单桩承载力 $R_a=0.25\times\frac{\pi}{4}\times0.5^2\times3\times10^3=147.2\mathrm{kN}$。由沉降控制：$50=1\times(\frac{2.6736}{E_{sp}}+\frac{0.2011}{3})\times100$，解得 $E_{sp}=6.173\mathrm{MPa}$，$\zeta=E_{sp}/3=2.06$，$f_{spk}=2.06\times75=154.5\mathrm{kPa}$。置换率 $m$ 满足 $154.5=m\times\frac{147.2}{0.785\times0.25\times1}+0.25\times(1-m)\times75$，得 $m=0.1856$。由 $m=n\times\pi\times0.25^2/(3\times3)=0.1856$，得 $n=8.51$，取8根。