This study investigated the dynamic properties of red mud (RM)-reinforced volcanic ash (VA) by dynamic triaxial tests. The effects of stress state (dynamic stress sigma d, confining stress sigma 3), dynamic frequency (f) and load waveform (F) on the accumulative plastic strain (epsilon p) have been investigated. The findings indicate a significant influence of the stress state on epsilon p. When sigma d reaches 120 kPa, the specimens exhibit insufficient strength, leading to shear failure. As sigma 3 increases, the dynamic stresses that lead to specimen destabilization also exhibit an upward trend. The effect of f on epsilon p is limited. The epsilon p does not exhibit a clear or consistent developing pattern with increasing f. As for the F, the epsilon p exhibited by the specimens subjected to sinusoidal wave loads is less than that observed under trapezoidal wave loads. Shakedown theory classifies deformation responses into plastic shakedown, plastic creep and incremental collapse. The epsilon p curve patterns of RM-reinforced VA exhibit plastic shakedown and incremental collapse without significant plastic creep characteristics under cyclic loading. A predictive model for epsilon p under cyclic loading is established, which has good predictability. This study presents a novel application of VA and RM, offering substantial research insights into waste recycling.

In previous train operations, traffic loads were typically considered continuous, disregarding the intermittent effects of successive trains on subgrade loess. To investigate the cumulative plastic strain behavior and critical dynamic stress of subgrade loess under intermittent train loads, a series of dynamic triaxial tests were conducted considering factors such as cyclic stress ratio, confining pressure, and frequency. The deformation characteristics of subgrade soil under different stress levels were analyzed, and the dynamic behavior of specimens was categorized based on the development trends of strain rate and cumulative plastic strain. Then the critical dynamic stress levels for plastic shakedown and plastic creep states were determined. The results indicate that intermittent effects suppress the development of cumulative plastic strain and excess pore water pressure in the soil. The more cycles of the unloading-drainage stage the soil undergoes, the stronger its resistance to failure. Under intermittent loads, cumulative plastic strain increases with higher cyclic stress ratios and frequencies. When the cyclic stress ratio is constant, the increase in confining pressure enhances soil stiffness, but this increase is insufficient to counteract the strain induced by greater dynamic stress amplitude, resulting in increased cumulative strain. Combining cumulative plastic strain and plastic strain rate, a classification standard for the deformation behavior of subgrade loess under intermittent loading conditions was established, and the critical dynamic stress was identified. The critical dynamic stress increases with higher confining pressure but decreases with frequency. Accordingly, empirical formulas for critical dynamic stress concerning confining pressure and frequency were proposed. These findings are crucial for understanding the mechanism of intermittent train load effects and analyzing subgrade settlement.

Soil modification is an effective method for enhancing the mechanical properties, including its strength, deformation capacity, and dynamic mechanical stability. Nanomaterials have broad prospects in soil modification due to their small particle size, large specific surface area, and non-toxic and harmless properties. Using the laboratory dynamic triaxial test method, this paper presents a scientific evaluation on the dynamic stability and freeze-thaw resistance of loess modified with nano-silica. This study has investigated the effects of nano-silica content, dynamic stress amplitude, confining pressures, and freeze-thaw cycles on the cumulative deformation behavior of nano-silica modified loess subjected to cyclic loading. Based on the shakedown theory, the shakedown state of 60 samples was evaluated, and an equation for the critical dynamic stress of modified loess was established under the shakedown limit state. The experimental results show that nano-silica can effectively fill the micropores in soil and form a cohesive gel that enhances the bonding between soil particles, significantly increasing the cohesion of the loess due to its nanoscale (10- 9) small size. The 2.5 % content of nano-silica is the optimal dosage for reinforcing loess. Under the same confining pressure condition, the failure strength of the 2.5 % nano-silica modified loess is about 1.4-2.1 times that of the loess, and the residual strength is about 1.2-1.5 times that of the loess. The incorporation of nano-silica significantly improves the dynamic stiffness and freeze-thaw resistance of loess, increasing the reinforcement factor by 51 %-69 % under unfrozen conditions and still increasing it by 43 %-64 % after experiencing one freeze-thaw cycle. Similarly, nano-silica significantly enhanced the dynamic strength and strength parameters of loess. Nano-silica exerts an influence on the shakedown state of the soil, wherein the impact becomes more significant with increasing dynamic stress amplitude.

The subgrade structure of high-speed railways is an important foundation for the safe and smooth operation of high-speed trains, and the scientific design of the subgrade structure provides a fundamental guarantee of its durability and technical economy. As, in the development of high-speed railways in China, higher speeds are being pursued, more requirements have been put forward for the dynamic stability of subgrade structures. To address this issue, this article focuses on the control requirements for the long-term stability of subgrade deformation, and various design methods for high-speed railway subgrade structures are presented. Considering the energy dissipation and dynamic stability characteristics of subgrade filling materials, the dynamic performance of coarse-grained soil filling materials in the bottom layer and graded crushed stones in the surface layer are revealed. The methods for determining the values of dynamic parameters such as the dynamic modulus and damping ratio are provided. Based on the dynamic shakedown theory, the stress-strain hysteresis characteristics of fillers and the variation law of dissipated energy are revealed. The correlation between unit volume dissipated energy and shakedown state under cyclic loading conditions is identified. A criterion for determining the critical shakedown state of high-speed railway subgrade structures based on equivalent unit volume dissipated energy is proposed, and a method for determining the design threshold of dynamic stress and dynamic strain is also proposed. The results show that the shakedown design critical values of equivalent unit volume dissipated energy in the bottom and surface layers of the foundation were between 0.0103 similar to 0.0133 kJ/m(3) and 0.0121 similar to 0.0149 kJ/m(3) , respectively. The critical dynamic strain range was 0.8 x 10(-3)similar to 1.3 x 10(-3). On this basis, a high-speed railway subgrade design method based on energy dissipation and dynamic shakedown characteristics was developed. The results can provide theoretical support for the design of high-speed railway subgrade structures with different filling material alternatives and control standards.

