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Home , Shear strength (soil)

Vilnius Gediminas Technical University Department of

RESEARCH OF SHEAR STRENGTH IN TRIAXIAL TESTS AND PROBABILISTIC ASSESSMENT OF RESULTS

Neringa Dirgeliene

University of Pisa, April 2008

1 •• Aim of the work – to improve the triaxial compression test of soil for determination soil strength parameters as precisely as possible and using them to forecast the soil bearing resistance more reliable.

2 1.1. LITERATURELITERATURE ANALYSISANALYSIS

• Literature analysis of experiments and numerical modeling shows that: ü triaxial test is the most reliable method to model -strain state of ground than ; ü stress-strain distribution are not uniform in both triaxial and direct shear tests specimens; ü sandy soil strength parameters obtained from triaxial test are bigger than the ones’s obtained from the direct shear test. • The main reasons of non-uniform stress distribution mentioned in the literature are: ü not only normal stress on soil sample surface acts, as usual is assumed, also tangential stress acts; ü influence of sample height/diameter ratio; ü insufficient drainage; membrane effects, etc. Tasks of the work is to analyse what influence does a non-uniformity have on the soil strength parameters and find ways to reduce or evualate it.

3 • Review of literature suggests that in order to get a more uniform stress-strain distribution in soil sample during triaxial test, it is necessary to reduce the sample height/diameter (H/D) ratio from 2 to 1 and to eliminate between the sample ends and the plates. • In the normative documents there is no common calculation method for characteristic, design values of soil shear strength parameters. • Partial factors method, where design values are used, doesn‘t assure an equal reliability of foundations. • Soil shear strength parameters determined experimentally are random values therefore its need to evaluate probabilistically. • Not long ago Lithuania started to apply Eurocodes. There was possibility to use probabilistic methods to design construction. These methods should be applied without using partial factors.

4 2. EXPERIMENTAL ANALYSIS OF SOIL SHEAR STRENGTH PARAMETERS IN TRIAXIAL TEST

• Consolidated-drained triaxial tests on poorly-graded with fine (SP-SM) have been carried out. Dense and loose samples properties were: density r = 1,871 gr/cm3, of e = 0,51 and r = 1,610 gr/cm3, e = 0,74.

100 90 80 70 60 50 40 30 20

Percentage passing, % 10 0 0,01 0,1 1 10 , mm

Fig 2. curve of sand 5 DistributionDistribution ofof thethe horizontalhorizontal componentcomponent ofof stressstress inin horizontalhorizontal crosscross--sectionsection inin thethe casecase ofof soilsoil axisymmetricaxisymmetric testtest

tu s 3 s 3 Fig 3. Device to analyse the distribution of horizontal component of stress in soil sample: 1 – metal cylinder; 2 – rubber membrane; 3 – soil sample; 4 – steel strip; 5 – fixed metal plate.

6 • Axisymmetric circular tests findings of dense sand show that horizontal component of stress inside soil sample is distributed non-uniformly. 55–61 % higher horizontal component of stress was found in the sides of soil specimen cross-section and smaller was found in the centre of soil specimen.

75 A (beginning of 60 displacement) C (beginning of 45 displacement) B (beginning of kPa , u 30 displacement) t A (steel strip is pulled out) 15 C (steel strip is pulled out) 0 B (steel strip is 0 30 60 90 pulled out)

s 3, kPa

Fig 4. Sand shear strength

7 ExperimentalExperimental analysisanalysis ofof soilsoil samplesample heighheigh/diameter/diameter ratioratio influenceinfluence onon soilsoil shearshear strengthstrength parametersparameters inin standardstandard triaxialtriaxial testtest

Fig 8. Scheme of standard triaxial test apparatus: 1 – rod; 2 – cap; 3 – soil sample; 4 – latex membrane; 5 – pedestal; 6 – porous stone.

8 a) b)

1200 1200

1000 1000

800 800

, kPa 600 600 3 , kPa 3 -s 1 -s 1 s 400 400 s

200 200

0 0 0 3 6 9 12 15 0 3 6 9 12 15 e1, % e1, %

50s k= Pa 50 kPa 100s = kPa 100 kPa 200s = kPa 200 kPa 3 3 3 50s 3kPa= 50 kPa 100s 3= kPa 100 kPa 200s 3= kPa 200 kPa

Fig 9. Stress-strain obtained in triaxial compression test on dense sand, when height/diameter ratio: a) H/D = 2; b) H/D = 1

9 ExperimentalExperimental analysisanalysis ofof influenceinfluence ofof freefree horizontalhorizontal movementmovement ofof samplesample basebase onon soilsoil shearshear strengthstrength parametersparameters duringduring triaxialtriaxial testingtesting

