1 Civil & Environmental Engineering Department

Measurement of Shear Strength of Soil with Unconfined Compression Test Shear Strength of Soil ™ Shear strength of soil is the internal resistance of soil to shearing forces. ™ Determination of the shear strength of soil is one of the most important aspects of geotechnical engineering. Ultimate shear strength and the deformation behavior of soil under an applied load are critical for design of foundations, earth structures, retaining structures, and many others. Shear strength is fundamentally due to the combination of friction between particles and the work required to cause the sample to change in volume, or: 1) Inter-granular friction, μ, and 2) Dilation, or volume change, ν. Naturally, any factor which influences friction or volume change will influence the strength of a specimen. The most influential factors (state parameters) that affect volume change include void ratio and confining stress (σ3’). Grain shape and roughness are two factors that influence friction. ™ Shear strength at failure is normally defined by Mohr-Coulomb Failure criteria. Mohr-Coulomb Failure criteria ™ Material fails with the combined effect of normal stress (σn’) and shear stress (τ). According to Mohr, τf = f (σ)

Figure 1 Mohr-Column Failure Envelope In most of the soil mechanics problems, failure envelope is considered as a straight line, given by the equation,

τ failure = c + σ n tan φ

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

2 Civil & Environmental Engineering Department Where,

c is the cohesion φ is the angle of friction. σn is the normal stress on the failure plane at failure. This equation is called Mohr-Coulomb Failure Criteria.

The strength parameters c’ and φ’ are determined from the slope and intercept on a Mohr diagram of a best-fit line tangent to a series of Mohr circles at failure. The influence of inter-granular friction, dilation, and true cohesion are assumed to be represented by these two parameters.

In saturated soil,

σ = σ’ + u

and

τ failure = c'+σ n ' tan φ ' Where,

c’ is the effective stress value of cohesion (very small) φ’ is the effective stress (or drained) angle of friction. σ’n is the normal stress on the failure plane at failure. Table 1 Typical values of drained angle of internal friction angles for sands and silts

™ For sand and gravel, c’ = 0 (they are called cohesionless soil) ™ For normally consolidated and remolded clays, c’ = 0

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

3 Civil & Environmental Engineering Department ™ For over consolidated clays, c’ = f (OCR) ¾

Below the shear envelope

- failure does not occur

¾

At and above shear envelope

- failure occurs

Inclination of Plane of Failure

Figure 2 Stress systems in a soil mass Here,

σ1’ = Major principal stress σ3’ = Minor principal stress

We can draw Mohr circle for the stress condition shown above as shown in the figure 3.

Figure 3 : Failure envelope developed from the Mohr Circle

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

4 Civil & Environmental Engineering Department Let’s extend failure envelope to touch the x-axis at f. Then, at a plane inclined at an angle of θ from major principal axis, φ’ + 900 = 2θ Therefore,

θ = 45 0 +

φ 2

From figure,

σ 1 ' = σ 3 ' tan 2 (45 0 +

φ' 2

) + 2c' tan(45 0 +

φ' 2

)

Here, c’ and φ’ are the effective shear strength parameters. ™ For earth structures and soil-structure interaction (foundations) the Factor of Safety against failure is given by:

⎛ Strength of soil ⎞ FS = ⎜ ⎟ ⎝ Shear stress to soil ⎠ Determination of Shear Strength Shear strength of soil can be measured in laboratory or in-situ. Laboratory Measurement There are different methods to measure shear strength of soil in laboratory.

a. Direct Shear Test b. Triaxial Shear Test c. Unconfined Compression Test d. Simple Shear Test e. Ring shear device

Figure 4 : Sketch of an unconfined compression test device

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

5 Civil & Environmental Engineering Department

Unconfined Compression Test Application

Unconfined compression test gives shear strength of soil. Shear strength is important in all types of geotechnical designs and analyses. Equipment Strain controlled unconfined compression test device Scale Balance sensitive to 0.1 g Moisture cans Oven Procedure 1. Get three trimmed soil specimens provided to you. 2. Measure the dimensions of the specimen (diameter and length). 3. Measure the weight of the specimen. 4. Load the samples into the unconfined compression device. They should be placed in between two platens. 5. Lower the upper platen slowly (or raise the lower platen depending upon the machine), just to make contact with the top of the soil specimen. 6. Set the vertical displacement dial gauge and loading proving ring dial gauge to zero. 7. Lower the upper platen (or raise the lower platen) at the speed of 0.5%/min. 8. Record the load and displacement dial gauge readings at every 5 or 10 seconds depending on the type of the soil. Usually the readings are taken at every 0.01 inch of displacement. 9. The compression load goes on increasing, peaks, and then decreases. 10. After it starts to decrease, stop the test. 11. Reverse the platen movement, and remove the specimen. 12. Draw a free hand sketch of the specimen after failure. 13. Determine the moisture content of the specimen. 14. Repeat this procedure for two more specimens. Calculations 1.

Calculate axial strain.

