Cyclic Behaviors of Saturated Sand-Gravel Mixtures under Undrained Cyclic Triaxial Loading

ABSTRACT

A few well-documented liquefaction case studies of gravelly soils during major earthquakes have increased concerns regarding the liquefaction susceptibility of gravelly sand soils. Understanding the failure mechanism of sand-gravel mixtures under undrained cyclic loading is important for better assessing their liquefaction susceptibility. The liquefaction mechanism and susceptibility of isotropically and anisotropically consolidated sand-gravel mixtures are investigated under undrained cyclic loading in a solid cylinder apparatus; and, the influences of the varying material properties, compactness states, and particle gradations are systematically studied. The authors introduce an index of the average flow coefficient (k_a) that describes the fluidity of saturated sand-gravel mixtures, and then propose the elaboration of a new liquefaction mechanism of saturated sand-gravel mixtures. The specimens would experience cyclic liquefaction when the excess pore pressure ratio reaches 100% under undrained isotropic consolidation, whereas the cyclic mobility would be induced when the cumulative axial strain reaches 5% under undrained anisotropic consolidation. Particles with both sizes smaller than 0.25 mm and mass contents less than 30% in sand-gravel mixtures primarily play a role of the fillers of intergranular voids (fines in coarse). The skeleton void ratio (e_sgk) is a unique physical state index to characterize the liquefaction susceptibility of saturated sand-gravel mixtures with the filler content less than 30%. The negative correlation between the cyclic resistance ratio (CRR) and e_sgk can be expressed as the power function.

Abbreviations: A_cl: Closed-loop area of each loading cycle in Fig. 5; ACU:   Anisotropically consolidated undrained; CRR:  Cyclic resistance ratio; CRR₁₅: CRR in 15 cycle; CRR₂₅: CRR in 25 cycle; CSR:  Cyclic stress ratio, Applied cyclic stress ratio in CTX test in the form of Equation (7)(7) $CSR=\frac{{\sigma }_{\mathrm{d}}}{2\sqrt{K_{\mathrm{c}}}{{\sigma }^{\prime }}_{3\mathrm{c}}}$(7) ; CTX: test Cyclic triaxial test; C_u, C_c:  Coeffıcients of uniformity and curvature for the particle-size distribution curve; D, d: Size of coarse and small spherical particles in an idealized binary packing model; D₅₀:  Median diameter of host coarse soils in binary mixtures; d₅₀: Median diameter; median diameter of host fine soils in binary mixtures; DA:  Double-amplitude; D_r: Relative density; initial relative density; D_r0: Post-consolidation relative density; e:  Global void ratio; initial void ratio; e₀: Post-consolidation void ratio; e_min, e_max: Minimum and maximum void ratios; e_sgk:  Skeleton void ratio; FC:  Fines content for particles with the sizes less than 0.075 mm; FC_th:  Fines content threshold value; f_f: Filler content by weight for particles with sizes less than 0.25 mm in the coarse-dominated grain contact sand-gravel mixtures; G_c: Gravel content; G_s: Specific gravityHCA Hollow cylinder apparatus; ICU:  Isotropically consolidated undrained; k_a:  Index of the average flow coefficient; K_c: Consolidation stress ratio, defined as the ratio of ${\sigma }_{3\mathrm{c}}^{\prime }$to ${\sigma }_{1\mathrm{c}}^{\prime }$m, n Fitting coefficients in Equations 11(11) $CR{R}_{15}=m{e}_{\mathrm{s}\mathrm{g}\mathrm{k}}^n$(11) –13(13) $CRR=m{e}_{\mathrm{s}\mathrm{g}\mathrm{k}}^n$(13) ; N_l:  Number of cycles required to cause an r_u = 100% for ICU CTX test or ε_p = 5% for ACU CTX test; q: Deviatoric stress; q_cyc: Peak cyclic deviatoric stress; q_s: Initial static deviatoric stress; R: Roundness proposed by Power (1953); R_d:  Particle size disparity ratio in binary packing model; r_u: Excess pore pressure ratio, defined as the ratio of Δ u to${\sigma }_{3\mathrm{c}}^{\prime }$; Δu: Excess pore pressure change induced by the action of cyclic shear stressSA Single-amplitude; α_d:   Cyclic shear stress ratio of any plane in the specimen; β:  Inclination angle to the horizontal axis in Mohr’s stress circle serve; $\dot{\gamma }$:  Shear strain rate; ${\dot{\gamma }}_{max}$,${\dot{\gamma }}_{min}$: Maximum and minimum shear strain rate of each loading cycle in Fig. 5; ε: Axial strain; ε_p: Accumulated permanent axial strain; η:  Apparent viscosity in fluid mechanics; ρ_d: Dry densities; ${\sigma }_{1\mathrm{c}}^{\prime }$,${\sigma }_{3\mathrm{c}}^{\prime }$: Initial effective vertical and lateral consolidation stress; σ_d: Applied sinusoidal cyclic axial stress amplitude; ${\sigma }_{\mathrm{s}}^{\prime }$:  Initial effective normal stress of any plane in the specimen; τ:  Shear stress; τ_s: Initial shear stress of any plane in the specimen; τ_d: Cyclic shear stress amplitudes of any cyclic shear effect plane; τ_max, τ_min:  Maximum and minimum shear stress of each loading cycle in Fig. 5

KEYWORDS:

• Sand-Gravel Mixture
• Cyclic Triaxial Tests
• Liquefaction
• Cyclic Resistance Ratio
• Fluidity
• Skeleton Void Ratio

Highlights

1. The failure modes of sand-gravel mixtures can be classified as either cyclic liquefaction or cyclic mobility.

2. The elaboration of a novel liquefaction mechanism of saturated sand-gravel mixtures was proposed.

3. The skeleton void ratio is a unique physical state index to characterize the liquefaction susceptibility of sand-gravel mixtures.

4. Relationship between CRR and the sand-gravel skeleton void ratio can be expressed as a power function.

Acknowledgments

The study described in this paper was supported by the Project of the Natural Science Foundation of China (Grant Nos. 51438004; 41172258; 51608267), the National Key Development Program for Fundamental Research (Grant No. 2014CB047005). These financial supports are gratefully acknowledged.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [41172258, 51438004, 51578501];National Program for Special Support of Top-Notch Young Professionals 2013; Zhejiang Provincial Natural Science Foundation of China [LR15E080001]; National Grand Science and Technology Special Project of China [2013ZX06002001-9]; National Key Development Program for Fundamental Research [2014CB047005].