,000 (kPa)	Jongpadit et al., 2010 Surarak et al., 2012 Likitlersuang et al., 2013 Viggiani, 2012 [48,51,52,53]
3	Frictional angle (${\varnothing }^{\prime }$)	$21.80°$	$17.80°$$–22.60°$	Moh et al., 1969 [15]
4	Cohesion ($C^{\prime }$)	0 (kPa)	0–17.50 (kPa)	Moh et al., 1969 [15]

.

4.2.2. Dynamic Consolidated Undrained Triaxial (DU) Tests

The cyclic consolidated undrained triaxial test followed the usual triaxial test protocol throughout the saturation and consolidation stages, but instead differed during the shearing stage due to the use of recurrent loading in several cycles. The traffic loading magnitude was established according to the definition of local legislation provided by the Department of Rural Roads (DRR). The rural road authorizes 10 tons per axle maximum for semi-trailers. The speed limit is set at 90 km/h. The load frequency is determined by inputting vehicle velocities of approximately 50 and 90 km/h, resulting in computed frequencies of 1.50 and 2.50 Hz, respectively, as per Kongpanickul et al. (2022), Al-Qadi et al. (2008), Kongpanickul (2019), and Liu and Xiao (2010) [6,21,36,37]. The loading pattern followed a sinusoidal formula [6,7,21,33].

Table 3. Summary of cyclic consolidated undrained triaxial tests for the Bangkok soft clay.

Order	Description	${{\mathit{\sigma }}_{\mathit{c}}}^{\mathit{\prime }}$ (kPa)	$\mathit{C}\mathit{S}\mathit{R}$	Load Frequency (Hz.)	The Number of Cycles
1	Threshold stress	300	0.73–0.75	1.50 and 2.50	-
2	Simulated vehicle loading	300	0.38		50,000
3		300	0.18		50,000

summarizes the cyclic consolidated undrained triaxial testing conducted for the Bangkok soft clay. The threshold stress of the soft clay was estimated to be approximately three-fourths of the undrained shear strength of the soil (CSR = 0.73–0.75). The simulation of cyclic loading was determined based on cyclic stress ratios (CSR) of 0.18 (equivalent to one traffic load) and 0.38 (equivalent to two traffic loads). The strain consequences were assessed through regression analysis by using the Li and Selig empirical model [8] to analyze the projected permanent strain equation, which is confirmed by the R square-indicator ($R^2$ $\approx$ 1). This equation can forecast the whole strain at specific cycles.

Figure 9a shows the progression of cumulative permanent and resilient strains (CSR = 0.18) at 0.65% and 0.70% of total strain at 2.50 Hz and 1.50 Hz frequencies, respectively. The resilient strain ranges around 0.20–0.45% for higher and lower frequencies during the test, while a lower load frequency leads to a 7% increase in axial strain reproduction versus a higher load frequency. At an even higher cycle stress ratio of 0.37, analogous tendencies are observed, as with the lower cyclic stress ratio, the frequency gap is 12.50%. The overall strain is a little above 1.50% axial strain for all cases. The elastic response fluctuations for both cases are practically the same, with a magnitude of only 0.40%. The additional contention for utilizing cyclic stress involves applying CSR values of 0.73 and 0.75 to analyze the threshold stress of soft soil. It is shown that increasing the applied load frequency may necessitate a higher cyclic load magnitude and number of cycles for the specimen to fail. The soil fails at 5% axial strain after 40 cycles under a 1.50 Hz frequency and at around 8% strain after 700 cycles under a 2.50 Hz frequency, as depicted in Figure 9c. Soil behavior can be categorized as either flow deformation (CSR = 0.73) or liquefaction and shear failure (CSR = 0.75) modes. Thus, this could mean that the failure condition of soil under repetitive loading is sensitive to load frequency.

