Critical Dynamic Stress and Cumulative Plastic Deformation of Calcareous Sand Filler Based on Shakedown Theory
Abstract
:1. Introduction
2. Experiments
2.1. Instrument
2.2. Samples
2.3. Loading Conditions
2.3.1. Dynamic Load Waveform
2.3.2. Dynamic Load Frequency
2.3.3. Definition of CSR and Determination of Load Amplitude
3. Results and Analysis
3.1. Consolidated Drained Test
3.2. Trend of Calcareous Sand Resilient Modulus
3.3. Definition of Shakedown Status of Calcareous Sand
3.4. Analysis of Cumulative Deformation Law of Calcareous Sand
3.4.1. Effects of CSR
3.4.2. Effects of Confining Pressure
3.5. Critical Dynamic Stress of Calcareous Sand
3.6. Trends of Particle Gradation under Different Shakedown Response Statuses
4. Conclusions
- (1)
- In the tri-axial consolidation drainage shear tests on calcareous sand, with the increase in the effective confining pressure, the particle breakage of calcareous sand intensified and the stress–strain curves of calcareous sand showed a change from the strain-softening to the strain-hardening state; the volumetric strain of calcareous sand showed a change from shear shrinkage and then shear expansion to continuous shear shrinkage.
- (2)
- The tri-axial test demonstrated that the evolution law of axial plastic strain in calcareous sand under different axial dynamic stress levels can be described by the shakedown theory, and the response behavior of calcareous sand can be grouped into three categories with the increasing of the axial dynamic stress, namely plastic shakedown, plastic creep and incremental plastic failure, respectively.
- (3)
- The axial plastic strains of calcareous sand increased with the cyclic stress ratio (CSR), while the critical CSR for plastic shakedown and plastic creep increased with an increase in the effective confining pressure.
- (4)
- The empirical critical stress formula for calcareous sand fillers was obtained with confining pressure as the variable, which could be used to determine the plastic shakedown of calcareous sand subgrade structures at any depth and its critical dynamic stress level under plastic creep.
- (5)
- At the initial stage of cyclic loading, calcareous sand samples compacted and the resilient modulus increased rapidly. A further increase in the number of loading cycles caused the particles to break; the finer particles filled the gap between coarse particles, further compacting the samples and increasing their resilient moduli. Hardin’s breakage potential model was also used to quantitatively describe particle breakage before and after the tests on calcareous sand samples, and the results showed that with an increase in CSR, the degree of breakage of sample particles first increased and then stabilized.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Confining Pressure σ3 (kPa) | Deviatoric Stress qCD (kPa) |
---|---|
40 | 541.34 |
60 | 622.04 |
80 | 657.48 |
100 | 719.41 |
Cumulative Evolutionary form of Deformation | Strain Rate | Note |
---|---|---|
A: Plastic shakedown | <1 × 10−5 | Ideal range of design materials |
B: Plastic creep | 1 × 10−5–8 × 10−5 | Admissible status within control |
C: Incremental plastic failure | >8 × 10−5 | Avoid occurrence |
Effective Confining Pressure σ3 | Cyclic Stress Ratio | Shakedown Response Status | Breakage Potential Bp | Extent of Breakage Bt | Relative Breakage Rate Br |
---|---|---|---|---|---|
60 | 0.23 | Plastic shakedown status | 194.13 | 23.49 | 0.121 |
60 | 0.41 | 48.14 | 0.248 | ||
60 | 0.57 | 48.92 | 0.252 | ||
60 | 0.72 | Plastic creep status | 50.09 | 0.258 | |
100 | 0.2 | Plastic shakedown status | 44.46 | 0.229 | |
100 | 0.25 | 47.17 | 0.243 | ||
100 | 0.35 | 56.88 | 0.293 | ||
100 | 0.81 | Plastic creep status | 58.82 | 0.303 |
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Wang, K.; Chen, Z.; Wang, Z.; Chen, Q.; Ma, D. Critical Dynamic Stress and Cumulative Plastic Deformation of Calcareous Sand Filler Based on Shakedown Theory. J. Mar. Sci. Eng. 2023, 11, 195. https://doi.org/10.3390/jmse11010195
Wang K, Chen Z, Wang Z, Chen Q, Ma D. Critical Dynamic Stress and Cumulative Plastic Deformation of Calcareous Sand Filler Based on Shakedown Theory. Journal of Marine Science and Engineering. 2023; 11(1):195. https://doi.org/10.3390/jmse11010195
Chicago/Turabian StyleWang, Kangyu, Zhenhuan Chen, Zhe Wang, Qianshen Chen, and Dihui Ma. 2023. "Critical Dynamic Stress and Cumulative Plastic Deformation of Calcareous Sand Filler Based on Shakedown Theory" Journal of Marine Science and Engineering 11, no. 1: 195. https://doi.org/10.3390/jmse11010195
APA StyleWang, K., Chen, Z., Wang, Z., Chen, Q., & Ma, D. (2023). Critical Dynamic Stress and Cumulative Plastic Deformation of Calcareous Sand Filler Based on Shakedown Theory. Journal of Marine Science and Engineering, 11(1), 195. https://doi.org/10.3390/jmse11010195