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**Settlement Calculation**

Figure 23.5 shows the e â€“ log Ïƒ_{v}' plots for normally consolidated and overconsolidated clay for settlement calculation. For normally consolidated clay the settlement (S) can be determined as:

\[S={{{C_c}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_{v0}} + \Delta {{\sigma '}_v}} \over {{{\sigma '}_{v0}}}}} \right)\] (23.4)

where H is total thickness of the soil layer.

**For over-consolidated clay: Case 1: Ïƒ' _{v0}+Î”Ïƒ'_{v} < Ïƒ'**

\[S={{{C_s}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_{v0}} + \Delta {{\sigma '}_v}} \over {{{\sigma '}_{v0}}}}} \right)\] (23.5)

**Case 2: Ïƒ' _{v0} < Ïƒ'_{c} < Ïƒ'_{v0}+Î”Ïƒ'_{v} **

\[S={{{C_s}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_c}} \over {{{\sigma '}_{v0}}}}} \right)\] + \[{{{C_c}} \over {1 + {e_0}}}H{\log _{10}}\left( {{{{{\sigma '}_{v0}} + \Delta {{\sigma '}_v}} \over {{{\sigma '}_c}}}} \right)\] (23.6)

where C_{s} is the swelling index.

Fig. 23.5. Settlement calculation (a) Normally consolidated clay

(b) Overconsolidated clay .

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