Triaxial Test

Laboratory Testing

Contents [hide show]

Triaxial Testing
Types of Triaxial Testing
Stress Development in Triaxial Testing
Skempton’s Coefficients
References:

Triaxial Testing

Soil triaxial testing is a fundamental procedure in geotechnical engineering, used to determine a sample’s shear strength parameters.

During triaxial testing, a cylindrical soil sample is enclosed in a rubber membrane and placed within a cell, commonly made of glass or plastic.

The sample within the cell usually has a length/diameter ratio of 2, while it is subject to a confining pressure, applied on all sides by compression of the fluid (usually water) that fills the chamber surrounding the sample.

In addition to this, an axial load is applied to the sample via a loading ram that sits on top, and the direction of this force dictates if the sample is going to act in compression or extension.

The diameter of the sample is usually 3.8cm, but can be much larger than that, reaching or even exceeding 10cm.

Due to the triaxial’s versatility, which allows for all types of soil to be tested, standards such as the ASTM D4767 specify that a sample’s maximum particle size should be less than 1/6 its diameter.

Drainage and loading paths can also be controlled by opening or closing the apparatus’ drainage valve, and a test schematic can be seen below.

Figure 1: Diagram of triaxial test equipment (After Bishop and Bjerrum, 1960, as presented in Das, B.M. (2007))

Triaxial loading takes place in two distinct stages. During the first phase, the fluid confining pressure is gradually applied, which is called the cell pressure (σ_cell). Whilst this cell pressure is building up, the drainage valve can be open to allow for the sample’s consolidation or closed to prevent it.

During the second phase of loading, the axial load is also gradually applied through the ram on top of the apparatus, while σ_cell is maintained constant. The drainage valve can either be open or closed again, allowing for drained or undrained loading conditions to take place respectively.

Types of Triaxial Testing

Depending on the selections made during these two phases, we can then have three different types of setups:

1. Consolidated-drained (CD) test or drained test.

2. Consolidated-undrained (CU) test.

3. Unconsolidated-undrained (UU) test or undrained test.

An additional test that can be conducted with the triaxial apparatus is the unconfined compression test, which involves shearing the specimen with no confining pressure.

Stress Development in Triaxial Testing

In order to gain a first impression of the stress development that takes place during triaxial compression, it would be worth first understanding the sample’s behavior in the absence of water first.

Figure 2: Typical stress conditions in a triaxial test (credits: Geoengineer.org)

Furthermore, if we assume that the vertical axis is called z axis and the two horizontal ones x and y, the confining cell pressure (σ_cell) is equal to the minor principal stress (σ₃), acting on the x axis.

In the most common form of a triaxial where isotropic cell pressure is applied (i.e. same pressure on all three axes), this stress is also going to be equal to σ₂, acting on the y axis, giving us the following relationship:

σ₃ = σ₂ = σ_cell (1)

Now, it only makes sense that this isotropic cell pressure will also be acting on the vertical z axis, where the axial force (F) is also applied, remembering that stress is just force over the cross-sectional area of application (A) (i.e. σ =F/A), we get the following relationship for the major principal stress (σ₁), which will be acting on the vertical axis (z):

σ₁= σ_c + F/A (2)

So, if the two stresses acting on the vertical axis are the cell pressure (σ_c= σ₃), and the stress resulting axially from the ram applied force (σ_a), then the stress applied from the ram on top of the apparatus will also be equal to the deviatoric stress (q):

σ_a = σ₁ – σ₃ = q (3)

Depending on the test type and drainage selections, water could be present within the sample. This water would lead to pore water pressures, and respectively effective stress conditions, rather than total stress ones. In this case, as figure 3 suggests, we will have:

σ₁’ = σ₁ – u (4)

σ₃’ = σ₃ – u (5)

Figure 3: Triaxial effective stresses (credits: Geoengineer.org)

Failure Envelope Determination

The Mohr-Coulomb failure criterion states that the shear strength of soil at failure (τ) is equal to:

τ = c + σ ∙ tanφ (6)

Where:

c is the soil’s cohesion

σ is the normal stress

φ is the angle of internal friction

Hence, when more than one tests are conducted on the same material, utilizing different cell pressures, the various critical Mohr’s circles that are formed at failure define the failure envelope, as the straight line that can be seen in figure 4. These envelopes then allow for the determination of the sample’s strength parameters, which are its cohesion (c) and angle of internal friction (φ).

Figure 4: Stress circles at yield; one touches Coulomb's envelope. a) Using effective strength parameters (Mohr-Coulomb) b) Using undrained strength parameters (Tresca). (credits PLAXIS 2D Material Models Manual)

Skempton’s Coefficients

Skempton suggested in 1954 that it is possible to obtain the relationship between incremental pore water pressure and incremental normal stresses, through the following formula:

Δu = B[Δσ₃ + A(Δσ₁ - Δσ₃)] (7)

During the first phase of loading in the triaxial, when cell pressure is applied, and under undrained conditions present for a saturated soil, a change in pore water pressure Δu_a is going to occur along with the obvious change of the minor principal stress, which is going to be Δσ₃ (or just σ₃ if we are starting from zero confining pressure). Skempton’s B coefficient is then given by:

B = Δu_a / Δσ₃ (8)

For a completely saturated sample, B is going to always be equal to approximately 1, while for a completely dry sample, B is going to be equal to zero.

During the second loading phase that the sample is axially loaded through the ram, resulting in the deviator stress (q), and a secondary pore water pressure increase corresponding to this axial loading and called Δu_d.

It is worth noting that the total pore water pressure increase for a fully undrained test would be equal to the summation of the two, formulated as:

Δu = Δu_a + Δu_d (9)

Skempton’s A parameter is derived from this second, axial, loading phase such that:

In the case of the undrained triaxial test, equation (7) can be rewritten as:

Finally, Das (2007) recommends determining Skempton’s B parameter from the first loading phase of the Consolidated-Drained test and the A one from the second loading phase of the Consolidated-Undrained.