Figure 9b shows the positive excess pore water pressure over the tests for the CSR values of 0.18 and 0.37. The soil specimen can indicate encountering a decrease in shear strength capacity. The extra pore water pressure evolves quickly during the initial cycles, reaching 20 kPa and 23 kPa at the load frequencies of 2.50 Hz and 1.50 Hz, respectively (CSR = 0.18). Subsequently, it increases marginally to 25 kPa during the test. It is shown that lower load frequency could cause an additional 10% increase in the total pore pressure compared to greater frequency, whereas the resilience behavior shows minimal variation when it reaches the greater cyclic magnitude scenario. The pattern remains consistent with the prior case in point. However, the fluctuation resilience gap is approximately 10 kPa, while the accumulated pore pressure exceeds 55 kPa after 15,000 cycles. Figure 10a,b show the cyclic stress behavior at different load frequencies. The stress trajectories change to the left of the failure envelope line but do not intersect with it. It can be assumed that no failures occurred during the test. When the cyclic stress ratio (CSR) reaches 0.73, the stress path shifts to the left and intersects the envelope line. The threshold stress of the soil can be determined by projecting a horizontal line onto the deviatoric axis. The threshold stress for both situations is 88 kPa for the lower frequency and 90 kPa for the higher frequency, estimated based on the cyclic stress ratio (CSR) of 0.73 and 0.75.

4.2.3. Validation of Cyclic Triaxial Results with the Li and Selig Empirical Model

The trial-and-error method was used to estimate the constant coefficient of an empirical model, similar to how regression analysis can be conducted to prove the accuracy of the model compared to laboratory results in terms of total accumulated axial strain.

Table 4. Summary of the curve fitting equation and R-square value of Li and Selig empirical model.

Order	CSR	Frequency (Hz.)	a	b	m	Equation	${\mathit{R}}^2$
1	0.18	1.50	2.50	0.11	1.348	${\epsilon }_p$$=2.50 N^{0.11}$ (${CSR}^{1.348}$)	0.970
2	0.18	2.50	2.57	0.11	1.385	${\epsilon }_p$$=2.57 N^{0.11}$ (${CSR}^{1.385}$)	0.981
3	0.37	1.50	6.40	0.042	1.820	${\epsilon }_p$$=6.40 N^{0.042}$ (${CSR}^{1.82}$)	0.957
4	0.37	2.50	6.30	0.039	1.840	${\epsilon }_p$$=6.30 N^{0.039}$ (${CSR}^{1.84}$)	0.950

summarizes the curve fitting equation and R-square value. Table 4 indicates a strong agreement with R-square values greater than or equal to 0.95 for all situations, as shown in Figure 11. For this reason, the curve fitting equation will be utilized to forecast the cumulative permanent strain with various targeted cyclic stress and cycles.

4.3. Finite Element Numerical Analysis

4.3.1. Model Description

The 2-D Plaxis V.20.02 software is widely acknowledged as an exceptionally efficient finite element software for tackling geotechnical engineering challenges, especially in the case of assessing embankment stability. This software offers a range of soil constitutive models that enable geotechnical engineers to mimic the conditions for erecting under real-world conditions. To assess the stability of embankments with this program, a number of valuable processes can be performed to establish a model for study. The earliest steps involve determining the soil condition parameters, while the subsequent steps involve establishing the model geometry and applying external loading. Subsequently, the next stages involve mesh production, boundary condition definition, and simulation. The final phase involves the computation and analysis of the model within the output module.

A finite element model (FEM) representing the dynamic triaxial testing setup was constructed to ascertain the behavior of the soil on the application of the cyclic loading. The modified Cam Clay (MCC) and Hardening soil constitutive (HSM) models were used in the model to mimic the soft soil behavior. The single-element technique [47,48] was used in the calibration procedure to replicate the CU test in the finite element software.

Table 5. Numerical simulation cases of traffic loading impact on the road embankment along an irrigation canal.

Case No.	Frequency (Hz.)	Thickness of Soft Clay (m.)	The Number of Cycles
1.1	2.50	5.50	50,000
1.2	1.50	5.50
2.1	2.50	10.00
2.2	1.50	10.00

summarizes the scenarios analyzed in the FEM study. As shown in Table 5, the simulated instances were categorized into two main groups based on the thickness of the soft clay (5.50 m and 10.00 m) and load frequency (1.50 Hz and 2.50 Hz). The validation of the simulation results necessitates contrasting the consolidated undrained cyclic triaxial test outcomes with the finite element method (FEM) results using regression analysis, affirmed by the R-square value ($R^2$ ≈ 1).

