Microscale analysis to characterize effects of water content on the strength of cement-stabilized sand–clay mixtures

Abstract

Cement stabilization is a useful and widely adopted method to improve the engineering properties of soils. However, characterization of the unconfined compressive strength, a simple and useful design property, is not straightforward due to complex interactions of various influence factors. This study investigated the effects of water content on the unconfined compressive strength of cement-stabilized clayey sands. The results show that the strength of the cemented binary mixtures increases with water content and water-to-cement ratio until a threshold value is reached and then decreases with further increase in water content and water-to-cement ratio. The unconfined compressive strength is correlated with ultrasonic wave velocity and shear wave velocity, respectively, showing two nearly unique correlations. Microscale analysis based on the coated sphere model revealed that the strength of the sample is affected by the bonding area and the strength of the binder material (cement–clay mixture). An empirical equation is also proposed based on the microscale analysis so as to capture the effects of water content on the strength.

Appendix

From Fig. 10b, it is possible to obtain the following relationship between R, t, and a.

$$a^{2} = \left( {R + t} \right)^{2} - R^{2}$$

(6)

Rearranging Eq. 6, the following equation is obtained,

$$\left( {\frac{a}{R}} \right)^{2} = \left( {\frac{R + t}{R}} \right)^{2} - 1$$

(7)

Based on the geometric relationships, one may obtain the following equation.

$$\frac{{V_{\text{coat}} }}{{V_{\text{sand}} }} = \frac{{\frac{4}{3}\pi \left( {R + t} \right)^{3} - \frac{4}{3}\pi \left( R \right)^{3} }}{{\frac{4}{3}\pi \left( R \right)^{3} }} = \left( {\frac{R + t}{R}} \right)^{3} - 1$$

(8)

Rearrange to obtain the following equation.

$$\frac{R + t}{R} = \left( {\frac{{V_{\text{coat}} }}{{V_{\text{sand}} }} + 1} \right)^{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}}$$

(9)

Combine Eqs. 7 and 9 to obtain the following equation.

$$\left( {\frac{a}{R}} \right)^{2} = \left[ {\left( {\frac{{V_{\text{coat}} }}{{V_{\text{sand}} }} + 1} \right)^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3}}} - 1} \right]$$

(10)

The derivation of the radius ratio a/R has also been performed by Fernandez and Santamarina [11] for cement-stabilized clean sand. This study is further expanded from Eq. 10. If fines are considered, it is reasonable to assume the following relationship between the volumes of coating (V_coat), cement (V_cement), fines (V_fines) and water (V_water),

$$V_{\text{coat}} = V_{\text{fine}} + V_{\text{cement}} + kV_{\text{water}}$$

(11)

where k is a parameter to represent the effect of the amount of water on the volume of the coating, taking into account the complex physical interaction between water and cement–clay mixture; it should be a function of both cement content and fines content. Equation 11 also assumes that the cement–clay and cement–water chemical reactions do not affect the volume of the mixture during sample preparation, and the volume of air in the coating is zero. The volumetric relationship can be rewritten in terms of FC, cc, and w_soil as follows:

$$\frac{{V_{\text{coat}} }}{{V_{\text{sand}} }} = \frac{\text{FC}}{{1 - {\text{FC}}}}\frac{{G_{\text{s,sand}} }}{{G_{\text{s,fines}} }} + \frac{cc}{{1 - {\text{FC}}}}\frac{{G_{\text{s,sand}} }}{{G_{\text{s,cement}} }} + k\frac{{w_{\text{soil}} }}{{1 - {\text{FC}}}}G_{\text{s,sand}}$$

(12)

where G_s,fines, G_s,cement, and G_s,sand are specific gravity of fines, cement, and sand, respectively. Combine Eqs. 10 and 12 to obtain the following equation.

$$\left( {\frac{a}{R}} \right)^{2} = \left[ {\frac{{G_{\text{s,sand}} }}{{1 - {\text{FC}}}}\left( {\frac{FC}{{G_{\text{s,fines}} }} + \frac{cc}{{G_{\text{s,cement}} }} + kw_{\text{soil}} } \right) + 1} \right]^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3}}} - 1$$

(13)

In Eq. 13, the contact radius increases with increasing water content if k > 0, when FC and cc are given. In addition, the cementitious bonding area also depends on the mass ratio of cement and fines to sand particles. Assuming G_s,sand = G_s,fines = G_s,cement = G_s, and k = 1, Eq. 13 can be deduced as follows:

$$\left( {\frac{a}{R}} \right)^{2} = \left[ {\frac{{{\text{FC}} + cc}}{{1 - {\text{FC}}}} + \frac{{G_{s} w_{\text{soil}} }}{{1 - {\text{FC}}}} + 1} \right]^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3}}} - 1$$

(14)

Equation 14 indicates that the bonding area also depends on the mass ratio of cement and fines to sand particles, i.e., (FC+ cc)/(1 − FC), when the difference of the specific gravities is ignored.