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### Material Behavior of Continuum Soil : Everything you need to know

Articles > Material Behavior of Continuum Soil : Everything you need to know

### Introduction:

The word "Continuum" means continuous. Soil particles since are always in contact with each other hence can be treated as a continuum. Soil can display elastic, plastic, or sometimes elastoplastic behavior. In material behavior of soil, we tend to analyze the stress-strain behavior of soil for elastic, plastic, elastoplastic behavior, etc.

### Elastic Behavior:

In this case, the soil material loading and unloading follow the same path. No strain energy is stored in the body when completely unloaded ie. strain is fully recoverable. Elastic behavior follows Hook’s Law, which states that in elastic range stress is directly proportional to strain. Therefore, when soil exhibits elastic behavior stress will directly be proportional to strain.

Now, the stress-strain curve can be either Linear or Nonlinear

• In the case of a linear stress-strain curve for any applied force on the Soil, we can directly find the deformation with the help of a linear graph

• In the case of the Nonlinear stress-strain curve though the loading and unloading follow the same path in the curve. But the curve has different slopes for different points on the curve, hence different secant modulus. So to find the deformation in this case we have to analyze different points in the curve. For more accuracy, we may break the nonlinear curve into different smaller segments ie. forming a multilinear curve.

### Plastic Behavior:

In this case, the soil when loaded and unloaded again does not follow the same path. An amount of Strain energy is stored in the body which does not allow the soil to regain its actual shape and thus the strain energy is not fully recoverable. Plastic behavior of soil is very rarely seen in practical fields because up to particular stress the soil will behave elastically and have the tendency to dissipate all the strain energy upon unloading, but beyond particular stress, the soil particles can no longer exhibit elastic tendency and get deformed permanently.

### Elasto-Plastic Behavior:

This is a combination of both elastic and plastic behavior that the soil exhibits upon loading. In this case, we have two types of strain

• Permanent strain(?p) : the permanent deformation

• Recoverable strain(?r): the strain that can be dissipated completely after unloading

The stress limit up to which the strain in the soil mass can be recovered is known as yield stress(σy). Beyond this yield stress, the strain in soil mass is permanent. Yield stress is not a constant value it keeps on varying as we keep on loading and unloading the soil mass.

### Visco-Elastic behavior:

In soil behavior, we have another type of behavior that is time-dependent but not instantaneous. This behavior which is a function of time is viscous behavior. This is basically observed in the case of mud sliding because it acts like a viscous fluid and the failure or any change is very slow and is a function of time. The stress-strain curve will show an elastic form of deformation ie. it will either be linear or nonlinear.

Another case of visco-elastic behavior can be seen during the excavation of tunnels. While excavating tunnels the time lag between excavation and the time of installation of support(support in form of grouting, steel joints, etc.) the viscoelastic behavior of soil plays an important role because this behavior will decide the time up to which the excavated tunnel can stand without any support and the supports are to be installed within that limited time or else the excavated tunnel will fail. Therefore, in this case, the deformation of soil is not instantaneous and it takes some time to deform.

### Elasto-Visco-Plastic:

In this case, a viscous soil shows similar behavior in the stress-strain curve as that of elastoplastic ie. up to certain stress it behaves like an elastic material but beyond that stress, it behaves like plastic with complete deformation. But since the soil is viscous this deformation will not be instantaneous instead it will be slow and time-dependent.

### Other Behavior:

Apart from the above-mentioned behavior, soil can exhibit some other types of behavior like-

• Elastic-Perfectly plastic: In this behavior, soil behaves like linearly elastic up to certain stress(σy), but beyond this stress, the graph turns out to be a straight line parallel to the x-axis ie. showing complete plastic behavior.

• Rigid or Perfectly-Plastic: Here when we apply stress to the soil, initially the soil particles do not tend to show any strain. But as soon as the stress reaches the ultimate stress(σy) value then there is an infinite amount of strain ie. The stress-strain graph represents a straight line parallel to the x-axis for infinite value.

Fig. graph for different behavior od Soil

Courtesy: Wikipedia

### Physical Model Representation of Soil Behavior:

In order to solve the problem of different behavior of soil, we can represent it in terms of a physical model which is similar to a mass(m) attached to an elastic spring having constant (k). Any model that represents a material behavior is known as a Rheological model.

• Elastic Case: It can be represented by a mass(m) attached to a spring. In this case, upon loading the mass(m) stretches the spring attached to it and after unloading the spring returns back to its normal position.

• Elasto-Plastic Case: In this case, we have a friction slider along with spring and mass(m). The friction slider does not allow deformation up to a certain amount of stress. But beyond certain stress, the mass starts moving and does not bounce back to its normal behavior.

• Visco-Elastic Case: In this case, we have a dashpot along with spring and mass(m). A dashpot is a pot containing a viscous oil with a piston. When pressure is applied to the soil the piston cannot move immediately because the oil cannot escape immediately, it takes time and after some time the oil gradually will escape from the dashpot. So deformation to occur it takes some time.

• Elasto-Visco-Plastic Case: In this case, we have a dashpot and a friction slider in parallel connected to spring and mass(m). Here when we apply pressure at first the friction slider does not allow any deformation, but after a certain amount of stress, deformation occurs very slowly due to the dashpot present. This type of behavior is seen in the case of a dam foundation between two hillocks. When the hills are cut a large slope is created and the safety of the slope depends upon the elastoplastic viscous behavior of the soil.

### Conclusion:

From the above discussion, we can predict the different varieties of deformations a soil mass can exhibit in practical life, and hence to have a piece of proper knowledge about the stability of the soil and other parameters one must study the stress-strain graph and the behavior of the soil material properly. When have different rheological models for different situations and each different situation has to be studied separately. The same soil can show two or more types of behavior at different segments hence all the segments of a soil mass has to be studied differently.