$(4$ pts$)$ Derive the expression for the composite bulk modulus using the series

representation below. Your final expression should be $E_s=\frac{1}{\frac{V_m}{E_m}+\frac{V_{}}{E_p}}$

$(4$ points$)$ If $E_m=1$ and $E_z=12,$ plot $E_z$ for $0V_{m}1.$ Also, on the same graph, plot

$E_t$ for Hirsch's model with x$=0\mathrm{.}55.$ If Hirsch's model is considered to be the most

accurate, which model $($series or parallel$)$ is a better choice if Hirsch's model is

not used

$(2$ point$)$ What problems could arise if the asphalt content of asphalt concrete is

too large?

$(6$ point$)$ List the primary distresses that we are concerned with when we specify

asphalt concrete binder. For each type of distress, list the specimen preparation

and test technique that we use to verify if our binder is adequate for the service

conditions our pavement will be exposed to$.$