$6.$C$.1$ Since laboratory or field experiments are generally expensive and time con$-$

suming, geotechnical engineers often have to rely on empirical relationships

to predict design parameters. Section $6\mathrm{.}6$ presents such relationships for pre$-$

dicting optimum moisture content and maximum dry unit weight. Let us use

some of these equations and compare our results with known experimental

data. The following table presents the results from laboratory compaction

tests conducted on a wide range of fine$-$grained soils using various compactive

efforts $(E).$ Based on the soil data given in the table, determine the optimum

moisture content and maximum dry unit weight using the empirical relation$-$

ships presented in Section $6\mathrm{.}6.$

a$.$ Use the Osman et al$.(2008)$ method $[$Eqs$.(6\mathrm{.}15)$ through $(6\mathrm{.}18)].$

b$.$ Use the Gurtug and Sridharan $(2004)$ method $[$Eqs$.(6\mathrm{.}13)$ and $(6\mathrm{.}14)].$

c$.$ Use the Matteo et al$.(2009)$ method $[$Eqs$.(6\mathrm{.}19)$ and $(6\mathrm{.}20)].$

d$.$ Plot the calculated $w_{\text{o}\text{p}\text{t}}$ against the experimental $w_{\text{o}\text{p}\text{t}},$ and the calcu$-$

lated ${}_{d(max)}$ with the experimental ${}_{d(max)}.$ Draw a $45$ line of equality on

each plot.

e$.$ Comment on the predictive capabilities of various methods. What can

you say about the inherent nature of empirical models?

Note:

${?}^a$ Tschebotarioff $(1951)$

${?}^b$ Modified Proctor test

${?}^{?}$ S Standard Proctor test

${?}^d$ Standard Proctor mold and hammer; drop: $305$ mm ; layers: $3$; blows$/$layer: $15$

${?}^e$ Modified Proctor mold and hammer; drop: $457$ mm ; layers: $5$; blows$/$layer: $26$

${?}^f$ Modified Proctor mold; standard Proctor hammer; drop: $305$ mm ; layers: $3$; blows$/$layer: $25$