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. meters 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 independent from confi

Unconfi pressure isequaltozero, shearstrength ( φ c σ where: criteria ofMohr-Coulomb failure isshown below: between normalstress andshearstress. Th linearcorrelation Mohr-Coulomb equationgives a AAnalysis ofdifferentequationsundrainedshearstrengthestimationsusingAtterbergLimitsonPontianak SoftClay Table 3.DatafromsoilinvestigationofexpandrunwayprojectatSupadioAirport. ( correlated toAtterberg limits.Results forthisratio overburden stress by manyresearchers have been Th Undrained ShearStrengthandAtterbergLimits where: s n e ratioofundrainedshearstrength ofclayto u / a σ s s l y i s ) are oftendefi i s q σ

s ned compressive strength testinwhichconfi — cohesion (kPa); o shearstress (kPa); — u internalfrictionangle( — 1 normalstress (kPa); — — unconfi f — vertical stress vertical (kPa); —

d i f f e r e n t

e = q ned by inthefollowing equations. = u σ ned compressive strength (kPa). a 1 t /2 = ning pressure ( c i o + n s σ

o q tan f u

2=c (2) /2 =c u n d (1) φ r a i n e o d ). σ

3 s ), sothat: h e a r is lineas

s t r e n g ning ning s t ) is h

e s t i m a for thisratiovalue to thevalue ofplasticityindex. more relationship than5%,Skempton [8]gives a linear plasticityindexof Normally consolidatedclaywitha where: W equation between thisratiotoliquidindex,I In andSimons addition,Bjerrum [2]alsopresent another I index. correlation between undrainedshearstrength toplasticity equationfor andSimonsBjerrum [2]present a power I limit. forundrainedshearstrength andliquid for correlation linearequation Karlsson and Viberg [5]present a = (W t C i o = (W n

s s s s

u n s — W i p L n plasticityindex(%); — — W g L — liquidlimit(%); —

A t t e p r s n )/(W u b )/W / e σ r u g i =0.11+0.0037I u /

u / σ L L L / σ i — W σ i m =0.18/I — W i =0.005 W i i =0.045Ip t s

o p n )

p P ) andconsistencyindex, o n t L i

a . 0.5 L n (6) 0.5 a k (4) p

(3) S o f t

C l a y L which I (5) L

47 Town and Urban Planning Architecture and Building Engineering SSlametlamet Widodo,Widodo, AAbdelazimbdelazim Ibrahim,Ibrahim, 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 Table 5.Ratio undrainedshearstrengthtooverburdenstress. AAnalysis ofdifferentequationsundrainedshearstrengthestimationsusingAtterbergLimitsonPontianak SoftClay Table 6.Correctedconstantforequation. analysis. When we lookintothedetermination testandequationsare resulted from regression tory respectively. variable ( lowequations are very correlation between dependent function. Coeffi through 1(d)show trend lineoflinear andpower previous methodgives diff for Equations usingregression analysis asa comparison n Bjerrum-Simons** Karlsson-Viberg Bjerrum-Simons Skempton a Table 6givessomeequationsfrom new labora- l y eerhr xsigeutosEutosfo aoaoyts Equations from regression analysis test Equations from laboratory Existing equations Researchers s i s

o f

s d / σ i f f i e ) andindependentvariables ofI r e cient ofdetermination(R n t

e q u s s s s / / / /σ a σ σ σ t i i i i i =0.045I =0.180/I =0.005 W =0.11+0.0037I o n s erent equation.Figure 1(a)

o f

u n p d

0.5 L L r

a 0.5 i n e d p

s h e a 2 r ) forfour

s t r p e s s s s ,W / / / / n σ σ σ σ g i i i i =0.118/I =0.004 W =0.0422I =0.11+0.0037I t L h , I

e s c

t i m a ( pressure orundrainedunconfi Firstly, undrainedshearstrength withouttheconfi Th Conclusions (R factor suffi level. t q i ere are twomainconclusions from analyzing thedata. p L o L u

0.5 ) forPontianak softsoilisaround almosttwiceof signifi certain cient datainother toachieve a n 0.5 s

u s i p n g 2 ), we mustcollectmore samplestofulfi

A t t e r b e r g

L s s s s i / / / / m σ σ σ σ i i i i i =0.12144/I =0.331-0.0026247 W =0.38124/I =0.37674-0.00856I t s

o n

P ned compressive strength o n t i a n a p L

k 0.30086 0.425287

S o f t

C p l a L y cant ned ll

49 Town and Urban Planning Architecture and Building Engineering SSlametlamet Widodo,Widodo, AAbdelazimbdelazim Ibrahim,Ibrahim, ShenShen HongHong

(a) (b)

(c) (d) σ σ σ σ Fig. 1. Correlation using regression analysis, a) s/ i vs. Ip, b) s/ i vs. Ip, c) s/ i vs. WL, d) s/ i vs. IL.

its cohesion value. It is familiar correlation between Proceedings. Research Conference on Shear Strength of the unconfi ned compressive strength and cohesion. Cohesive Soils, ASCE, 1960: 1771–1726. Th is value coincides with 50-percentile of data [3] Das, B.M. Principles of Geotechnical Engineering. Univer- distribution. Secondly, Skempton’s equation shows sity of Texas at El Paso, USA, 1985. the close correlation with this subsoil. Furthermore, [4] Dawson A., P. Kolisoja, and N. Vuorimies. Understanding Low-Volume Pavement Response to Heavy Traffi c Loading. when we want to estimate using regression analysis, RoadexIII Northern Periphery, 2008. large number of soil sample is needed to obtain [5] Karlsson, R. and L. Viberg. “Ratio c/p’ in relation to a certain signifi cant level and then for diff erent site of liquid limit and plasticity index with special reference subsoil can be done with the same procedure as described to Swedish clays”. Proc. Geotechnical Conf., Oslo, in this paper. Norway, 1 (1967): 43–47. [6] Design of Soft Soil Stabilization with Tenax Geogrids. Technical References Reference GRID-DE-3, Tenax Corporation, 2001. [7] Pusat Litbang. Panduan Geoteknik-4, Desain dan [1] Ang, H.S., and W.H. Tang. Probability Concepts in Konstruksi, Puslitbang Prasarana Transportasi, WSP Engineering Planning and Design. Vol. I: Basic Principles. International, 2001. New York: John Wiley & Sons, 1975. [8] Skempton, A.W. “Th e Planning and Design of New [2] Bjerrum, L., and N.E. Simons. “Comparison of Shear Hongkong Airport”. Proceeding. London: Institute of Strength Characteristics of Normally Consolidated Clay”. Civil Engineering 7 (1957): 305–307.