The geometry modeling of the evaluation of the embankment stability case was developed using the 2-D Plaxis software, incorporating survey data and information that was accessible. This software has been used to model an actual embankment environment before the failure. The categorization of soil profile consists of two primary classifications: pavement structures (including asphalt concrete, crushed rock base, and soil aggregate subbase) and subgrade layers such as weather crust, soft clay, medium clay, and stiff clay, based on the data in Figure 7. The aforementioned groups are determined by the collection of recorded and survey data. Following that, the pavement structures and soil parameters that were gathered and calibrated were assigned to the geometry of the embankment model. Similarly, a vehicle cycle loading of 50,000 cycles in a sinusoidal pattern was simulated on the pavement surface. Figure 12 depicts the configuration of the soil layers and meshes used in the analyses.

4.3.2. Results of 2-D Cyclic Loading Simulation

The modified Cam Clay (MCC) model and the Hardening soil model (HSM) were utilized to imitate the cyclic loading of a vehicle in the Plaxis program. Calibrating these soil characteristics ensures that the input parameters accurately reflect the real soil behavior and laboratory results. Figure 13 illustrates the comparison between finite element and laboratory data using the MCC model, whereas the HSM model could have been analyzed using the same technique. Both results exhibit excellent agreement, suggesting that the parameters accurately represent the soil response according to the constitutive model and are consistent with the existing literature [48,50,51,53,54]. On top of that, input parameters for soil layers, excluding soft soil, can be derived from prior research to model the soil and pavement layers’ behavior.

Table 6. Summary and comparison of the input MCC and HSM soil models of Bangkok soft clay.

Materials	Soil Model	Behavior	MCC.					HSM. and MCM.
			${\mathit{\lambda }}^{\mathit{*}}$	${\mathit{K}}^{\mathit{*}}$	M	${\mathit{E}}_{50}$ (kPa)	${\mathit{E}}_{\mathit{o}\mathit{e}\mathit{d}}$ (kPa)	${\mathit{E}}_{\mathit{u}\mathit{r}}$ (kPa)	m	${\mathit{E}}^{\mathit{\prime }}$ (kPa)	${\mathit{C}}^{\mathit{\prime }}$ (kPa)	${\mathit{\varnothing }}^{\mathit{\prime }}$ (Deg)
Asphaltic concrete	LEM	Drain	-	-	-	-	-	-	-	$1.90 \times {10}^6$	-	-
Granular material	MCM.	Drain	-	-	-	-	-	-	-	400,000	80	39
Soft clay	MCC, HSM	Undrain	0.36	0.049	0.84	7900	7100	20,800	1	-	0.05	20.25
Weather crust	MCM		-	-	-	-	-	-	-	15,000	40	20
Medium clay	MCM.		-	-	-	-	-	-	-	12,000	10	25
Stiff clay	MCM		-	-	-	-	-	-	-	20,000	10	26

summarizes the key input parameters of this study.

Figure 14 shows the results of total displacement, accumulated axial strain, and excess pore water pressure versus the number of cycles for the scenarios analyzed. Figure 14 reveals that the critical point of the embankment is the end of the toe slope at −0.50 m. from the soft clay surface. Moreover, Figure 14b represents the accumulated strain response upon 50,000 load cycles, which aligns with the deformation results discussed. Lower load frequency has a greater impact on 13% of the total axial strain compared to higher load frequency. Also, the thickness of the soft clay could correspond to an additional 40% total axial strain. The biggest axial strain is 0.25%, indicating that the induced strain is below the threshold strain. Thus, cyclic loading is unable to create failure. Similarly, the pore water pressure excess exhibits a positive value throughout the simulation, as depicted in Figure 14c. The peak excess pore water pressure reaches 13 kPa in deep soft clay cases and 10 kPa in shallow cases over time. There is a small differential in pressure between the loads at different frequencies, with lower frequencies causing somewhat greater excess pore water pressure than higher frequencies.

