Dynamic and post-dynamic shear strength of protecting expansive-clay liner on highways and environmental facilities

3.1 Specimen preparation

The specimens were prepared by dry mixing sand and expansive soil in a 70:30 ratio. To establish the compaction characteristics of the mixture, incremental additions of distilled water were made, followed by a series of standard Proctor compaction tests conducted in accordance with ASTM D698 (2000). The resulting compaction curve indicated an OMC of 13.70% and a maximum dry density (MDD) of 18.03 kN/m³.

All ECL specimens were prepared by mixing the dry components with distilled water to achieve the OMC. The mixture was sealed in airtight plastic bags and stored in a humidity-controlled chamber for 24 h to ensure uniform moisture distribution. The specimens were then statically compacted to the MDD. For dynamic and post-dynamic shear strength testing, the specimens were compacted in five layers using a plunger mold, in accordance with BS EN 13286-53. Each specimen measured 50 mm in diameter and 100 mm in height, as shown in Fig. 2(a). Special grooves, 1.5 mm in depth, were formed at the top and bottom surfaces of each specimen (Figs. 2a and b) to accommodate bender elements (BLs) used for shear-wave velocity measurements (Fig. 2c).

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Fig. 2.

Specimen preparation: (a) Compacted specimen showing top-groove, (b) Accommodated groove on bottom of specimen, and (c) BLs for shear wave velocity measurements.

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For unsaturated soil characterization, separate specimens were statically compacted into stainless steel rings with a diameter of 50 mm and a height of 20 mm.

4.1 Unsaturated characteristic of compacted liner

The drying SWCC of the designed liner was evaluated using a combination of the axis translation and vapor equilibrium techniques, covering the full practical range of soil suction (Fig. 3). The axis translation technique was performed using a Fredlund SWCC device, capable of measuring suction up to 1,500 kPa in accordance with ASTM D6836. In this procedure, a saturated specimen was placed on a saturated high air-entry value (HAEV) ceramic disk, which allowed only water flow while isolating the air and water phases. Water release and absorption were monitored using graduated burettes. Suction was applied in increments, with each increment maintained for several days until equilibrium was reached, defined as the cessation of measurable water flow. The corresponding water content for each suction step was calculated to construct the SWCC.

To impose suctions exceeding 1,500 kPa, a vapor equilibrium technique using saturated salt solutions was employed, following ASTM E104 (2007) and ASTM D5298 (2003). Saturated salt solutions with nominal suction values up to 113 MPa were prepared. In this method, soil specimens were suspended above the solutions in airtight containers, which were then enclosed within thermally insulated boxes. The specimen weights were recorded at regular intervals (typically every 7–10 days), and equilibrium was considered achieved when the weight change between two consecutive measurements was less than 0.5%. Upon reaching equilibrium, the water content was determined by oven-drying, and the suction values were matched accordingly.

The results from these tests yielded the complete SWCC for the liner material, as shown in Fig. 4. The experimental data were fitted across the entire suction range using the Fredlund and Xing (1994) model. The curve indicates a saturated water content of 26%, with an air-entry value (AEV) of approximately 25 kPa. The residual water content was found to be as low as 2%, with a corresponding residual suction of approximately 50,000 kPa. All tested specimens exhibited suction values within the selected range, as shown in Fig. 4.

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Fig. 4.

Soil-water characteristic curve (SWCC) and unsaturated properties of the tested liner material (red arrow).

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4.2. Dynamic load testing

4.2.1 Testing device: Dynamic triaxial system

A dynamic triaxial testing system was employed in this study to conduct the experimental program. Fig. 5 depicts the system and its primary components. The equipment, manufactured by GDS Instruments Ltd., UK, features a high-precision electromechanical actuator with a maximum load capacity of 10 kN and an operational frequency of up to 10 Hz. The system is also equipped with a pressure cell capable of withstanding working pressures up to 3000 kPa, along with a pore water pressure controller, a back pressure controller, and a computer-integrated software platform for test control and data acquisition. The setup includes two pairs of BLs, installed at both the pedestal and the top cap, which are used to measure the shear wave velocity through the specimen during testing.