Fig. 10. Scheme of improved triaxial test apparatus: 1 – rod; 2 – cap; 3 – soil sample; 4 – latex membrane; 5 – pedestal; 6 – porous stone; 7 – thrust bearing; 8 – stainless steel plates

10 a) b)

1200 1200 1000 1000

800 800 , kPa , kPa

600 3 600 3 -s -s 1 1 400 s s 400

200 200 0 0 0 3 6 9 12 15 0 3 6 9 12 15 e1, % e1, %

50s 3 =50kPa kPa s1003=100kPa kPa s2003=200 kPa kPa 50s 3 =50kPa kPa 100s 3=100 kPa kPa s2003=200 kPa kPa

Fig 11. Stress-strain curves obtained in triaxial compression test on dense sand samples when height/diameter ratio: a) H/D = 2; b) H/D = 1

11 • Comparison of test results obtained in triaxial apparatus for dense sand sample, which H/D = 2, with free horizontal movement of base and for sample with regular ends (standard triaxial compression testing) shows that shape of graphs e1 = f(s 1 – s 3) are different.

600

500

400

300 , kPa 3 -s

1 200 s 100

0 0 3 6 9 12 15

e1, %

H/D = 2, regular ends H/D = 2,free horizontal movement of base H/D = 1, regular ends H/D = 1, free horizontal movement of base

Fig 12. Stress-strain curves obtained in triaxial compression tests on dense sand samples, when s3 = 100 kPa 12 Fig 13. Dense sand sample, which H/D = 2, in Fig 14. Dense sand sample, which H/D = 2, in standard triaxial test apparatus improved triaxial test apparatus

13 3.3. NUMERICALNUMERICAL MODELINGMODELING OFOF STRESSSTRESS--STRAINSTRAIN DISTRIBUTIONDISTRIBUTION ININ SOILSOIL SAMPLESAMPLE DURINGDURING TRIAXIALTRIAXIAL TESTTEST

• Drucker-Prager model was used to simulate the behaviour of sand performing nonlinear analysis. The yield criterion can be defined as:

F = 3asm + s f - k = 0,

where a and k - material constants which are assumed unchanged during the analysis; sm - the mean stress; s f - the ; a and k are functions of two material parameters and obtained from experiments where f is the angle of internal friction and c is the material strength.

14 Values of soil shear strength parameters Parameters Parameters Soil shear strength parameters for for failure specimen plane 37,9 30,0 Angle of internal friction j, ° 26,0 17,0 Cohesion c, kPa

Fig 15. Finite elements of soil sample 15 a) b)

Fig 16. txy distribution in the samples: a) with regular ends;b) with free horizontal movement of base

16 a) b)

Fig 17. Horizontal soil displacements ux distribution in the samples: a) with regular ends;b) with free horizontal movement of base

17 • Analysis of stress–strain distribution in sample using finite element method shows that for sample with regular ends tangential stress in the contact plane sample-plate builds up. Such stress restricts displacement of sample ends in horizontal direction. In the case of free horizontal movement of sample base horizontal displacement of sample base occurs. • In this case vertical component of stress in the bottom of sample is up to 10 % smaller in comparison with vertical component of stress for sample with restricted ends.

18 4. ASSESSMENT OF RELIABILITY OF SOIL STRENGTH PARAMETERS AND SOIL BEARING RESISTANCE

• Design values of dense sand, which ratio H/D = 2, shear strength parameters were calculated by means of methods provided in Eurocode. Design values of the residual angle of internal friction obtained for sample with free horizontal movement of base are up to 10,8 % smaller than for sample with regular ends. Design values of the residual cohesion are lower in 43 %. a) b)

23,4 35 29,3 30,5 25 30 27,4 24,8 20 16,2 25 13,8 20 15 , ° d kPa

7,9 f 15 d, 10 c 10 5 5 0 0 regular ends free horizontal regular ends free horizontal movement of base movement of base peak value of cohesion residual value of cohesion peak angle of internal friction residual angle of internal friction

Fig 20. Design values calculated according to Eurocode 7: a) angle of internal friction; b) cohesion 19 AssessmentAssessment ofof soilsoil bearingbearing resistanceresistance reliabilityreliability byby solvingsolving optimizationoptimization problemproblem

• Design values of soil shear strength parameters determined using EN 1997 and SNiP are not the most probable. Method was proposed to calculate arguments design values of the design condition which would satisfy the design condition zd = 0 itself and the probability function of these values would be at maximum:

f (x1, x2 ,...xn ) ® max

zd = gi (x1d , x2d ,...xnd ) = 0,

where f(x1, x2,..., xn) –• the probability density function of limit state arguments; gi(x1d, x2d,...,xnd) – design condition.

