# Control by Hilf’s Rapid Method

10.3.7.2.1 Introduction: simplified procedure

Hilf’s Rapid Method (1959) was developed to provide a swift compaction control, understood as the deviation of the water content and dry unit weight of the compacted fill relative

Figure 10.24 Water replacement method for the determination of the unit weight of a rockfill (photo: Eduardo Fortunato).

to the optimum water content and the maximum dry unit weight, respectively, with the absolute value of the former being unknown.

The method essentially consists of the following steps: i) a certain mass of fill that has just been compacted is collected and appropriately protected from evaporation in order to preserve its water content; ii) this mass is divided into n specimens, with the total weight of each specimen being determined; iii) to each specimen is added a known mass of water, followed by mixing to form a homogeneous mass, similar to the procedure carried out in a compaction test; and iv) each specimen is then compacted in a Proctor mold, applying a compaction effort similar to that in the field, and the unit weight of these cylindrical samples is determined.

10.3.7.2.2 Evaluation of the relative compaction

Consider Z, the ratio (expressed as a percentage) of the weight of the added water, AWM and the initial weight, W, of each soil specimen. From the results of the procedure stated above, a curve relating Z (along the дг-axis) and the unit weight, /, of the several compacted specimens can be obtained, as shown in Figure 10.25. Designating Ws as the weight of the solid phase (particles) of each specimen, w^n as the water content of the mass removed from the fill, and w as the water content of each specimen, the following can be obtained:

For any value of Z, the general equation is valid for correlating the unit weight with the dry unit weight:

By dividing both members of this equation by 1+Z and subsequently replacing Z by the second member of Equation 10.13, the following expression is obtained after some developments:

Figure 10.25 Hilf’s method: added water versus the unit weight and the converted unit weight.

When analyzing this equation, it is possible to observe that the (l+Wfiu) factor of the first member is constant, although unknown. Thus, if the curve y=f(Z) in Figure 10.25 is divided by (1 +Z), another expression can be obtained:

which is the so-called curve of converted unit weights, which, apart from a constant and unknown scale factor, consistently represents the relationship between yd and Z.

This relationship is particularly valid at the maximum point of the curve:

Therefore, the relative compaction (RC) of the fill, that is, the ratio between the dry unit weight of the fill, ydfill, and the maximum dry unit weight obtained in the Proctor test (see Equation 10.2) can be expressed as:

or, considering Equations 10.14 and 10.17:

In conclusion, the relative compaction can be obtained by dividing the unit weight of the fill, yfill, by the ordinate of the maximum point of the curve of converted unit weights.

It is worth noting that the Z value on the x-axis can be either positive or negative. Negative values are associated with a certain weight of water being removed from the fill, which makes the method less immediate. However, this can be crucial to obtain an adequate definition of the curve of converted unit weights, particularly in fills compacted relatively close to the optimum. As a rule, four points are recommended to establish the curve, with three being the minimum, in combination with the hypothesis that the curve has the shape of a parabola close to the peak.

10.3.7.2.3 Assessment of the deviation of the water content from the optimum

By designating Zmax as the abscissa of the peak of the curve of converted unit weights, it corresponds to the optimum water content. Thus, considering Equation 10.13:

When taking Equation 10.15 into account, the following can be obtained: or:

which, for Z = Z„M„ can be expressed as:

Combining this equation with Equation 10.20, the following can be obtained:

In this equation, in addition to wfin, wopt is also, strictly speaking, unknown, as it expresses the optimum water content of the field compaction curve instead of the laboratory curve. Nevertheless, the difference between the abscissas of the peaks of both curves is relatively small. An error of a few percentage points in the value of wopt introduced in the second member of the equation has little effect on the value of the first member, i.e., in the deviation of the water content of the fill from the respective optimum value.

The accuracy of this estimation can be further improved by using the chart represented in Figure 10.26 which, based on the results on 1,300 soils, relates the optimum water content with the unit weight at the same water content.[1]

The author of the method stresses one additional advantage of its use: the fact that this information obtained and treated for a swift control for compaction - though not including,

Figure 10.26 Optimum water content versus unit weight calculated at a water content equal to the optimum (curve based on 1,300 experimental results; adapted from Hilf, 1959).

as seen, the values of the dry unit weight and water content - can be included, at a later stage, to obtain the absolute values of these parameters for record purposes. For this, the water content of the fill should be determined by oven drying.

• [1] Note that this unit weight is equal to f(Z„ux) in Figure 10.25.