Long-term traffic loadings will induce strong vibrations in the saturated ground, and it probably produces excessive settlements of saturated ground and even various distresses (such as cracks and leakage) of the tunnel structure. To better understand the long-term cyclic deformation behaviors of saturated clay subjected to cyclic traffic loading, a series of cyclic undrained hollow cylinder apparatus tests were performed on Shanghai saturated clay. The secondary cyclic compression stage of permanent axial strain, energy dissipation, and damping ratio are employed to identify the distinct shakedown ranges of saturated clay. Moreover, attempts are made to establish a link between the permanent deformation behavior invoked by different levels of dynamic stress and a kinematic yielding framework. The cyclic test results of Shanghai clay can be classified as plastic shakedown, plastic creep, and incremental collapse, and Y-2 and Y-3 yield limits are interpreted as threshold cyclic dynamic stress to divide the shakedown ranges. Additionally, the effective cyclic dynamic stress ratio can better identify the shakedown ranges of saturated clay. Eventually, a criterion is recommended to identify distinct shakedown ranges of saturated clay. The findings will contribute to the safe design of the transport infrastructure in saturated ground.

When a material is subjected to cyclic loading, there are changes in the material's geomechanical behaviour that need to be characterized for a safe design. For unbounded granular materials, the shakedown theory is used to explain the soil's behaviour under cyclic loading. However, it is not clear yet if such theory is extendable to unreinforced and fibre-reinforced stabilized soils. To this end, a series of unconfined compression cycling loading tests were performed, to study the effect of the number of cycles and initial deviatoric stress level on the behaviour of an unreinforced and reinforced stabilized soil. The results were analysed in terms of shakedown theory, elastic and plastic deformation energy and damping ratio. It was observed that shakedown theory seems to represent the behaviour of the stabilized unreinforced and fibre-reinforced soils under cyclic loading, with threshold between the plastic shakedown and the plastic creep shakedown behaviour at around an absolute axial strain 1 x 10-3. The effect of increasing binder content (from 12 to 39%), comparable to reducing the initial deviatoric stress level (from 85 to 15%), promoted a reduction in plastic deformation (from 2.09 to 0.19% without fibres, and 2.21 to 0.24% with fibres) and damping ratio (from 25.17 to 10.01% without fibres, and 29.18 to 15.95% with fibres) due to the lower degradation of the solid matrix. It also promoted an increase in the difference between elastic and plastic energy (from - 1.04 to 13.92 kJ/m(3) without fibres, and - 1.68 to 10.19 kJ/m(3) for the first cycle).

The shakedown state of the subgrade is crucial for the sustainable design and long-term stability evaluation of pavement structures. In order to characterize the plastic deformation and shakedown behavior of subgrade soil in seasonal frozen regions, cyclic triaxial tests were conducted on the thawed subgrade soil after seven cycles of freeze-thaw. The influences of the numbers of cycle loading, the amplitude of cyclic deviator stress, and the confining stress were considered variables. The evolution features of accumulative plastic strain, accumulative plastic strain rate, and critical dynamic stress were experimentally analyzed. Based on the shakedown theory, the ensuing discoveries were that the accumulative plastic strain response-behavior of thawed subgrade soil was typically divided into plastic shakedown, plastic creep, and incremental collapse under the long-term cyclic loading. Furthermore, the shakedown standard for thawed subgrade soil was also proposed based on the evolution of the accumulative plastic strain rate. The critical dynamic stresses can be obtained by the proposal formula to determine the different plastic deformation ranges.

Pavement foundation stiffness is a critical parameter for pavement design and improving pavement durability. When the subgrade soil is subjected to repeated traffic loading, the initial nonlinearity behavior and permanent strain of subgrade per load repetition are high. As the number of load repetitions increases, the subgrade strain decreases, and it begins to behave more elastically. This condition allows for a more accurate measurement of the resilient modulus (MR) value of subgrade soils. The stress-strain behavior of the soil depends on several factors such as the index properties, stress history, and confining pressure. In this study, the stress-strain responses of sand and fine soils are thoroughly investigated via laboratory-resilient modulus tests, and the shakedown theory was adopted to evaluate the stress-strain response of four subgrade soils. A total of four different subgrade soils were tested. The results showed that the sandy soil exhibited a quasi-brittle behavior characterized by sudden failure when the applied stress exceeded the recoverable strain. The resilient behavior of this material was highly dependent on the confining pressure. The fine materials showed stress-softening behavior and were less dependent on confining pressure. The fine soil exhibited the behavior of over-consolidated soils when the material was subjected to cyclic loading at low confining pressure. The analysis of permanent strain revealed that the summary resilient modulus (SMR) measured for the soils with the lowest fines contents did not accurately reflect the SMR of the material. This material continued to exhibit high permanent strain when the SMR was measured. This suggests that the initially calculated SMR may not be indicative of the material's stiffness.