12

某淤泥地基打设排水板后采用堆载预压处理，堆载至 2020 年 7月 16 日后，某原地表测点的实测沉降值见下表。现用双曲线法预测后期沉降，使用线性函数回归的$\cfrac{t-t_0}{S_t - S_0}$与$(t-t_0)$ 关系曲线见下图。计算 2020 年 12 月 31 日该位置处的固结度最接近下列哪个选项?($S_0$为$t=t_0$时间对应的初期沉降量，$S_t$后为任意 1 时间对应的派降量，$t_0$为所选取初始沉降对应时间。)

沉降观测日期	累计沉降量(mm)	$t - t_0(m)$	$S_t - S_0(mm)$	$(t-t_0)/(S_t-S_0)(d/mm)$
2020-7-16	512.6	0	0	/
2020-9-24	1336.9	70	824.3	0.0849
2020-10-3	1352.1	79	839.6	0.0941
2020-10-6	1359.3	82	846.8	0.0968
2020-10-9	1364.5	85	851.9	0.0998
2020-10-12	1368.1	88	855.5	0.1029
2020-10-15	1371.4	91	858.8	0.1060
2020-10-18	1374.4	94	861.8	0.1091
2020-10-24	1378.1	100	865.5	0.1155
2020-10-27	1380.1	103	867.5	0.1187
2020-10-30	1382.7	106	870.1	0.1218
2020-12-31	?	168	/	/

(A) 80%

(B) 85%

(C) 90%

(D) 95%

解答

$$\cfrac{t-t_0}{S_t - S_0} = 0.001 × 168 + 0.0127 = 0.1807 \\~\\ S_t - S_0 = 168 / 0.1807 = 929.72 \\~\\ S_t = 929.72 + 512.6 = 1442.32 mm \\~\\ \cfrac{t-t_0}{S_t - S_0} = 0.001 × (t - t_0) = 0.0127 \Rarr \cfrac{1}{S_t - S_0} = 0.001 + \cfrac{0.0127}{t-t_0} \\~\\ t = \infin \Rarr \cfrac{1}{S_{\infin} - S_0} = 0.001 \Rarr S_{\infin} = 1000 + 512.6 = 1512.6mm \\~\\ U_t = 1442.3/ 1512.6 = 0.954$$

选D