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Fig. 5.

Schematic of the dynamic triaxial testing system.

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4.2.2 Testing procedures

As shown in Fig. 5, compacted specimens were placed on the pedestal inside the triaxial cell and enclosed in a flexible rubber membrane. The two pairs of BLs were attached to the top and bottom ends of each specimen. The testing sequence included several key stages: isotropic consolidation, shear wave velocity measurement, application of cyclic dynamic loading, and post-dynamic testing through monotonic deviator stress application. A comprehensive overview of these procedures has been provided in the flowchart in Fig. 3, with further details outlined in the subsequent sections.

4.2.2.1 Consolidation process

During the consolidation stage, a confining pressure (σ_c) of 50 kPa was applied gradually at a rate of approximately 8 kPa/h, allowing the specimens to undergo isotropic consolidation under controlled conditions (Fig. 3). Radial and axial deformations were continuously monitored using the system’s software. Notably, all specimens were tested in an unsaturated state and were specifically prepared to avoid pore water pressure generation during loading. To ensure this, the pore water drainage valve remained open during consolidation, facilitating dissipation of any excess water. Equilibrium was assumed to be reached when no significant volume change was observed over a continuous 24-h period.

4.2.2.2 Determination of shear wave velocity (v)

Two pairs of BL devices were attached to the dynamic triaxial system as wave generators and wave receivers to measure the shear wave velocity. The first element was fastened to the lower pedestal, and the second element was fastened to the upper cap. A wave generator is placed at the base of each specimen. The S-wave type was transported via the effective length (L_tt). The wave receiver is an additional component at the top of the specimen, and the bottom element is the source of the wave. The test was performed at frequencies ranging from 4 kHz to 10 kHz (Fig. 3).

According to ASTM D8295 (2019), the standard frequency range for bender element testing is between 1 kHz and 50 kHz. The optimal frequency range depends on several factors, including the soil type, stiffness of the specimen, signal clarity, and the potential for near-field effects. To identify the most appropriate frequency range for the current study, preliminary trials were conducted across the full frequency spectrum. The selected range (4–10 kHz) produced coherent waveforms, minimized signal variation, achieved strong curve fitting, and effectively eliminated near-field distortions.

The shear wave velocity was calculated using the π-method approach (i.e., Greening and Nash 2004; Da Fonseca et al. 2009). In this method, the shear wave velocity assists from the relationship between the frequencies and wavelength, L=f*n. Therefore, it is necessary to obtain the correct relation in an appropriate range of frequencies. The selected range used in this study was examined, and the results were appropriate with excellent correlation. These findings are consistent with prior studies on similar soils, which also identified the 2-10 kHz range as optimal for generating coherent data while avoiding near-field effect (i.e., Viana da Fonseca et al. 2009; Arroyo et al. 2006).

Multiple wave pulses were transmitted and recorded at each selected frequency. The arrival and transmission times of both generated and received signals were determined using the “peak-to-peak” method. The relationship between the frequency and wavelength (n = F*t) for each attempt was established, as shown in Fig. 6, and the shear wave velocity was determined. The slope of the best-fit line in Fig. 6 represents the arrival time (t) and shear wave velocity, calculated using Equation 1: The results yielded a shear-wave velocity of 173 m/s for the tested specimens.

(1)

$V_s=\frac{L_{tt}}{t}$

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Fig. 6.

Measurement of shear wave velocity using bender element testing.

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4.2.2.3 Dynamic and cyclic testing

As mentioned earlier, the dynamic tests were conducted under a confining pressure of 50 kPa, with various levels of dynamic axial stress: 50, 100, 200, 250, 300, and 400 kPa. These values correspond to CSRs of 0.25, 0.5, 1.0, 2.0, 2.5, 3.0, and 4.0, respectively, as shown in Fig. 3. Each specimen was subjected to a sinusoidal cyclic loading pattern for approximately 10,000 cycles, with a loading frequency of 2 Hz (equivalent to approximately 50 cycles per min). These parameters were selected to replicate the range of dynamic and impact loads typically induced by heavy traffic or railway operations on protective liner systems beneath embankments and highway shoulders (Leng et al. 2017; Li et al. 2021).

