Omar Khalid
The plasticity modulus of soil, also known as the modulus of plasticity, is a measure of soil stiffness. It is determined from the stress-strain curve within the plastic behaviour range. The stress-strain response can be represented by two straight lines, describing an initial linear elastic stiffness and the yield stress or strength at failure during plastic straining. The plastic modulus is calculated by dividing the load by the permanent deformation. This value is obtained by subjecting a soil sample to repeated loading and monitoring the deformation.
| Characteristics | Values |
|---|---|
| Determination | From the stress-strain curve within the plastic behaviour range |
| Deformation Modulus (E) | Depends on the load level |
| Plastic Modulus Calculation | Divide the load by the permanent deformation |
| Plastic Straining | Plastic strains continue indefinitely at constant stress |
| Plastic Straining and Yield Stress | The ratio of plastic strains is related to the yield stress, which also represents the failure stress |
| Plastic Straining and Yield Curve | The relationship between the ratio of plastic strains is such that the plastic strain vector is normal to the yield curve |
| Elasticity and Plasticity | Combined into elasto-plasticity |
| Stress-Strain Response | Can be represented by two straight lines, to describe an initial linear elastic stiffness and the yield stress or strength at failure during plastic straining |
| Soil Behaviour | The Critical State Soil Mechanics Theory is used to predict soil behaviour under a variety of loading types |
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What You'll Learn
Plasticity and soil behaviour
Plasticity is an important property of fine-grained soils, especially those containing clay minerals. It refers to the soil's ability to deform without cracking or fracturing under an external force and remain deformed after the force is removed. This behaviour is due to the presence of adsorbed water, which forms a layer around the clay particles, allowing them to slip over one another during deformation and preventing them from returning to their original positions.
The plasticity of soil is influenced by its water content. As the water content decreases, the plasticity also decreases. The plastic limit of soil is the water content below which it loses its plastic behaviour and starts to crumble when rolled into threads. This limit is determined through laboratory tests, where soil samples are air-dried and sieved to obtain fine grains, and then mixed with water to reach a mouldable consistency.
The Atterberg limits, which include the liquid limit (LL) and plastic limit (LP), define the moisture content range within which the soil exhibits plastic behaviour. Below the LP, the soil behaves fragily, while above the LL, it behaves like a liquid and flows easily. The difference between the LL and LP is known as the plasticity index (PI). These limits are important for understanding the long-term effects of land use and the impact of tillage on soil behaviour.
The particle size distribution, structure, porosity, and organic matter (MO) content also influence the plasticity of soil. These factors affect water retention, flow behaviour, aeration, temperature, shrinkage, expansion, and resistance to compaction and erosion. The relationships between these properties and plasticity are complex and have been studied under traditional tillage (LT) and no tillage (NL) systems, with varying results.
Computational plasticity models have been developed to predict soil behaviour under different loading conditions. These models are based on the Critical State Soil Mechanics Theory and employ multiple nested surfaces to simulate the yield surface and subsequent loading responses. By using these models, researchers can gain insights into how soils with different plasticity characteristics respond to various loading scenarios.
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Stress-strain curve
The plastic modulus of soil is a measure of its stiffness or rigidity. It is a property that characterises the soil's resistance to deformation under applied stress. This can be visualised using a stress-strain curve, which shows the relationship between the stress applied to a soil sample and the resulting deformation or strain.
The stress-strain curve is a fundamental tool in soil mechanics, providing insights into the behaviour of soils under different loading conditions. It is often used in conjunction with laboratory tests, such as triaxial compression or shear tests, to determine the mechanical properties of soils, including their stiffness and strength.
The curve typically has a non-linear shape, indicating that the relationship between stress and strain is not proportional. At the beginning of the curve, where the stress is low, the soil exhibits linear elastic behaviour, and the deformation is reversible. This region is characterised by the gradient of the curve, which represents the stiffness modulus. As the stress increases, the curve deviates from linearity, and the soil enters a non-linear, inelastic regime where the deformation becomes permanent.
The stress-strain curve can provide valuable information about the soil's behaviour at different stress levels. For example, the curve can indicate the yield point, which is the stress level at which the soil begins to deform plastically and irreversibly. Beyond the yield point, the curve may exhibit a plateau region, where the soil exhibits a constant volume strength. The ultimate strength of the soil can be determined by the peak of the curve, after which the soil fails or ruptures.
Additionally, the stress-strain curve can be used to determine the plastic modulus of soil. The plastic modulus is related to the deformation modulus (E), which depends on the load level. By performing repeated loading tests and monitoring the deformation, one can identify three types of deformation: total, permanent, and resilient. The plastic modulus can then be calculated by dividing the load by the permanent deformation.
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Deformation and load level
The deformation modulus (E) depends on the load level. At some load level, the modulus is equal to the ratio of deviation stress to strain. This can be determined from the stress and strain relationship curve obtained from a triaxial compression test corresponding to certain load levels.