ε=

ΔL L

ΔL = Vertical deformation of the specimen. 2. Calculate vertical load on the specimen. Vertical load = Load cell reading x 1 Lb 3. Calculate the corrected area of the specimen (Ac) Ac =

A0 1− ε

A0 = Initial cross-sectional area i.e. π x D2/4 4. Calculate the stress σ on the specimen.

σ=

Load Ac

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

6 Civil & Environmental Engineering Department 5. Plot σ versus axial strain. Peak σ is qu. Then calculate su.

su =

qu 2

Figure 5 Stress-strain curve and Mohr circle generated from UC Test

Table 2 Relationship between consistency and UC strength

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

7 Civil & Environmental Engineering Department Soil Mechanics Laboratory

Unconfined Compression Test Laboratory Data Sheet I. GENERAL INFORMATION Tested by: Lab partners/organization: Client: USUF Boring no.: NA Recovery date: NA Soil description:

Date tested: Project: 324L Recovery depth: NA Recovery method: NA

II. TEST DETAILS Initial specimen area, Ao: Initial specimen diameter, Do: Initial specimen length, Lo: Initial specimen volume, Vo: Moist mass of specimen, M: Dry mass of specimen, Ms: Moisture content, w: Total unit weight, γ: Dry unit weight, γd: Specimen preparation method: Hand Compaction Deformation indicator type: Dial gauge Axial strain rate, Δε1/Δt: Deformation dial gauge conversion factor, KL: x10-3 in Force measurement instrument type: Load cell Proving ring dial gauge conversion factor, KP: 1 lb III. MEASUREMENTS AND CALCULATIONS Load Axial Axial Deformation Reading Deformation Load Reading (GP) (P) (GL) (ΔL)

Axial Strain (ε1)

Corrected Area (A)

Axial Stress (σ)

EQUATIONS:

ε1 = ΔL/Lo A = Ao/(1-ε1)

σ1 = P/A ΔL = GLKL P = GPKP su = qu/2

Unconfined compressive strength, qu: Undrained shear strength, su:

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

8 Civil & Environmental Engineering Department Soil Mechanics Laboratory

Unconfined Compression Test Laboratory Data Sheet I. GENERAL INFORMATION Tested by: Lab partners/organization: Client: USUF Boring no.: NA Recovery date: NA Soil description:

Date tested: Project: 324L Recovery depth: NA Recovery method: NA

II. TEST DETAILS Initial specimen area, Ao: Initial specimen diameter, Do: Initial specimen length, Lo: Initial specimen volume, Vo: Moist mass of specimen, M: Dry mass of specimen, Ms: Moisture content, w: Total unit weight, γ: Dry unit weight, γd: Specimen preparation method: Hand Compaction Deformation indicator type: Dial gauge Axial strain rate, Δε1/Δt: Deformation dial gauge conversion factor, KL: x10-3 in Force measurement instrument type: Load cell Proving ring dial gauge conversion factor, KP: 1 lb III. MEASUREMENTS AND CALCULATIONS Load Axial Axial Deformation Reading Deformation Load Reading (GP) (P) (GL) (ΔL)

Axial Strain (ε1)

Corrected Area (A)

Axial Stress (σ)

EQUATIONS:

ε1 = ΔL/Lo A = Ao/(1-ε1)

σ1 = P/A ΔL = GLKL P = GPKP su = qu/2

Unconfined compressive strength, qu: Undrained shear strength, su:

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008

9 Civil & Environmental Engineering Department Soil Mechanics Laboratory

Unconfined Compression Test Laboratory Data Sheet I. GENERAL INFORMATION Tested by: Lab partners/organization: Client: USUF Boring no.: NA Recovery date: NA Soil description:

Date tested: Project: 324L Recovery depth: NA Recovery method: NA

II. TEST DETAILS Initial specimen area, Ao: Initial specimen diameter, Do: Initial specimen length, Lo: Initial specimen volume, Vo: Moist mass of specimen, M: Dry mass of specimen, Ms: Moisture content, w: Total unit weight, γ: Dry unit weight, γd: Specimen preparation method: Hand Compaction Deformation indicator type: Dial gauge Axial strain rate, Δε1/Δt: Deformation dial gauge conversion factor, KL: x10-3 in Force measurement instrument type: Load cell Proving ring dial gauge conversion factor, KP: 1 lb III. MEASUREMENTS AND CALCULATIONS Load Axial Axial Deformation Reading Deformation Load Reading (GP) (P) (GL) (ΔL)

Axial Strain (ε1)

Corrected Area (A)

Axial Stress (σ)

EQUATIONS:

ε1 = ΔL/Lo A = Ao/(1-ε1)

σ1 = P/A ΔL = GLKL P = GPKP su = qu/2

Unconfined compressive strength, qu: Undrained shear strength, su:

EGCE 324L (Soil Mechanics Laboratory) Instructor: Binod Tiwari, PhD

Spring 2008 Date: 4/21/2008