Federal Highway Administration Design Manual: Deep Mixing for Embankment and Foundation Support

APPENDIX B. CALCULATIONS FOR LABORATORY PREPARATION
OF SOIL-CEMENT MIXTURES FOR APPLICATION TO WET MIXING

A laboratory is given soil specimens, values of the water-to-binder ratio (w:b) and slurry, and values of one of the following measures of the amount of binder in the mixture: binder factor (α), binder factor in-place (α_in-place), binder content (α_w), or total water-to-binder ratio (w_T:b). The following steps can be used to determine the quantities of soil, binder, and water to be used for preparing soil-cement specimens.

For the soil, use ordinary laboratory test procedures to determine values of the water content (w), the total unit weight (γ_soil) and the dry unit weight (γ_{d, soil} ) as well as values of the specific gravity of solids (G_s) and the degree of saturation (S) if the soil is unsaturated. If w and γ_soil are known, γ_{d, soil}  can be determined from figure 155.

Figure 155. Equation. Dry unit weight expressed in terms of the total unit weight of the soil and the water content.

Alternatively, if Gs, w, and S are known or can be estimated, then γ_{d, soil} can be determined using figure 156 for any value of S and figure 157 where S = 1.

Figure 156. Equation. Dry unit weight expressed in terms of the specific gravity, water content, and degree of saturation.

Figure 157. Equation. Dry unit weight expressed in terms of the specific gravity and water content for saturation equal to 1.

For some of the relationships given for the mixture, the value of S is an input. For soils from below GWT, the value of S may be taken as 1. For soils above GWT, if G_s, w, and γ_{d, soil} are known, S can be determined using figure 158.

Figure 158. Equation. Degree of saturation.

For the slurry, use the water-to-binder ratio of the slurry, w:b and the specific gravity of solids of the binder (G_b) to determine the value of the dry unit weight of the slurry (γ_{d, slurry} ), as shown in figure 159.

Figure 159. Equation. Dry unit weight of slurry.

Determine the value of the volume ratio (VR) for the mixture using figure 21 and figure 22 if α_in-place is specified. If α  is specified, use figure 20. If a_w is specified, use figure 23. If w_T:b is specified, use figure 24.

Determine the necessary volume of soil-cement mixture (V_mix) using figure 160.

Figure 160. Equation. Volume of soil-cement mixture.

Where the factor of 1.2 is used to account for spillage during specimen preparation.

Determine the weight of soil (W_soil) to be used using figure 161.

Figure 161. Equation. Weight of soil.

Determine the weight of binder (W_b) to be used in the slurry using figure 162.

Figure 162. Equation. Weight of binder used in the slurry.

Determine the weight of water to be used in the slurry (W_w,slurry) using figure 163.

Figure 163. Equation. Weight of water used in the slurry.

The water-binder slurry is prepared by blending binder of weight (W_b) with slurry of weight (W_w,slurry). The soil-cement mixture is then prepared by mixing the slurry with soil of weight (W_soil).

The actual mixture created and cured in the laboratory may deviate from the intended actual weights of soil, binder, and slurry water that are weighed and used to create the mixture, which may also be slightly different from the target amounts calculated. The procedure to determine actual values of α_in-place, α, α_w, and w_T:b from actual values of W_b, W_w,slurry, and W_soil involves first determining w:b from figure 164 and γ_d,slurry from figure 159.

Figure 164. Equation. Water-to-binder ratio of slurry.

The value of VR is then determined from figure 165.

Figure 165. Equation. Volume ratio of mixed soil.

Finally, as-mixed values of α_in-place, α, α_w, and w_T:b can be determined using figure 166 through figure 170.

Figure 166. Equation. As-mixed binder factor in-place for any degree of saturation.

Figure 167. Equation. As-mixed binder factor in-place for saturation equal to 1.

Figure 168. Equation. As-mixed binder factor expressed in terms of VR and dry unit weight of slurry.

Figure 169. Equation. Binder content of mixed soil.

Figure 170. Equation. Total water-to-binder ratio of mixed soil.

For some mixtures using some soils, bleed water may rise to the top of the specimen during curing. One approach is to report the measured strengths for the values of α_in-place, α, α_w, and w_T:b without correcting for the bleed water not incorporated in the cured specimens. The reasoning behind this approach is that if the same w:b and VR are used in the field mixing as are used in the laboratory mixing, bleed water will also occur in the field, so the laboratory strengths will be relevant to the field conditions. In fact, it is likely that more bleed water will occur in the field than in the laboratory due to the higher stresses involved in the field. Other factors being equal, mixtures containing less water will exhibit higher strength. Of course, differences in mixing efficiency and curing conditions will also produce differences between laboratory and field strengths. In this approach, the values of α_in-place, α, α_w, and w_T:b may be labeled "as mixed."

An alternate approach when bleeding occurs is to subtract the bleed water from the slurry water prior to calculating the actual values of α_in-place, α, α_w, and w_T:b applicable to the laboratory specimens. This approach is useful when investigating relationships between mixture strength and actual ratios of binder, water, and soil in the mixture. The weight of bleed water from all the specimens in the batch (W_{w,bleed,specimens}) can be determined by weighing the cured specimens before and after pouring off the bleed water. The adjusted weight of slurry water (W_{w,slurry,adjusted}) is then determined using figure 171.

Figure 171. Equation. Adjusted weight of slurry water.

Where:
W_{w,slurry,mixed} = Total weight of slurry water used in the mixture prior to placing the mixture in the molds.
W_mix = Total weight of the mixture prior to placing the mixture in the molds.
W_specimens = Sum of the weights of all the specimens made from the batch.

The value of W_{w,slurry,adjusted} can be used in place of W_w,slurry in figure 164, and the resulting adjusted value of w:b can be used in figure 159 to determine an adjusted value of γ_{d, slurry}. The adjusted value of γ_{d, slurry} can be used together with the actual values of W_b and W_soil in the mixture to determine an adjusted value of VR from figure 165. Then, the adjusted values of α_in-place, α, α_w, and w_T:b may be labeled "as cured" in this approach.