Background Table $1-$ Some soil properties

$\backslash$table$[[$Parameter$,$Clay,Limestone,$],[$Unit weight,$\backslash$table$[[$Above water$],[$table$]],18$kN$/$m$^(3),23$kN$/$m$^(3)],[,\backslash$table$[[$Below water$],[$table$]],20$kN$/$m$^(3),24$kN$/$m$^(3)],[\backslash$table$[[$Stiffness in vertical direction$],[($relationship between vertical stress$],[$and strain$)]],\backslash$table$[[90$ MPa $($under$],[$undrained$],[$conditions$)]],\backslash$table$[[10$ GPa $($drained$],[$and undrained$],[$conditions$)]],]]$

Table $2-$ Oedometer settlement results for $200$ kPa load step.

$\begin{array}{cc}\text{T}\text{i}\text{m}\text{e}since\text{s}\text{t}\text{a}\text{r}\text{t}of\text{l}\text{o}\text{a}\text{d}\text{a}\text{p}\text{p}\text{l}\text{i}\text{c}\text{a}\text{t}\text{i}\text{o}\text{n}& \text{S}\text{e}\text{t}\text{t}\text{l}\text{e}\text{m}\text{e}\text{n}\text{t}[mm]\\ 10sec& 0\mathrm{.}014\\ 20sec& 0\mathrm{.}016\\ 40sec& 0\mathrm{.}016\\ 1\text{m}\text{i}\text{n}& 0\mathrm{.}018\\ 2\text{m}\text{i}\text{n}& 0\mathrm{.}022\\ 4\text{m}\text{i}\text{n}& 0\mathrm{.}028\\ 8\text{m}\text{i}\text{n}& 0\mathrm{.}034\\ 15\text{m}\text{i}\text{n}& 0\mathrm{.}044\\ 30\text{m}\text{i}\text{n}& 0\mathrm{.}054\\ 1h& 0\mathrm{.}064\\ 2h& 0\mathrm{.}070\\ 4h& 0\mathrm{.}076\\ 6h& 0\mathrm{.}080\end{array}$

Table $3-$ Void ratios at end of each oedometer load step

$\begin{array}{cc}\text{L}\text{o}\text{a}\text{d}[kPa]& \text{V}\text{o}\text{i}\text{d}\text{r}\text{a}\text{t}\text{i}\text{o}[-]\\ 0& 0\mathrm{.}650\\ 50& 0\mathrm{.}634\\ 100& 0\mathrm{.}625\\ 200& 0\mathrm{.}612\\ 400& 0\mathrm{.}597\\ 800& 0\mathrm{.}573\\ 1600& 0\mathrm{.}535\\ 3200& 0\mathrm{.}488\end{array}$

As part of the construction of High Speed $2($HS$2),$ re$-$landscaping is required to ensure track gradients do not exceed limit values. Soil removal may result in $$heave$,$ i$.$e$.$ upwards movement of the soil surface. This must be within specific tolerances to ensure the rail track does not deform too much while operational.

Your job is to predict changes in ground surface levels over time for a location along the HS$2$ trajectory.

Ground profile

The ground profile consists of layers of relatively impermeable clays and very permeable, heavy fractures limestones$,$ see Figure $1.$ The ground water table is located at $5$ m depth. Some soil properties for these layers are given in Table $1.$ An oedometer test was conducted on a clay sample taken from the middle of the $20$ m thick clay layer. The data for this test can be found in Tables $2$ and $3.$ The oedometer sample diameter was $70$ mm and its initial thickness was $20$ mm$.$

As part of the rail construction, the $10$ m high clay hill on the surface was entirely excavated to allow construction of a level railway line, see Figure $1.$

$1.$ Calculate heave $($resulting from the removal of the clay hill$)$ as function of time at the location where you think heave will be largest. Using your calculations, draw a graph showing how the heave changes over time at this location.

$2.$ Draw a graph showing how the long$-$term heave varies along the rail track. Estimate the largest gradient anywhere along the rail track, and indicate where along the track these may occur.

$3.$ Comment on your predictions. How reliable and representative do you think your predictions are?

You may use the following simplifying assumptions by:

$$ ignoring any heave associated with soil creep.

$$ assuming plane$-$strain conditions.

$$ assuming any soil movements are purely vertical. In other words, you may

assume that horizontal strains are zero.

Have a single excel file with supporting calculations.Figure $1-$ Ground profile $($not to scale$)$