The Cam-Clay constitutive model is one of the most widely used mathematical representations to describe the mechanical behavior of undrained clayey soils. The model is named after A.W. Skempton and R.V. Whitman, who developed it in the 1960s.
The Cam-Clay model is based on the idea that the behavior of undrained clayey soil is governed by two main mechanisms: soil compressibility and shear strength. The model also takes into account the fact that the clayey soil undergoes volume changes during loading and unloading. The model uses three fundamental parameters to describe the soil behavior:
- Compressibility index (Cc): represents the compressibility of the clayey soil and indicates how much the soil volume changes in response to a pressure variation. A high value of Cc indicates higher compressibility.
- Dilation index (Av): indicates the volume change of the soil when subjected to undrained shear conditions. A high value of Av indicates higher dilation.
- Undrained shear strength angle (ϕu): represents the shear strength of the clayey soil when subjected to undrained shear conditions. A high value of ϕu indicates higher shear strength.
The “Cam-Clay model” was developed in the 1960s at the University of Cambridge. The model is based on the critical state theory and was designed to simulate the behavior of normally consolidated clays under triaxial compression conditions. The underlying assumption of the model is a logarithmic relationship between mean effective stress and void ratio. Additionally, the model assumes a linear relationship between stiffness and pressure, which is realistic for normally consolidated (NC) clays. It distinguishes between the primary loading process and subsequent loading and unloading processes.
The Cam-Clay model assumes that the clayey soil behaves as an elastoplastic material. During loading, the soil compresses and can reach a critical state called the Cam-Clay state, where compressibility and shear strength reach maximum values. The Cam-Clay model is commonly used to analyze slope stability, consolidation of clayey soils, and the behavior of excavations in cohesive soils.
In order to improve its agreement with experimental data and extend its applicability, numerous modifications to the original Cam-Clay formulation have been proposed. In particular, the “Modified Cam-Clay” model proposed by Roscoe and Burland [67] is preferred over the original model. The Modified Cam-Clay has been shown to be sufficiently accurate in describing the behavior of normally consolidated or lightly overconsolidated clays under quasi-static and monotonic loading conditions [93]. This model has been successfully applied to analyze various geotechnical problems, such as tanks or embankments founded on clays (one of the early applications of this type is reported in [90]). Furthermore, its use requires the determination of a few parameters, which can be obtained through standard laboratory tests. These characteristics justify its frequent utilization, both in research and practical applications.
Logarithmic relationships between pressure p and specific volume v. Yield surface and critical state surface in the space of principal stresses.
English: The use of Cam-clay and Modified Cam-clay requires the determination of four dimensionless parameters:
- Virgin compression index (λ)
- Swelling index (k)
- Slope of the critical state line (M)
- Initial specific volume (v0)
Theoretically, only two laboratory tests are needed to determine these parameters: the first test, an isotropic compression test (including an unloading path if the sample is initially normally consolidated), allows the derivation of the parameters λ, k, and vc1. The second test, a standard triaxial test under drained conditions, is aimed at determining M.
The distinction between the yield surface and the critical state surface allows Cam-clay to overcome one of the main limitations of classical elastoplastic models (such as Drucker-Prager, modified Tresca, Mohr-Coulomb [28, 26, 71]). In Cam-clay and Modified Cam-clay, the implications of the associative flow rule hypothesis are qualitatively in good agreement with the actual behavior of soils.
Mohr-Coulomb and Cam Clay
The Mohr-Coulomb model and the Cam Clay model are two approaches used in soil mechanics to describe the behavior of soils under loading and deformation. The Mohr-Coulomb model is based on the theory of strength of materials and is widely used to analyze the stability of soils. According to this model, the shear strength of a soil is determined by two main parameters: the internal friction angle (ϕ) and the cohesion (c). The internal friction angle represents the soil’s ability to resist deformation caused by tangential stress, while cohesion is the internal resistance force of the soil that opposes rupture.
On the other hand, the Cam Clay model is a form of plastic analysis specifically developed for clayey soils. This model considers the soil behavior in three main phases: compressibility, shear, and consolidation. Compressibility represents the volume reduction of the soil due to applied stress, shear describes the plastic deformation process of the soil, while consolidation relates to the dissipation of water within the soil and the resulting void reduction.
While the Mohr-Coulomb model is more general and can be applied to different types of soils, the Cam Clay model is specifically suited for clayey soils. The Cam Clay model takes into account the particular characteristics of clays, such as their compressibility and high sensitivity to water. The Cam Clay model can predict the behavior of clayey soils under both static and dynamic loading conditions.
Both models have their advantages and limitations and are used in different geotechnical analysis contexts. The choice between the Mohr-Coulomb model and the Cam Clay model depends on the specific characteristics of the soil in question and the objectives of the analysis. In general, the Mohr-Coulomb model is simpler and can be applied to a wider range of soils, while the Cam Clay model offers a more accurate description for clayey soils.
