CE 240 Soil Mechanics Foundations Lecture 11 1 Shear Strength of Soil I Das Ch 11 Class Outlines Shear strength in soils Introduction Definitions Mohr Coulomb criterion Introduction Lab tests for getting the shear strength Direct shear test Introduction Procedure calculation Critical void ratio Shear Strength The strength of a material is the greatest stress it can sustain So that the unit of strength is the same as stress Pa in SI unit system Significance of Shear Strength The safety of any geotechnical structure is dependent on the strength of the soil If the soil fails the structure founded on it can collapse Understanding shear strength is the basis to analyze soil stability problems like lateral pressure on earth retaining structures Chs 12 13 slope stability Ch 14 and bearing capacity Ch 15 Shear Failure in Soils Slope Failure in Soils Failure due to inadequate strength at shear interface Static Transcosna Grain Elevator Canada Oct 18 1913 West side of foundation sank 24 ft Bearing Capacity Failure Dynamic Foundation failure by liquefaction after the 1964 Niigata Earthquake USGS Dynamic Lateral Spreading caused by the 1906 San Francisco Earthquake at Moss Landing CA USGS Professional Paper 993 Shear Strength in Soils The shear strength of a soil is its resistance to shearing stresses It is a measure of the soil resistance to deformation by continuous displacement of its individual soil particles Shear strength in soils depends primarily on interactions between particles Shear failure occurs when the stresses between the particles are such that they slide or roll past each other Shear Strength in Soils cont Soil derives its shear strength from two sources Cohesion between particles stress independent component Cementation between sand grains Electrostatic attraction between clay particles Frictional resistance between particles stress dependent component Shear Strength of Soils Cohesion Cohesion C is a measure of the forces that cement particles of soils Dry sand with no cementation Dry sand with some cementation Soft clay Stiff clay Shear Strength of Soils Internal Friction Internal Friction angle is the measure of the shear strength of soils due to friction Mohr Coulomb Failure Criteria This theory states that a material fails because of a critical combination of normal stress and shear stress and not from their either maximum normal or shear stress alone Mohr Coulomb Failure Criterion Shear Strength S C Normal Stress n h f c n tan c n f c n tan c n 11 2 11 3 where f shear strength c cohesion c effective cohesion angle of internal friction effective angle of internal friction coefficient of friction effective coefficient of friction tan 0 51 0 58 0 58 0 70 0 70 0 78 0 58 0 70 0 70 0 84 0 84 1 00 0 67 1 11 0 49 0 70 Mohr Coulomb shear failure criterion 1 3 n 3 Failed Zone f 1 f c n c 3 ff 2 1 From trigonometric equalities we have Way 1 Increase the normal stress in one direction 1 3 n f major principle stress 3 Minor principle stress Confining stress 1 Way 2 directly apply the shear stress Consider the following situation A normal stress is applied vertically and held constant A shear stress is then applied until failure Normal stress n Shear stress Normal stress n Determination of Shear Strength Parameters The shear strength parameters of a soil are determined in the lab primarily with two types of tests 1 Direct Shear Test and 2 Triaxial Shear Test 1 2 Normal stress n 1 Shear stress 3 Soil 3 Direct Shear Test Direct shear test is Quick and Inexpensive Shortcoming is that it fails the soil on a designated plane which may not be the weakest one Used to determine the shear strength of both cohesive as well as non cohesive soils ASTM D 3080 Direct Shear Test cont The test equipment consists of a metal box in which the soil specimen is placed The box is split horizontally into two halves Shear stress Vertical force normal stress is applied through a metal platen Shear force is applied by moving one half of the box relative to the other to cause failure in the soil specimen Normal stress n 3 Soil Direct Shear Test Direct Shear Test Direct Shear Test Shear stress Direct Shear Test Data Peak Strength Residual Strength Direct Shear Test Data Volume change H Direct Shear Test Procedure 1 Measure inner side or diameter of shear box and find the area 2 Make sure top and bottom halves of shear box are in contact and fixed together 3 Weigh out 150 g of sand 4 Place the soil in three layers in the mold using the funnel Compact the soil with 20 blows per layer 5 Place cover on top of sand 6 Place shear box in machine 7 Apply normal force The weights to use for the three runs are 2 kg 4 kg and 6 kg if the load is applied through a lever arm or 10 kg 20 kg and 30 kg if the load is applied directly Note Lever arm loading ratio 1 10 2kg weight 20 kg Direct Shear Test Procedure 8 Start the motor with selected speed 0 1 in min so that the rate of shearing is at a selected constant rate 9 Take the horizontal displacement gauge vertical displacement gage and shear load gage readings Record the readings on the data sheet 10 Continue taking readings until the horizontal shear load peaks and then falls or the horizontal displacement reaches 15 of the diameter Calculations 1 Determine the dry unit weight d 2 Calculate the void ratio e 3 Calculate the normal stress shear stress e Gs w N A d 1 V A Figures Peak Stress Shear stress s s3 s2 s1 N3 30 kg N2 20 kg N1 10 kg Horizontal displacement H Shear Stress s psf Figures cont 2 s2 3 s3 1 s1 C Normal Stress psf Vertical displacement Figures cont Horizontal displacement Reading Assignment Das Ch 11 HW Problem 11 1