Previous numerical studies on heavy-haul railway and highway infrastructure have assessed dynamic loading conditions, including CSR magnitude and loading frequency, associated with various types of vehicular and train traffic (Tang et al. 2003, Shi et al. 2013, Yin and Wei 2013). As summarized in Table 1, the dynamic shear strength of soils is significantly influenced by parameters such as loading frequency, number of applied cycles, and CSR. These studies report frequency ranges extending up to 10 Hz and CSRs reaching values as high as 10 under severe dynamic and impact conditions, with applied cycle numbers increasing to 100,000 or more. Specifically, under unsaturated conditions similar to those examined in this study, Leng et al. (2017) reported CSRs up to 10 and loading durations exceeding 100,000 cycles to reflect the intense demands placed on liner systems used in transportation infrastructure. The frequency of vibrations induced by heavy traffic or high-speed rail typically ranges from 0.1 to 10 Hz, with the most common range being between 0.5 and 2 Hz (Chen and Bian 2006, Huang et al. 2011, Li et al. 2021).

In the present study, a maximum CSR of 4.0 was applied to evaluate the mechanical response of the liner material under extreme dynamic loading conditions. Specimens subjected to this range of axial cyclic stress either experienced failure or achieved stability after a specific number of cycles.

4.3 Post-dynamic shear testing

Following dynamic loading, specimens that did not reach a failure state were subjected to undrained shear testing to determine post-dynamic shear strength. These specimens were axially loaded at a strain rate of 0.3 mm/min, and the stress–strain behavior was monitored and recorded using the system’s data acquisition software (Fig. 3). Furthermore, some specimens that experienced failure during dynamic testing were also included in this phase. All post-dynamic tests were terminated at a strain level of 5%.

5.1 Failure criterion

The typical behavior of soil specimens under dynamic loading was identified based on the accumulated deformations observed during laboratory tests of dynamic loading. Three different states can be categorized: failure, critical, and stable state (Heath 1972; Yang 2009; Leng et al. 2017). During dynamic loading, the accumulation of deformation was monitored, and the failure state was assumed when the deformation reached a critical level of 5% or more. In this study, 5% strain in the first couple of cycles was considered a failure state, which also means that the specimens could reach 10% failure after a few cycles of dynamic loading. As outlined in Table 1, the range of the failure criteria is within 10% strain. Other studies have considered 2.5% to 5% for the failure state and test termination (i.e., Wang et al. 2012). For this liner material the consideration is taking into account, changes in permeability associated with deformation are considered. Al-Mahbashi and Alnuaim (2023) evaluate the effects of dynamic loads on the permeability of a similar ECL material used in this study. The results showed that applying 70 kPa of dynamic stress for 500 cycles induced approximately 1% cumulative deformation and consequently caused a six-fold reduction in permeability. The repeated dynamic loads induced the degradation of the internal structure of the specimen, which altered the micropores and void ratio (Wane et al. 2013; Cai et al. 2016).

5.2 Stress-strain and dynamic characteristics under different cyclic stresses

This section presents the stress-strain behavior of the tested specimens under imposed dynamic cyclic stress. The variation in the hysteretic loop with the applied cycles of the dynamic load is also highlighted. This behavior is an important consideration for the modeling and precise design of liner materials. Selective cycles of 1, 10, 100, 1000, and 10000 have been presented in Figs. 7 (a and b) for the specimens under axial dynamic stresses of 100 and 200 kPa. These cycles assisted in tracing the deformation of the hysteresis loops during dynamic loading, and the small window on the left side of the charts highlights the first and tenth cycles.

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Fig. 7.

Stress-strain hysteresis loops during cyclic loading for specimens under: (a) ${\sigma }_d$=100 kPa, and (b) ${\sigma }_d$= 200 kPa.

