## Laboratory Experimental Tests

### Method : Shear Box Test (Casagrande Box)

Test Procedure

The sample is placed between two half-boxes:

- An upper half-box (C₁), which can slide horizontally,

- A lower fixed half-box (C₂).

The soil is placed between two porous stones, allowing for drainage. Alternatively, the porous stones can be replaced with solid plates, preventing drainage—at least in theory.

Shear box apparatus
Casagrande shear box diagram

The device includes a loading mechanism that applies a vertical load (P) through a piston.

The test involves pulling the upper half-box (C₁) horizontally to shear the soil along the failure plane. The horizontal force (F) is measured as a function of displacement (Δ[1]l) (see figure below). The test is performed at a controlled speed (V).

Key Parameters:

A = Cross-sectional area of the sample along plane π

σ = P/A = Normal stress applied to the sample

τ = F/A = Shear strength at failure

### Note :

If this test is repeated on multiple specimens of the same soil under different normal stresses , the intrinsic curve (failure envelope) of the soil can be determined by plotting the measured shear stresses (τ)[2] against normal stresses (σ)[3] on a Coulomb diagram (τ-σ plot) (as shown in the figure).

Stess-displacement curve
Determination of c and φ

### Definition :

The values of cohesion (c) and friction angle (φ) depend on the test conditions, including shear rate and drainage:

Shear Rate:

- Quick shear test (for undrained conditions): 0.6 mm/min (~15 minutes per test)

- Slow shear test (for drained conditions): 0.03 mm/min (~3 hours minimum per test)

Test Types:

1. UU Test (Unconsolidated Undrained)

   - Evaluates short-term soil behavior (immediate stability).

   - No consolidation or drainage allowed.

2. CU Test (Consolidated Undrained)

   - Measures the undrained cohesion (Cu) variation with preconsolidation stress.

   - Takes up to 4 days (relatively short).

3. CD Test (Consolidated Drained)

   - Represents long-term soil behavior (fully drained conditions).

   - Can take up to 2 weeks in some cases

### Advice :

Always match test conditions (drained/undrained) to field scenarios. For example, use UU tests for short-term stability in clayey slopes.

### Method : Triaxial Shear Tests

Around 1930, Casagrande developed a new compression test to overcome the limitations of the direct shear test. This led to the creation of the triaxial test, which is now widely used in geotechnical engineering.

Test Setup:

- The soil specimen is cylindrical, typically with a slenderness ratio (H/D) of 2.

- It is placed inside a pressure cell (triaxial cell) filled with a confining fluid.

- The specimen is enclosed in a flexible, impermeable membrane to prevent fluid penetration while allowing deformation.

- One or both ends (depending on the setup) are in contact with a porous stone to facilitate drainage.

Key Features:

- The test allows for controlled stress conditions (σ₁, σ₂ = σ₃).

- It can simulate various drainage conditions (UU, CU, CD).

- Provides more accurate and versatile results compared to the direct shear test.

Triaxial test apparatus
Triaxial test principle

There are many types of triaxial tests due to the possible combinations related to drainage and the type and sequence of stress applications. However, nearly all triaxial tests begin with a consolidation phase followed by a shearing phase.

Consolidation Phase:

The consolidation phase is designed to bring the sample to a desired stress state, often intended to match the stress conditions the sample would encounter in the field under project conditions. During the consolidation phase, the cell pressure is increased to a chosen confining pressure value. This pressure confines the sample hydrostatically and represents the minor principal stress (σ₃).

During this consolidation phase, drainage may or may not be allowed:

If drainage is not allowed, the term "unconsolidated" is used to describe the triaxial test, and the letter U is used in the acronym.

If drainage is allowed and the pore water pressure in the sample generated by the application of σ₃ can dissipate to zero, the term "consolidated" is used to describe the test, and the letter C is used in the acronym.

Shearing Phase:

During the shearing phase of the test, the vertical load (Q) on the sample is gradually increased, and the stress in the vertical direction rises. This stress is the major principal stress (σ₁):

σ 1 = σ 3 + F / A %sigma_1=%sigma_3+F/A

Where:

σ₃ = Confining pressure

F = Vertical load

A = Cross-sectional area of the sample

If drainage is not permitted during the shearing phase, the term "undrained" and the letter U are used.

If drainage is allowed and the excess water (pore pressure) is maintained at zero (very slow loading), the term "drained" and the letter D are used.

Thus, the following triaxial tests are possible:

UU Test: Unconsolidated Undrained test

CU Test: Consolidated Undrained test

CD Test: Consolidated Drained test

CD and CU tests with pore pressure measurements are used to obtain the effective shear strength parameters (c' and φ').

The result of a triaxial test (as shown below) is a stress-strain curve that typically relates the deviatoric stress (σ₁ - σ₃) to the vertical strain (ε = Δh/h), where h is the initial height of the sample and Δh is the change in height of the sample.

Example of triaxial test results
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Triaxial test process

### Method : Unconfined Compression Test (UCT)

The Unconfined Compression Test (UCT) is a highly simplified form of triaxial testing in which the specimen is not subjected to lateral confining pressure (σ₃ = 0) during compression.

Test Procedure:

- A cylindrical soil specimen is placed on the platform of a compression machine.

- The specimen is compressed at a constant strain rate until failure.

- This test is only applicable to fine-grained, cohesive soils (e.g., clays).

Key Characteristics:

- The UCT is essentially a UU (Unconsolidated Undrained) test with σ₃ = 0.

- For saturated soils, the unconfined compressive strength (Rc) is determined, which is equal to the deviatoric stress at failure.

- Since σ₃ = 0, Rc = 2Cu, where Cu is the undrained shear strength.

R c = 2 C u R_{c}=2C_{ u }

## Notes

1. Δ: Change in a quantity

2. τ: Shear Stress

3. σ: Normal Stress