Additionally, to confirm the accuracy of the numerical output, the validation method involves comparing it with the laboratory result and using regression analysis to calculate the R-square indicator ($R^2$) for assessing reliability. The DU experiment results with a CSR value of 0.18 were utilized to validate the Plaxis model results. This was conducted since the cyclic stress distribution on the soft Bangkok clay layer had a similar magnitude in both cases. The validation results are presented in Figure 15. With an R-square value ($R^2$) exceeding 0.80, the numerical outcome can be considered reliable. However, it is observed that the validation procedure can only be accomplished by considering the total axial strain term, as the resilience response effect cannot be accurately accommodated.

The modified Cam Clay (MCC) soil model is incompatible with the strength reduction algorithm of the Plaxis software. The Hardening soil model (HSM) can be accomplished with this approach, and the generation of the geometry model can proceed in a similar manner as described in the preceding section. Even so, the simulation phase is distinct and can be determined according to Table 6. The factor of safety (FS) is a crucial stress ratio that indicates the unsafe condition of the slope and embankment combined with the critical slip surface. The safety analysis in Plaxis (2D) software can be performed to evaluate factors of safety (FS), and the shear strain contour can show the critical slip surface for different numerical scenarios. Figure 16 shows that the shear strain distribution points to the crucial slip surface can intersect the soft clay layer in all scenarios, indicating a potential deep-seated failure mechanism. Before cyclic stress, the factors of safety values were 1.623 (Case 2) and 1.655 (Case 1). After cycle stress, the factor of safety ranged from 1.284 to 1.331 for cases 1.1 and 1.2, and from 1.281 to 1.308 for cases 2.1 and 2.2.

Table 7. Summary of results of embankment stability analysis.

Order	Case No.	FS before Traffic Loading Simulation	FS after Traffic Loading Simulation
1	Case 1.1	1.655	1.284
2	Case 1.2	1.655	1.331
3	Case 2.1	1.623	1.281
4	Case 2.2	1.623	1.308

presents a summary of FS information, showing that cyclic loading may lead to a 20% decrease in the factor of safety (FS). This can reinforce the earlier argument that cyclic loading cannot result in the embankment collapsing. Lower load frequency can lead to a nearly 5% diminution in the factor of safety, while a greater thickness of soft clay may result in a 4% drop in the factor of safety.

5. Conclusions

The primary contribution of this research revolves around using the combination of conventional and dynamic triaxial tests, the Li and Selig empirical model, and the finite element method with MCC and HSM soil models to examine the effects of cyclic stress from vehicles on the soft Bangkok clay. Taking into account the results of the laboratory testing and the numerical modeling, the following key conclusions can be drawn.

The results of the DU test indicate that the repetitious application of stress leads to a decrease in the effective stress in the Bangkok soft clay. This, in turn, results in the accumulation of strain and an increase in pore water pressure throughout the entire duration of the DU test. When the cyclic stress was applied to the Bangkok soft clay with a magnitude ranging from small to medium (CSR < 0.40), it was observed that there was a consistent decrease in effective stress. This study revealed that a maximum cumulative total strain of 1.50% and excess pore pressure of 65 kPa were produced. This could be because the applied magnitude of cyclic stress is less than the threshold cyclic stress of the Bangkok soft clay. It is important to note that the stress ratio was insufficient to cause the soil specimen to collapse. In addition, the Li and Selig empirical model accurately represents the equations when tested with the best-fitting data using the DU test, specifically for the cyclic stress below a certain threshold ($R^2$ > 0.95), in relation to the cumulative total strain. The results of this finding could be utilized to forecast the overall strain at a particular cyclic stress ratio (CSR) and number of cycles for the Bangkok soft clay.