20 (S) E/s E

P ß -aEß

aRß

R/s R

Fig 21. Izolines of the reliability index b: (S) – design condition g = Rd – Ed = 0; P – design point 21 ProbabilisticProbabilistic assessmentassessment ofof soilsoil bearingbearing resistanceresistance calculatedcalculated accordingaccording toto improvedimproved triaxialtriaxial apparatusapparatus resultsresults

• Spread width B calculated according to the parameters of residual shearing strength, determined by usual triaxial test apparatus is smaller by 23 % than that calculated according to the data obtained in the improved triaxial test apparatus.

1,99 2,00

1,75 1,53 1,50 1,20 1,25 1,25 1,00 B , m 0,75 0,50 0,25 0,00 regular ends free horizontal movement of sample base

according to peak shear strength according to residual shear strength

Fig 22. Values of foundation width B 22 • Reliability index of soil bearing resistance designed according to EN 1997 and arguments values Gd*, Qd*, tanjd*, cd*, Bd* at design point have been calculated using the FORM method. It was accepted that permanent action G, variable action Q, soil strength parameters tanj, c and foundation width B are random values whereas other arguments are known without deviations.

2,5 G 2,0 Q 1,5

m 1,0 tanj x/x 0,5 c 0,0 Xm Xk Xd Xd* B -0,5

Fig 23. Mean, characteristic, design values of soil bearing design condition arguments obtained for sample with free horizontal movement of sample base using residual shear strength parameters 23 • Reliability index of bearing resistance for sample with regular ends calculated by means of first order probabilistic methods for design approach 3 is ß=4,4 using residual soil shear strength parameters. For sample with free horizontal movement – ß = 4,8.

6,0 4,8 5,0 4,4 4,4 4,0 4,0

b 3,0

2,0

1,0

0,0 regular ends free horizontal movement of sample base

according to peak shear strength according to residual shear strength

Fig 24. Reliability index b values of soil bearing resistance

24 •• In order to determine which design condition argument makes the highest influence on the uncertainty of margin of resistance, the importance factor of argument should be calculated: Dz(A) a 2 = [ × s ]2 / s 2 , X i X i z i=1,2,…,n. DX i

0,7 0,614 •• The calculations made 0,6 demonstrate that the 0,5 biggest influence on the 0,4 0,348 xi uncertainty of margin of a 0,3 bearing resistance is made 0,2 by the tangent of the angle 0,1 of internal friction and 0,005 0,009 0,023 0 cohesion. G Q tanj c B

Fig 25. Influence of design condition arguments on the uncertainty of the margin of soil bearing resistance using test results of improved apparatus 25 5. GENERAL CONCLUSIONS

1. Axisymmetric circular tests findings of dense sand show that horizontal component of stress inside soil sample is distributed non-uniformly. 55–61 % higher horizontal component of stress was found in the sides of soil specimen cross-section and smaller was found in the centre of soil specimen. 2. It was suggested method for reducing restraint effects of sample ends on soil shear strength testing by improving triaxial test apparatus with free horizontal movement of sample base. Analysis of stress-strain distribution in sample using finite element method shows that for sample with regular ends tangential stress in the contact plane sample-plate builds up. It are not evualated for calculation of shear strength design parameters. 3. Comparison of test results obtained in triaxial apparatus for dense sand sample with free horizontal movement of base and for sample with regular ends (standard triaxial compression test) shows that shape of graphs are different.

26 4. Design values of dense sand, which ratio H/D = 2, shear strength parameters were calculated by means of methods provided in Eurocode. Design values of the residual angle of internal friction obtained for sample with free horizontal movement of base are up to 10,8 % smaller than for sample with regular ends. Design values of the residual cohesion are lower in 43 %. It explains proposition given in literature that sandy soil strength parameters obtained from triaxial test are higher than parameters, obtained from the direct shear test. 5. Spread foundation width was calculated using results obtained from standard triaxial test according the residual values of soil shear strength parameters are 23 % smaller than foundation width calculated using improved apparatus results. 6. Applying probabilistic methods it was determined that uncertainty of ground ultimate limit state design condition is the most significantly influenced by the angle of internal friction and cohesion. Therefore, soil strength parameters determination methods should be improved intending to correct soil ground calculation methods.

27 TThhaannkkss ffoorr yyoouurr aatttteennttiioonn!!

28 RESEARCH OF SOIL SHEAR STRENGTH IN TRIAXIAL TESTS AND PROBABILISTIC ASSESSMENT OF RESULTS

Neringa Dirgeliene

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