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.

When loose, saturated sands and non-plastic silts are subjected to undrained cyclic loading, they will generate positive pore pressures. This increase in pore pressures leads to a decrease in effective stress with a corresponding decrease in shear strength and increase in liquefaction susceptibility. For combinations of sand and non-plastic silt, the threshold fines content can be defined as the non-plastic silt fines content at which the soil changes from sand-like behavior to silt-like behavior. Soils below the threshold fines content behave like sands and soils above the threshold fines content behave like silts. During cyclic triaxial and cyclic direct simple shear tests performed on specimens of sand and silt prepared to the same relative density but different fines contents, two rates of pore pressure generation were observed. When compared at five cycles of loading, soils with silt contents above the threshold fines content were found to produce pore pressure ratios as much as 50% higher than those observed for soils with silt contents below the threshold fines content. When evaluated in terms of cycles, cycle ratio, and dissipated energy ratio, the rate of pore pressure generation was found to be more rapid for soils above the threshold fines content than for soils below the threshold fines content.

The amount of energy dissipated in the soil during cyclic loading controls the amount of pore pressure generated under that loading. Because of this, the normalized dissipated energy per unit volume is the basis for both pore pressure generation models and energy-based liquefaction analyses. The pattern of energy dissipation in the soil in load-controlled cyclic triaxial and load-controlled cyclic direct simple shear tests and displacement-controlled cyclic triaxial and displacement-controlled cyclic direct simple shear tests is quite different. As a result, the pattern of pore pressure generation associated with load-controlled tests is markedly different from that in displacement-controlled tests. Pore pressure generation patterns for each of the four test types were proposed based upon the manner in which the load was applied during the test and the soil's response to that loading. The results of four tests, two load controlled and two displacement controlled, were then used to verify these patterns. Pore pressure generation rates in load-controlled and displacement-controlled tests are different when plotted against their cycle ratios. Conversely, the tests produce nearly identical patterns when plotted against energy dissipation ratio. This occurs because of the relationship between energy dissipation ratio and pore pressure generation is independent of the loading pattern.

Upon dynamic loading, saturated soils lose their strengths and undergo deformations resulting in volumetric-induced settlements that vary according to the excess pore pressure generation and dissipation variations. Traditionally, these settlements have been evaluated using standard charts based on one soil type and its relative density (RD). To assess these settlements, this study established a unique experimental methodology based on two laboratory testings: triaxial simple shear and piezoelectric ring actuator technique. Fifty-seven tests were performed on Ottawa F65 sand under strain-controlled cyclic and post-cyclic conditions. A chart was generated, revealing a relationship between the dissipated energy from cyclic loading and volumetric strain (e v ), based on the shear wave velocity as a controlling factor. This study was compared with previous studies to verify the compatibility of the proposed approach. Another novelty was revealed by studying e v variation with the dissipated pressure. This variation is presented in a post-seismic chart in which deformations are tracked based on the initial soil state and maximum excess pore pressure generation ratio ( Ru max ) at the end of the loading phase. For each RD, the soil is divided between liquefied and non-liquefied states according to a specific Ru max ( Ru maxtrigger point ). The calculation of the volume compressibility coefficient is proven to serve as a liquefaction-triggering criterion identifying the liquefied state.

The undrained cyclic behavior of rubber-sand mixture (RSM) is usually investigated under the cyclic loads with unidirectional shear stress. However, bidirectional shear stress exists in many engineering practices subjected to complex loads, under which the liquefaction resistance of soil may be overestimated. Furthermore, the soil behavior under bidirectional shear stress exhibits quite differently from that under unidirectional shear stress. Therefore, undrained cyclic behavior of RSM under bidirectional shear stress should be further investigated. In this study, several specimens made by RSM with different rubber contents (from 10 % to 30 % by volume) are consolidated under two conditions, K0 consolidation and the combination of K0 consolidation with consolidation shear stress (CSS). Subsequently, numerous tests are conducted under the unidirectional and bidirectional cyclic loading paths to investigate the cyclic undrained behavior of RSM. The results show that the bidirectional shear loads incur a larger normalized pore water pressure (PWP) than unidirectional shear loads. In addition, an energy-based method is employed to understand the relationship between cumulative energy and normalized PWP. During the stage of rapidly accumulating PWP, the dissipated energy required to generate the same normalized PWP is identical, and it is independent of the shapes of loading paths.

The factors that influence dissipated energy and pore pressure generation patterns with respect to the cycle ratio and dissipated energy ratio were analyzed using the results of cyclic triaxial and cyclic direct simple shear tests. These analyses revealed several interesting differences in pore pressure generation patterns when related to cycle ratio than to dissipated energy ratio. Soils with different pore pressure generation patterns when plotted against the cycle ratio were found to have nearly identical pore pressure generation patterns when plotted against the dissipated energy ratio. The differences exist as the result of the fundamental differences between cycle ratio and dissipated energy ratio. The fundamental difference is that pore pressure generation is directly linked to the process of energy dissipation; it is not inherently linked to cycles of loading. Therefore, to achieve an understanding of the pore pressure response of a soil that is independent of the specifics of the applied loading, one needs to evaluate it in terms of energy dissipation, not in terms of cycles of loading, especially irregular loadings.

Since the 1964 Niigata and Alaskan earthquakes, which incurred severe liquefaction damage, liquefaction-related design for infrastructures and buildings has been developed exclusively on the principle of force equilibrium. However, the energy concept is increasingly recognized as superior for simplified and robust liquefaction designs because of the uniqueness of energy capacity in soil failures regardless of the differences in earthquake loads. The energy-based liquefaction evaluation method (EBM) has been pursued by many investigators where dissipated energy for liquefaction is focused in place of liquefaction strength defined in the conventional stress-based method (SBM). Furthermore, the EBM enables sound liquefaction-related designs without resorting to sophisticated but highly variable/tricky numerical analyses and contributes as a scale to measure the reliability of those numerical tools. Thus, the EBM, though short of practical use in today's engineering works, should be able to serve as a simplified liquefaction evaluation tool besides the SBM. We reviewed the basic idea as well as the recent developments of the EBM together with the supporting data. We also discussed how to simplify and approximate the energy-based liquefaction behavior to implement robust evaluations in practical problems. The EBM liquefaction evaluation steps were delineated and exemplified by case studies for practicing engineers compared to the SBM.