A Method to Estimate Dynamic Pore Water Pressure Growth of Saturated Sand-Gravel Materials
Abstract
:1. Introduction
2. Test Design
2.1. Test Apparatus and Sample Preparation
2.2. Test Conditions
3. Analysis of Dynamic Triaxial Test Results of Saturated Sand-Gravel Material
3.1. Dynamic Pore Water Pressure Curve
3.2. Relationship between the Strain and the Cyclic Numbers
3.3. Effective Stress Path
4. The Estimation Model of the Number of Cycles Required to Reach Liquefaction, NL
4.1. The Verification of NL
4.2. The Modification of NL
5. Estimation of the Dynamic Pore Water Pressure of the Saturated Sand-Gravel Material
6. Conclusions
- (1)
- Dislocation and slip occur between the grains of the saturated sand-gravel material under cyclic loading. This causes both reversible and irreversible two-part volume strains, causing an increase in the periodic fluctuation of the dynamic pore water pressure. The increase in the dynamic pore water pressure is more obvious and the amplitude is larger due to the large pores between the sand-gravel materials. The dense saturated sand-gravel material with its large consolidation stress ratio shows a small volume shrinkage and a large volume expansion, where dilatancy can inhibit the increase in the pore water pressure in the sand-gravel.
- (2)
- During cyclic loading, volume expansion or shrinkage occurs alternately in the saturated sand-gravel material. The mean effective stress of the sand-gravel material decreases, causing the dynamic shear modulus of the material to decrease and the dynamic strain of the material to increase under the same dynamic stress conditions.
- (3)
- Even if the relative density of the sand-gravel material reaches 90%, there is still the possibility of liquefaction under dynamic loading. Earth-rock dams that are built on sand-gravel overburdens and earth-rock dams filled with sand-gravel materials in earthquake-prone areas should use our proposed analysis and evaluation method to investigate the possibility of sand-gravel liquefaction. We used test data and considered the influence of relative density to modify the existing empirical formula and provide an evaluation method for the number of cycles required to reach liquefaction. We propose a pore water pressure growth model that is suitable for both sand-gravel and sandy materials. Comparisons and validations demonstrated that the proposed model accurately describes the three types of pore water pressure growth processes during liquefaction. The pore pressure growth model proposed in this paper can be used to analyze the liquefaction resistance of the dam foundations and dam structure of high earth-rock dams and high sand-gravel dams located on deep overburdens.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Pore Water Pressure Model | Equation | Explanation | Reference |
---|---|---|---|
Stress model | is the dynamic pore water pressure; is the initial confining pressure; is the number of cycles required to cause liquefaction; is the experimental constant related to the type of material. | Seed [6] | |
Strain model | is the tangent modulus of the one-dimensional unloading curve at a point corresponding to the initial vertical effective stress; are test constants. | Martin et al. [11] | |
Transient model | are increments of the pore water pressure during ; is the pore water pressure without dissipation at ; is the dissipation pore water pressure at . | Xie [12] | |
Energy model | is the dissipated energy; and are test constants. | Cao et al. [13] | |
Endochronic theory | K is the damage parameter; the variable includes the shear strain amplitude and number of cycles. A and B are test parameters. | Finn [14] | |
Effective stress path model | Under loading conditions, additional plastic shear deformation occurs in the soil. The variation of pore water pressure is equal to the variation of the mean effective stress. | Ishihara [15] |
Sand-Gravel Materials in Xinjiang | Mean Grain Size d50/mm | Specific Gravity Gs | Minimum Dry Density ρmin/g·cm−3 | Maximum Dry Density ρmax/g·cm−3 | Relative Density Dr | Dry Density ρd/g·cm−3 |
14 | 2.75 | 1.85 | 2.34 | 0.9 | 2.28 |
Test Number | Kc | σ3c (kPa) | σd (kPa) | |
---|---|---|---|---|
S1 | 1.5 | 50 | 70.50 | 0.56 |
S2 | 100 | 142.90 | 0.57 | |
S3 | 121.25 | 0.49 | ||
S4 | 200 | 291.45 | 0.58 | |
S5 | 245.25 | 0.49 | ||
S6 | 227.65 | 0.46 | ||
S7 | 300 | 438.45 | 0.58 | |
S8 | 393.15 | 0.52 | ||
S9 | 346.30 | 0.46 | ||
S10 | 2.0 | 50 | 95.10 | 0.63 |
S11 | 100 | 190.95 | 0.64 | |
S12 | 175.75 | 0.59 | ||
S13 | 200 | 387.65 | 0.65 | |
S14 | 342.25 | 0.57 | ||
S15 | 296.75 | 0.49 | ||
S16 | 300 | 582.80 | 0.65 | |
S17 | 519.35 | 0.58 | ||
S18 | 447.15 | 0.50 |
Test Number | Kc | σ3c (kPa) | ud (kPa) | NL |
---|---|---|---|---|
S1 | 1.5 | 50 | 49.93 | 174.4 |
S2 | 100 | 99.95 | 65.4 | |
S3 | 100.01 | 147.5 | ||
S4 | 200 | 197.1 | 42.35 | |
S5 | 198.54 | 74.3 | ||
S6 | 199.79 | 153.3 | ||
S7 | 300 | 295.87 | 30.37 | |
S8 | 298.07 | 43.35 | ||
S9 | 299.94 | 84.3 | ||
S10 | 2.0 | 50 | 49.24 | 145.3 |
S11 | 100 | 95.3 | 44.3 | |
S12 | 95.06 | 105.25 | ||
S13 | 200 | 187.77 | 23.3 | |
S14 | 193.42 | 35.25 | ||
S15 | 195.93 | 78.25 | ||
S16 | 300 | 280.62 | 18.25 | |
S17 | 282.71 | 32.2 | ||
S18 | 281.03 | 73.2 |
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Chen, J.; Fu, Z.; Chen, S.; Shi, B. A Method to Estimate Dynamic Pore Water Pressure Growth of Saturated Sand-Gravel Materials. Appl. Sci. 2024, 14, 7909. https://doi.org/10.3390/app14177909
Chen J, Fu Z, Chen S, Shi B. A Method to Estimate Dynamic Pore Water Pressure Growth of Saturated Sand-Gravel Materials. Applied Sciences. 2024; 14(17):7909. https://doi.org/10.3390/app14177909
Chicago/Turabian StyleChen, Jinyi, Zhongzhi Fu, Shengshui Chen, and Beixiao Shi. 2024. "A Method to Estimate Dynamic Pore Water Pressure Growth of Saturated Sand-Gravel Materials" Applied Sciences 14, no. 17: 7909. https://doi.org/10.3390/app14177909