If a soil or granular material specimen of unconfined compression or CBR mould size is subjected to repeated loading, and the deformation is monitored, three types of deformation can be observed: total, permanent, and resilient deformation. The total deformation is the sum of permanent and resilient deformation. The permanent deformation is the irreversible part of the total deformation, while the resilient deformation is the recoverable part.
The plastic modulus of soil can be determined by dividing the load by the permanent deformation. This value is important in pavement engineering, where the performance of pavement materials is related to the resilient modulus and plastic deformation, which are in turn affected by environmental conditions and traffic loading.
For example, a series of triaxial tests were conducted on a residual lateritic soil for 10,000 load repetitions, with some specimens subjected to 100,000 load repetitions. These tests characterized the behaviour of cohesive subgrades under repeated loading, including the resilient modulus and plastic deformation. The results showed that under low-stress levels, the resilient modulus of cohesive subgrades exhibits strain-hardening behaviour, while the rate of plastic strain accumulation decreases. Conversely, under high-stress levels, cohesive soil tends to soften after a specific number of load applications and accumulates excessive plastic strain.
Computational plasticity models for soils under cyclic loading have been developed based on the Critical State Soil Mechanics Theory. These models employ multiple nested surfaces to predict soil behaviour under various loading types.
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Soil mechanics theory
Soil mechanics is a branch of science that deals with the study and understanding of the physical properties and behaviour of soil. The first scientific study of soil mechanics was undertaken by French physicist Charles-Augustin de Coulomb, who published a theory of earth pressure in 1773. Coulomb's work and a theory of earth masses published by Scottish engineer William Rankine in 1857 are still primary tools used to quantify earth stresses.
Soil mechanics helps determine the type of pavement (rigid or flexible) that will last longer for roads and highways. It is also used to decide the most suitable method for excavating underground tunnels. Soil mechanics describes the mechanical behaviour of granular materials, which includes powders, grains, mineral ores, and natural soils. The mechanical behaviour covers strength, shear stiffness, volumetric compressibility, and seepage of water.
The theories of soil mechanics apply equally to sands (coarse-grained soils) and clays (fine-grained soils). The classification of fine-grained soils is determined primarily by their Atterberg limits and not by their grain size. If it is important to determine the grain size distribution of fine-grained soils, a hydrometer test may be performed. In this test, soil particles are mixed with water and shaken to produce a dilute suspension in a glass cylinder. A hydrometer is then used to measure the density of the suspension over time.
Soil mechanics also involve the study of soil characteristics, which vary more rapidly vertically (with depth) than horizontally. Subsurface examination techniques include trench-digging, boring, and pumping subsurface matter to the surface with water. Seismic testing and measurement of electrical resistance are also useful in evaluating soil. The theories for soil mechanics originated in the middle of the eighteenth century, with Coulomb's experiments on the strength of soils. He found that the resistance of soil to shear loading had two components: one cohesive and the other frictional.
One of the major contributions to soil mechanics was made by Austrian civil engineer Karl Terzaghi, who, in the 1920s, set out a clear theory for accounting for the influence of pore pressure on soil strength and deformation. He proposed an effective stress, σ′, which controls all soil behaviour and discovered that for saturated soil, this is related to total stress σ and pore pressure u. This equation has been found to apply to a wide range of loadings and soils and is used universally for the geotechnical analysis of saturated soils.
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Elasticity and plastic straining
The relationship between stress and strain can be visualised using a stress-strain curve. The linearity limit, or the proportionality limit, is the point beyond which stress is no longer proportional to strain. When the stress becomes larger than the linearity limit but remains within the elasticity limit, the behaviour is still elastic, but the relationship between stress and strain becomes nonlinear. This nonlinear behaviour indicates that the material is becoming harder to deform as it approaches its breaking point.
For ductile materials such as metals, the stress gradually decreases as the strain increases, making it easier to deform as it approaches the breaking point. On the other hand, brittle materials such as rock, concrete, and bone exhibit plasticity through slip at microcracks. In cellular materials such as liquid foams or biological tissues, plasticity is observed through cell rearrangements.
The decomposition of strain into elastic and plastic parts is one of the key concepts in plasticity theories. During plastic loading, the principal components of the plastic strain rate tensor are parallel to the components of stress acting on the material. This results in a plastic strain increment that is proportional to the stress, unlike elastic deformation. Under multi-axial loading, most polycrystalline solids follow the Levy-Mises flow rule, which relates the principal components of strain rate to the principal stresses during plastic loading.
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Frequently asked questions
The plasticity modulus of soil is a term used to describe the relationship between stress and strain within the plastic behaviour range.
The plasticity modulus can be determined from the stress-strain curve.
The stress-strain curve is obtained from a triaxial compression test, which measures the relationship between stress and strain within a material.
The deformation modulus (E) depends on the load level. It is equal to the ratio of deviation stress to strain.
The plasticity modulus can be calculated by dividing the load by the permanent deformation. The deformation modulus is a type of deformation that can be obtained by subjecting a soil sample to repeated loading and monitoring the deformation.
