Soil Shear Strength: Direct Shear and Triaxial Tests

The stability of every slope, foundation, and retaining wall depends on a single critical property: the soil's ability to resist sliding. Understanding soil shear strength is a fundamental requirement for preventing catastrophic geotechnical failures. This article delves into the core theory and the two most common laboratory methods engineers use to measure this vital parameter: the direct shear test and the triaxial test.

The Mohr-Coulomb Failure Criterion

To quantify shear strength, engineers rely on the Mohr-Coulomb failure criterion. This is a linear model that defines the shear strength of a soil as a combination of cohesive resistance and frictional resistance. It is expressed by the famous equation:

$${\tau }_f=c+\sigma \tan \varphi$$

Here, ${\tau }_f$ is the shear strength at failure, $c$ is the cohesion (the shear strength intercept when normal stress is zero), $\sigma$ is the normal stress acting on the failure plane, and $\varphi$ is the angle of internal friction. This model treats soil as a material that gains strength both from inherent "stickiness" (cohesion, typical in clays) and from particle interlocking and friction (the $\tan \varphi$ term, dominant in sands and gravels). Crucially, this criterion can be applied in terms of either total stress or effective stress. The effective stress principle, defined by ${\sigma }^{\prime }=\sigma -u$ (where $u$ is pore water pressure), is paramount, as soil strength is controlled by the stress carried by the soil skeleton itself. Therefore, we distinguish between total stress parameters ($c$, $\varphi$) and effective stress parameters ($c^{\prime }$, ${\varphi }^{\prime }$).

The Direct Shear Test: Procedure and Interpretation

The direct shear test is a straightforward, historically common method for determining shear strength parameters. A soil sample is placed in a horizontally split metal box. A vertical load ($N$) is applied to create a known normal stress ($\sigma =N/Area$). Then, a horizontal shear force is applied to the top half of the box, forcing the soil to shear along a predetermined horizontal plane.

The procedure involves testing multiple, nominally identical, specimens under different normal stresses. For each test, the shear force is increased until failure, and the shear stress at failure (${\tau }_f$) is recorded. These pairs of normal and shear stress at failure are then plotted on a $\tau$ vs. $\sigma$ graph. A best-fit line drawn through these data points is the failure envelope. The intercept of this line on the shear-stress axis is the cohesion ($c$), and its slope is the friction angle ($\varphi$). While simple and inexpensive, the test has significant limitations: the failure plane is forced, not natural; drainage conditions are poorly controlled; and only the stresses on the failure plane are known, making the complete stress state within the sample indeterminate.

Triaxial Test Fundamentals and Types

The triaxial test is a more sophisticated and versatile method. A cylindrical soil specimen is enclosed in a thin rubber membrane and placed inside a pressure chamber. It is first subjected to an all-around confining pressure (${\sigma }_3$). Then, an additional axial stress (called the deviator stress, $q$) is applied through a piston until the sample fails. This setup allows for precise control of drainage and measurement of pore water pressure. The major and minor principal stresses at failure (${\sigma }_1$ and ${\sigma }_3$) are known, enabling the plotting of Mohr's circles to define the failure envelope. The three primary test types are defined by their drainage conditions during the shearing phase:

1. Unconsolidated-Undrained (UU) Test: The sample is not allowed to drain during the application of either confining pressure or deviator stress. This rapidly measures the undrained shear strength ($s_u$), represented by a horizontal failure envelope ($\varphi =0$). It models short-term loading conditions in low-permeability clays, like rapid excavation or immediate bearing capacity.
2. Consolidated-Undrained (CU) Test: The sample is allowed to fully consolidate under the confining pressure (drainage open), then sheared without drainage. Pore pressures are measured, allowing engineers to calculate effective stresses. This test yields both total stress parameters and, more importantly, effective stress parameters ($c^{\prime }$, ${\varphi }^{\prime }$). It simulates situations where soil consolidates under a static load (e.g., a new embankment) but then experiences a rapid, undrained loading (e.g., an earthquake).
3. Consolidated-Drained (CD) Test: The sample is consolidated under the confining pressure, then sheared so slowly that no excess pore pressures develop. This test directly measures the effective stress strength parameters ($c^{\prime }$, ${\varphi }^{\prime }$). It represents long-term, drained conditions, such as the steady-state stability of a slope or the bearing capacity of a foundation under sustained load.

Selecting the Appropriate Test for Field Conditions

Choosing the correct laboratory test is a critical engineering decision based on simulating in-situ stress paths and drainage conditions. Misapplication can lead to dangerously unconservative or overly conservative designs.

For the analysis of short-term stability in saturated, fine-grained soils (clays), where loading is rapid and no drainage occurs, the UU test provides the undrained shear strength ($s_u$). For long-term stability in all soils, or in coarse-grained, free-draining soils (sands) under any condition, the effective stress parameters from a CD or CU test must be used. The CU test is particularly valuable for analyzing staged construction or sudden loading events where the soil's initial stress state is known to change. The key is to match the drainage conditions and stress path of the laboratory test to those expected in the field for the specific failure mechanism being analyzed.

Common Pitfalls

1. Using Total Stress Parameters for Drained Analysis: A major error is applying UU test results ($\varphi =0$ analysis) to a long-term slope stability problem. Over decades, pore pressures equilibrate, and strength is governed by effective stress. Using undrained strength here significantly overestimates the actual long-term safety factor.
2. Ignoring Sample Disturbance in Sensitive Soils: The process of extracting and trimming a soil sample, especially soft clays, can remold and weaken it. Laboratory tests on severely disturbed samples will yield strength parameters lower than the in-situ strength, leading to overly conservative and expensive designs. Engineers must consider quality class and correlate lab data with field tests.
3. Misinterpreting the Cohesion Intercept ($c^{\prime }$): For granular soils like clean sand, the true effective cohesion ($c^{\prime }$) is essentially zero. A non-zero intercept on the Mohr-Coulomb plot is often an artifact of testing at low confining pressures and does not represent genuine cohesive strength. It should not be relied upon in design without careful justification.
4. Applying a Single Test Type Universally: Assuming one test (often the simpler direct shear) is sufficient for all projects is a critical mistake. A proper site investigation requires selecting test types based on the soil profile, groundwater conditions, and the various loading scenarios the structure will encounter during and after construction.

Summary

• Soil shear strength is modeled by the Mohr-Coulomb failure criterion: ${\tau }_f=c+\sigma \tan \varphi$, which must be applied using either total stress or, more fundamentally, effective stress principles.
• The direct shear test is simple and useful for granular soils but forces a failure plane and offers poor control over drainage and stress state.
• The triaxial test is the standard for accurate measurement, with its type—UU (undrained), CU (consolidated-undrained), or CD (drained)—dictated by the need to simulate specific field drainage conditions during shear.
• The selection of laboratory test type is not arbitrary; it must be a conscious simulation of the drainage conditions and stress path expected in the field for the geotechnical problem at hand.
• The most frequent analytical errors involve confusing total and effective stress analyses and applying strength parameters from one drainage condition to a design scenario with another.