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Analysis of Different Equations of Undrained Shear Strength Estimations Using Atterberg Limits on Pontianak Soft Clay

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Analysis of Different Equations of Undrained Shear Strength Estimations Using Atterberg Limits on Pontianak Soft Clay Analysis of different equations of undrained shear strength estimations using Atterberg Limits on Pontianak Soft Clay Slamet Widodo, Abdelazim Ibrahim, Shen Hong Technische Universität Bergakademie Freiberg Gustav Zeuner Strasse 1, 09599 Freiberg, Sachsen, Germany; e-mail: [email protected] or [email protected] Many researchers have done study to estimate the value of undrained shear strength for fi ne grained soils like clay or silt. Determining of undrained shear strength and compressibility parameters in laboratory are really tedious and time consuming. Th erefore, a correlation between undrained shear strength and Atterberg limits is useful for restraint of testing number and costs. Central tendency parameters such as an average, deviation standard and coeffi cient of variation are performed to analyze the data of soft clay in Pontianak, Indonesia. Based on analysis that undrained shear strength coincides with 50 percentile of distribution data meanwhile undrained compressive strength is around twice of cohesion for testing using unconfi ned pressure. Th is relationship is the most familiar equation. Moreover, undrained shear strength using mean value is more realistic for correlation between undrained shear strength and Atterberg limits on some equations from previous fi ndings. Keywords and phrases: undrained shear strength, Atterberg limit, cohesion, soft clay. Introduction compressive strength (qu), have been proposed by some previous research results and used as subgrade failure Undrained shear strength is a very important parameter criteria for pavement design as depicted in Table 1. in engineering. Undrained shear strength is a parameter to the bearing capacity of soil that could bear on it. Some Table 1. Undrained unconfined compressive strength. laboratory tests needed to obtain these values are expensive and time consuming, while soil properties like Researchers and/or Sources Equation Giroud and Noiray (1981) q = 3.14 c moisture content and Atterberg limits can be performed u u Barenberg (1992) q = 3 c faster and cheaper. u u Philips (1987 ) qu = 2.8 cu Rodin (1965) qu = 3.14 cu Literature Review Roadex III (2008 ) qu = 4 cu Bearing capacity for subsoil can be stated in some parameters. Several sources come from research in which Soil consistency can be estimated using value of correlations of the parameters were proposed. Atterberg unconfi ned compressive strength (Terzhagi &Peck, limits can be employed to get bearing capacity of subsoil. 1967) as shown in Table 2. By using regression analysis and central tendency para- Table 2. Soil consistency. me ters in statistical analysis we can obtain a correlation. Consistency qu (kPa) Bearing Capacity of Subsoil Very soft < 24 Th ere are some approaches to know bearing capacity of Soft 24 – < 48 subsoil. Undrained shear strength shows capability or Medium 48 – < 96 bearing capacity of soil. Relations between undrained Stiff 96 – < 192 Very stiff 192 – < 383 shear strength of soil (su) and undrained cohesion (cu) in the case without confi ning pressure called unconfi ned Firm > 383 46 AAnalysisnalysis ooff ddifferentifferent equationsequations ofof undrainedundrained shearshear strengthstrength estimationsestimations usingusing AtterbergAtterberg LimitsLimits onon PontianakPontianak SoftSoft ClayClay Mohr-Coulomb equation gives a linear correlation Normally consolidated clay with a plasticity index of between normal stress and shear stress. Th is line as more than 5%, Skempton [8] gives a linear relationship criteria of Mohr-Coulomb failure is shown below: for this ratio value to the value of plasticity index. s = c + σ tan φ (1) σ su/ i = 0.11 + 0.0037 Ip (3) where: s — shear stress (kPa); Bjerrum and Simons [2] present a power equation for σ — normal stress (kPa); correlation between undrained shear strength to plasticity c — cohesion (kPa); index. φ o — internal friction angle ( ). σ 0.5 su/ i = 0.045 Ip (4) Unconfi ned compressive strength test in which confi ning In addition, Bjerrum and Simons [2] also present another pressure is equal to zero, shear shear strength (s) is equation between this ratio to liquid index, IL which IL σ independent from confi ning pressure ( 3), so that: = (Wn — Wp)/(WL — Wp) and consistency index, σ IC = (WL — Wn)/WL — Wp) s = 1/2 = qu/2 = c (2) s/σ = 0.18 / I 0.5 (5) where: σ1 — vertical stress (kPa); u i L qu — unconfi ned compressive strength (kPa). Karlsson and Viberg [5] present a linear equation for correlation for undrained shear strength and liquid Undrained Shear Strength and Atterberg Limits limit. Th e ratio of undrained shear strength of clay to s/σ = 0.005 W (6) overburden stress by many researchers have been u i L correlated to Atterberg limits. Results for this ratio where: WL — liquid limit (%); σ (su/ i) are often defi ned by in the following equations. Ip — plasticity index (%); Table 