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A hysteretic loop is characterized by the nonlinear behavior of the tested materials and a non-uniform shape, which is defined as the area inside the loop. From Figs. 7 (a and b), it is clear that the loop was nonconcentric and asymmetric, and the shape of this loop underwent significant changes with an increase in the number of cyclic loadings. A plausible change in the hysteresis loop was observed up to approximately 100 cycles, and the area of this loop expanded as the cycle number increased. After the 100^th cycle, no further changes are observed in the hysteresis loops. Owing to the considerable clay content, the nonlinearity of stress-strain is significant owing to the deformation and creep response of their skeleton; a similar observation was reported in a study conducted by Yuan et al. (2025).

Fig. 8(a) shows the variation in the secant shear modulus (G) during the initial cycles across different CSR levels. The results reveal rapid degradation in shear modulus, associated with increased deformation of the hysteresis loop. Specifically, a reduction of approximately 25% in shear modulus was observed as the CSR increased from 2.0 to 4.0, a trend attributed to elevated energy dissipation, similar to that reported by Hussain and Sachan (2020). Fig. 8(b) presents the degradation index (δ) across the full range of applied cycles for various CSR values. The degradation index is defined as the ratio of the shear modulus at a given number of cycles to the initial modulus, providing a measure of stiffness loss over time. A decrease in δ indicates progressive softening of the soil due to cumulative damage within the internal structure. This degradation continues until the accumulated damage exceeds the bonding energy of the particle network, resulting in structural breakdown (Kumar et al. 2017, Jalili and Fafari 2025, Wang et al. 2022). In this study, degradation plateaued at approximately 78% of the initial modulus, beyond which no further softening was detected. Similar patterns of modulus degradation and hysteresis evolution under comparable frequency ranges have been documented in previous studies (Hussaind and Sachan 2020, Pandya and Schan 2022, Yuan et al. 2025), supporting the findings reported here.

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Fig. 8.

Dynamic response characteristics of the tested soil: (a) shear modulus variation during initial cycles and (b) degradation index over loading cycles.

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5.3 Dynamic shear strength

Fig. 9 shows the deformation response during the initial 30 cycles of dynamic loading for selected specimens subjected to dynamic loads of 50, 100, and 250 kPa. As the number of loading cycles increased, deformation initially accumulated up to a threshold level, referred to as the critical zone. According to widely accepted failure criteria, specimens either transitioned into a failure state or reached an equilibrium condition. Beyond this point, and up to 10,000 cycles, no significant changes in deformation were observed. The dynamic loading promoted densification of the soil structure and enhanced particle interlocking, although this effect was both limited and proportional to the magnitude of the applied axial dynamic stress.

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Fig. 9.

Deformation pattern during cyclic loading at: (a) 50 kPa, (b) 100 kPa, and (c) 250 kPa dynamic stress.

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Additional insights into the accumulation of deformation are provided in Fig. 10, which displays the cumulative axial strain over the entire range of loading cycles. In this figure, negative strain values represent compressive strains. Specimens subjected to higher dynamic stresses exhibited more rapid strain accumulation. As per the adopted failure criteria, specimens exhibiting strains exceeding 5% to 10% within the first few cycles were classified as having reached failure. Notably, the specimen tested under a dynamic stress of 400 kPa exhibited rapid strain accumulation and failed within approximately five cycles. Similarly, the specimen subjected to 300 kPa failed after 14 cycles. In contrast, specimens subjected to dynamic stresses below 200 kPa displayed a decelerated strain development, reaching a stable state after approximately 100 cycles, with no significant additional strain accumulation observed up to 10,000 cycles.

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Fig. 10.

Accumulated axial strain as a function of the number of dynamic loading cycles.

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Fig. 11 presents the relationship between CSR and the number of dynamic loading cycles for all tested specimens. Based on the proposed failure criteria, the mechanical response of the specimens can be categorized into two distinct zones: a failure zone and a stable zone. Under high CSR conditions, representing extreme dynamic loading, specimens exhibited failure within a small number of cycles. This failure zone, representing the dynamic shear strength threshold, is characterized by a narrow band that includes critical specimens (those approaching 5% strain) and demonstrates a rapid failure trend (i.e., low cycle count, N) as CSR increases.

