Question

Problem No. 4: Using the reported undrained shear strengths at liquid limit and plastic limit, derive a relationship between the compression index Cc and plasticity index Pl. Assume that the ratio of undrained shear strength to vertical effective stress, is 0.3. Compare the result with the data presented in Fig. 1 ..63. 5.0.00 Cur P1/385 (n-117. r2 0.448. s.D. o.os11 1.4 Ce Cur O Mayne, 1980 1.2O Nakase, et ol., 1988 Been, et ol., 1987 A AWesley, I988 o oF 1.0 ▼ ▽ Lombe a whitman,1969 Ce 4Olsen, et al., 1986 NA Imai, et at., 1984 ● NA Morin a Dawe, 1987 (Refs. 4-11) C 0.8 0.6 Modified com cloy 0.4 PI Cur 370 o2 o 20 30 40 50 60 70 80 90 0o Plasticity Index, PI (%) Figure 1 Compression and unload-reload indices as a function of plasticity index (from Kulhawy and Mayne, 1990). Reprinted with permission from EPRI.

Answer 1

$Regression:~C_c=PI/73\\ r^2=0.663~means~66.3\%~of~total~variation~in~index~C_c~is~explained\\ by~plasticity~index~through~this~regression~line.\\ S.D.=0.160~means~average~distance~that~data~points\\fall~from~the~regression~line.\\ Regression:~C_{ur}=PI/385\\ r^2=0.448~means~44.8\%~of~total~variation~in~idex~C_{ur}~is~explained~by~plasticity~index\\ through~this~regression~line.\\ So~first~regression~line~is~better~since~it ~explains~more~variation~in\\ the~response.\\$

$However~the~SD~of~2nd~regression~equation=0.051~is~much~less~than\\ the~SD~of~first~regression~equation=0.160~and~this~means~the~absolute~distance~of~the\\ observations~from~2nd~regression~line~is~less~than~the~absolute~distance~of~the~ observations~from~the~first~regression~line.\\$$However~the~SD~of~2nd~regression~equation=0.051~is~much~less~than\\ the~SD~of~first~regression~equation=0.160~and~this~means~the~average~distance~of~the\\ observations~from~2nd~regression~line~is~less~than~the~average~distance~of~the~ observations~from~the~first~regression~line.\\$

$We~generally~prefer~SD~than~r^2.~SD~gives~precision~and~it~has~a~same~unit\\ as~response~whereas~r^2~is~unit less~and~r^2~does~not~give~intuitive~feel~for~how~close~the~predicted\\ values~are~to~the~observed~values. ~So~2nd~regression~line~is~better~than~first~regression~line~since\\ 2nd~regression~line~has~more~precision~than~first~regression~line.$