3. Data from soil investigation of expand runway project at Supadio Airport. Town and Urban Planning Architecture Building Engineering Town 47 SSlametlamet Widodo,Widodo, AAbdelazimbdelazim IIbrahim,brahim, ShenShen HongHong su — undrained shear strength (kPa); ratio of 2.05 and this value is very close with previous σ i — overburden shear (kPa). arithmetic average value of 2.08. It is moderate value. Nevertheless, for pavements design purpose in the case Central Tendency Parameters of bearing capacity of subsoil, it is usual for representative Parameters of central tendency consist of the average value of a segment road to be taken 75 percentile as value, coeffi cient of variation and standard deviation [1]. design value should be even 90 percentile. Th ese parameters are relatively very familiar in calcu- lating and analyzing of data and making conclusion Table 4. Dispersion for value of qu/c. afterwards. qu / c Dispersion 4.20 Σ Average: X = Xi / n (7) 3.37 Standard deviation for sample: 3.29 15 percentile σ = [Σ (Xi — X)2/(n — 1)]0.5 (8) 2.86 Coeffi cient of variation: Cov = σ/X (9) 2.32 25 percentile 2.32 Regression analysis also will be performed to give 2.27 comparison from analysis using central tendency 2.22 parameter as mentioned above. 2.14 2.05 50 percentile Data Collecting 2.02 1.92 Main data for calculation and analysis came from soil 1.70 investigation of the expand runway project of Supadio 1.65 airport in Pontianak, Indonesia. Th ere are 10 boreholes 1.58 75 percentile along at left and right of existing runway having 2.250 m 1.40 length and 30 m width. It will be extended 2.550 m 1.37 85 percentile length and 45 m width. Data of soil investigation for the 1.26 90 percentile project is shown in Table 3. 0.87 0.80 Discussion for Analysis Results Data shown in Table 3 above will be analyzed more Undrained Shear Strength detail in the next paragraph. Herein bearing capacity of Ratio between undrained shear strength and overburden subsoil namely unconfi ned compressive strength and stress can be correlated with Atterberg limits as described undrained shear strength are important parameters. on the equation 3 through equation 6. In the presented four equations linear correlation and power function are Bearing Capacity of Subsoil used. Bearing capacity of subsoil can be expressed by using Table 5 shows that average value of ratio for undrained shear strength. Value of undrained shear 50-percentile is equal to 0.18 kPa. Th is value agrees with strength without confi ning pressure is equal to Skempton’s equation with value of 0.182 kPa and little unconfined compressive strength. This value is diff erent with Bjerrum-Simons’ fi rst equation round of theoretically twice as big as cohesion. Th e rightmost 0.192 kPa. Th ese values are diff erent from Karlsson- column of Table 3 shows that the ratio unconfi ned -Viberg’s equation and Bjerrum-Simons’ second equation compressive strength to cohesion taken from laboratory round of 0.228 kPa and 0.274 kPa respectively. Bjerrum- testing vary from 0.8 to 4.2 and arithmetic average is -Simons’ second equation gives higher result than the σ 2.08 while average of cohesion is 11.44 kPa. Based on others [2, 5, 8]. Meanwhile value of s/ i when using the data above we obtain the arithmetic average value of Mohr-Coulomb’s equation gives 0.186 kPa. In this unconfi ned compressive strength as bearing capacity of calculation, shear strength is used vertical stress this subsoil to be 23.8 kPa which it is 2.08 times as much (overburden stress) as normal stress because internal as cohesion. For value of unconfi ned compressive friction angle is very small. strength around 23,8 kPa can be classifi ed as very soft From the fi ndings as shown in Table 5, it can be seen σ soil and almost soft soil. Standard deviation for this value that the ratio s/ i coming from Skempton’s equation is is 0.85 kPa and coeffi cient of variation is 40.86 percent. the best fi t with 50 percentile of laboratory test. By using By using descending dispersion of data for ratio of Mohr-Coulomb’s equation a good enough estimation can qu/c and taking 50 percentile (mean value) we obtain the be also made, but results from other equations are poorer. 48 AAnalysisnalysis ooff ddifferentifferent equationsequations ofof undrainedundrained shearshear strengthstrength estimationsestimations usingusing AtterbergAtterberg LimitsLimits onon PontianakPontianak SoftSoft ClayClay Table 5. Ratio undrained shear strength to overburden stress. Table 6. Corrected constant for equation. Researchers Existing equations Equations from laboratory test Equations from regression analysis σ σ σ Skempton s/ i = 0.11 + 0.0037 Ip s/ i = 0.11 + 0.0037 Ip s/ i = 0.37674 - 0.00856 Ip /σ 0.5 σ 0.5 σ 0.30086 Bjerrum-Simons s i = 0.045 Ip s/ i = 0.0422 Ip s/ i = 0.38124 / Ip σ σ σ Karlsson-Viberg s/ i = 0.005 WL s/ i = 0.004 WL s/ i = 0.331 - 0.0026247 WL σ 0.5 σ 0.5 σ 0.425287 Bjerrum-Simons** s/ i = 0.180 / IL s/ i = 0.118 / IL s/ i = 0.12144 / IL Equations using regression analysis as a comparison for factor (R2), we must collect more samples to fulfi ll previous method gives diff erent equation.
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