The outcomes of the DU experiment displayed that the soft clay in Bangkok could be susceptible to collapse when exposed to repeated loading at stress levels below the undrained shear strength of the soil, particularly at approximately 75 percent of the undrained shear strength with fewer than 800 cycles. The Bangkok soft clay exhibited flow deformation failure mode under cyclic loading at a load frequency of 1.50 Hz, and experienced combined liquefaction and shear failure modes at a load frequency of 2.50 Hz. It is evident that cyclic stress could lead to a significantly higher level of strain at failure (5–8%), which is roughly double the level of strain at failure caused by monotonic stress (2–4%). This could occur due to the loading–unloading conditions that induce additional cumulative strain in the soil before it fails.

The results of the DU experiments and finite element analysis demonstrate that imparting a lower load frequency to the Bangkok soft clay could result in a small increase in cumulative axial strain and additional excess pore water pressure, specifically a decrease of 12% in both additional strain and excess pore water pressure. The longer duration of cyclic stress at lower load frequencies could have a more significant effect on the slight increase in axial strain. In contrast, a higher thickness of deformable clay could lead to a significant rise in overall axial deformation and surplus pore water pressure, constituting approximately over one-third of the total value. The cause of this phenomenon remains uncertain, as only 5% of the reduction in the factor of safety could be attributed to the combined effects of varying load frequencies and the thickness of the soft clay. In light of the Plaxis results, it could be inferred that the thickness of soft clay has a more significant influence on reducing the effective stress of the soft soil than the load frequency.

The validation of this phenomenon could be observed by examining the best fit of accumulated strain ($R^2$ > 0.83) in the results of the DU tests and finite element analysis. The MCC and HSM soil constitutive models could be used to simulate the behavior of the soft clay under specific cyclic stress conditions, where the cyclic stress is lower than the yield locus conditions. The collected data suggest that there is a gradual increase of slightly over two-fold in the development of excessive pore water pressure and cumulative axial strain when the magnitude of cyclic stress doubles, but remains below the threshold cyclic stress.

On the basis of the results of the DU tests and finite element analysis, it is evident that merely the cyclic loads from vehicles are insufficient to cause the embankment to collapse. The results of the numerical modeling indicate that vehicle cyclic loading could lead to a 25 percent reduction in the factor of safety of the embankment under traffic loading. Nanthananthan et al. (2005) [4] found that changes in water levels in canals can cause a decrease of half in the factor of safety for road embankments located next to irrigation canals. Nanthananthan et al. (1998 and 2005) [3,4] stated that maintenance activities, such as participating in dredging operations during the summer months, is essential for preserving the stability of embankments. Therefore, the primary causes of failure in the order of significance could be the rapid drawdown of water in the canal, vehicle loading, and maintenance activities. However, it is important to acknowledge that the extent of failure in maintenance efforts remains uncertain due to the intricate nature of maintenance information and the varying levels of maintenance carried out during the operation of the embankment.

Certain limitations for the study are provided below. Studying threshold stress and strain in soft soil can impact multiple uncontrollable parameters comprising loading frequency, stress history, soil physical state, degree of disturbance, and soil suction conditions. The soil specimen in the laboratory is expected to be completely isotropic, but in reality, the soil condition might be either partially isotropic or anisotropic. In this work, the impact of perpetual loading on fatigue under cyclic loading conditions was not considered, potentially leading to increased strain. The soil constitutive model in the commercial program has limited capabilities to assess cyclic loading effects and does not incorporate the impact loading from the contact between the wheel and pavement surface. The limitations suggest specific recommendations for future studies. To monitor the road embankment’s behavior on soft soil foundation along the canal accurately, inclinometers, strain gauges, and accelerometers need to be installed in the field. These instruments will collect the necessary data to assess the risk of embankment failure during construction and operation. To enhance the accuracy of soil response, it is recommended that complex laboratory tests reminiscent of the hollow cyclic triaxial test be conducted, which considers stress rotation effects. Additionally, using a sophisticated soil constitutive model that can better capture cyclic behavior is advised to simulate the impact of cyclic stress. When designing road embankments near canals, it is crucial to consider the impact of cyclic loading from traffic on the long-term stability of the embankment.