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Fig. 11.

Relationship between CSR and number of failure cycles for all tested specimens.

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The relationship between CSR and failure cycles in this zone can be expressed linearly, with test data (indicated by red square markers) fitted to a mathematical model as formulated in Equation 2:

The boundaries of the critical and stable zones can be further defined using the following formulation (Equation 3):

It can be concluded that the specimens were able to withstand dynamic loads of 100 kPa (corresponding to CSR < 1.0) without exhibiting significant accumulation of deformation strains. This finding aligns with the observations of Lai et al. (1998), who reported minimal degradation in shear strength for bentonite-based materials under CSR values below one. For liner systems, the development of permanent deformation is particularly critical, as it directly affects the void ratio and, consequently, the hydraulic performance of the liner. Hydraulic conductivity is a key design parameter in the construction of barrier systems, and unexpected increases in this value may lead to compromised containment performance. Al-Mahbashi and Alnuaim (2023) found that applying dynamic loads to sand–ECL specimens led to significant changes in both immediate and long-term hydraulic conductivity by as much as 120%. This alteration was attributed to soil structure densification induced by dynamic loading. Therefore, in this study, failure of the liner material was defined as reaching a cumulative deformation of 5%.

In a similar context, Fig. 12 presents the relationship between dynamic shear stress (σ_d/2) and the number of loading cycles. The initial segment of the curve is marked by a sharp, linear decline, representing the failure zone, followed by a region of reduced degradation rate, which follows an exponential trend, as modeled in Equation 4:

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Fig. 12.

Dynamic shear strength versus number of loading cycles, illustrating failure and stabilization trends.

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5.4 Post-dynamic shear strength

The post-dynamic (or cyclic) shear strength behavior of the liner material has been presented in Figs. 13(a and b). Fig. 13(a) depicts the stress-strain response of specimens subjected to shearing after dynamic loading, alongside data from identical specimens tested without dynamic loading for comparison. Fig. 13(b) summarizes the relationship between peak shear stress and the applied dynamic stress ${\sigma }_d$. The data point corresponding to zero dynamic stress, highlighted with a red circle, represents the peak shear strength of the specimen tested under static conditions and serves as the reference value. The results indicate a noticeable increase in post-dynamic shear strength. At a low dynamic stress level of ${\sigma }_d=50 kPa$, the increase is modest, approximately 3%. However, the strength gain reaches a maximum of 25% ${\sigma }_d=100 kPa$. Beyond this point, the increase slightly declines and stabilizes at approximately 22% for dynamic stresses up to 400 kPa. These findings are consistent with previous studies reporting that cohesive soils may exhibit shear strengths up to three times higher under dynamic loading compared to static conditions, while non-cohesive soils generally show minimal gains (Dudziński and Stefanow 2019; Sentsova et al. 2019). The observed increase in post-dynamic shear strength is theoretically attributed to several mechanisms: enhanced effective stress in saturated soils; apparent cohesion induced by matric suction in unsaturated soils; and increased stiffness resulting from material hardening. Densification caused by dynamic loading inherently improves stiffness and, consequently, post-dynamic strength (Seed et al. 1966, Turner and Kulhawy 1992, Allotey and ElNaggar 2005). At the microstructural level, dynamic loading promotes particle rearrangement, breakdown of large aggregates, orientation toward more stable configurations, and enhanced particle interlocking. These transformations have been confirmed through microstructural investigations using scanning electron microscopy (SEM), X-ray tomography, and digital imaging techniques (Wang et al. 2022, Wijewickreme and Sancho 2023, Wu et al. 2024). Furthermore, Wang et al. (2022) proposed a novel parameter to quantify microstructural changes induced by cyclic loading, based on aggregate orientation and rearrangement. Their SEM analyses clearly illustrate these structural modifications.

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Fig. 13.

(a-b) Static shear strength and post-dynamic shear strength.

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