Arching and heave of bottom of cut

Arching in soils

Arching is the transfer of pressure from a yielding part of a soil mass to the neighbouring stationary parts by shear resistance of the soil. It reduces the load on the yielding part and increases it on the adjacent parts (shown by Terzaghi's trap door experiment). It explains the non-triangular pressure on braced cuts and tunnel linings.

Heave of the bottom of a cut in soft clay

In a deep cut in soft or medium clay, the weight of the soil beside the cut ($\gamma H$) acts as a surcharge on the soil at the base level. If this exceeds the bearing capacity of the clay below the base, the clay is pushed into the excavation, so the bottom heaves up and the ground behind the wall settles.

   ~~~~~~~ ground ~~~~~~~
   |  gamma*H  |   |  gamma*H  |
   |  surcharge| cut | surcharge |
   |           |_____|           |
   |      ,-""  ^ heave "-.       |
   |     (   failure arc    )     |

• Cause: $\gamma H$ at the cut base level compared with bearing capacity $\approx 5.7c$ (Terzaghi) when $\gamma H/c$ is large (above about 5.7).
• Factor of safety (Terzaghi):

$$FS = \frac{5.7c}{\gamma H - \sqrt{2}\,cH/B}$$

($B$ = width of the cut).

• Effects: heaving of the cut bottom, increased pressure on sheeting and struts, settlement of ground outside, possible failure of struts.
• Remedies: deeper embedment of sheet piles into a stiffer layer, a stiff base (concrete slab or grouted block), lowering water level, cutting in stages or with berms.