Limitations of Current Soil Mechanics Theory

Beijing Jiaotong UniversityProf. ZHAO Chenggang

Outline

1. The reasons for uncertainty in soil mechanics theory

2. Discussions on effective stress principle3. To suggest a study method of soil

deformation and strength from a multi-field perspective

We all know that the predicted results from the soilmechanics theory has large uncertainties.Soil mechanics is a discipline with half theory and halfexperience.

We found out that the action of engineering experienceis inversely proportional to that of scientific theory forany disciplines.The greater the proportion of science role , the smallerthe proportion of engineering experience role. On thecontrary, the greater the proportion of engineeringexperience role, the smaller the proportion of sciencerole.

if the critical spirit is lacked and the limitations of existing soil mechanics theory are not revealed, It is impossible to change the semi-theoretical and semi-empirical status of soil mechanics.This report is to discuss the two most important limitations in the current soil mechanics.1）the uncertainty in soil mechanics theory 2）the limitations of effective stress

1. The reasons for uncertaintyin soil mechanics theory

The soil is sediments of loose and weakcohesive mineral particles, and the liquidand gas are filled in the soil pores.The cohesion force between the soilparticles is weak. Therefore it makes themechanical behavior of soils to be differentfrom that of other construction materials.For the weak cohesion, the interaction ofthe solid-liquid-gas phases can not beneglected, which includes capillary effect,crystallization effect of salt in water, doublelayer effect.

The soil is sensitive to changes with manyfactors, especially with the surroundingenvironments. Therefore, the soil is a kind ofeasy variable material.Many factors (such as degree of saturation,temperature, physical - chemical action …)have important effects on the soil strength andstiffness that is the same order of magnitudeas the effect of frictional and cohesion action.On the other hand, the effect of other factorson the strength and stiffness of constructionmaterials (such as concrete) can be ignoredbecause of its strong cohesion force.

The soil behavior (such as strains and strength)is complex and its influencing factors arenumerous.

The above factors are not independent, and thespecific forms of the above formulas areunknown.

( , , , , , , , , , , , ,...) (1)&ij ij w a r p ijf u u S e h h T S t c

( , , , , , , , , , , , , ,...) (2)&f ij w a r ij p ijf u u S e h h T S t c

The above factors need to be simplified and the secondary factors should be ignored.

If only one independent variable, i.e., the effective stress is selected, the constitutive relations can be expressed by

If two variable, i.e., the effective stress and void ratio are selected, the constitutive relation (Cam-clay model) can be expressed by

( ) (3)ij ijf

( , ) (5)ij ijf e

( ) (4)f f

The reasons for uncertaintySoil is a kind of easy variable material, andit is very sensitive to many factors.For simplify, the influences of manyimportant factors are ignored in currentsoil mechanics. But it does not mean thatthey do not exist. On the contrary, they willstill be shown the effects on soil behaviors.A simplified theory can not reflect thoseinfluences, which can cause a theory to hasvery large uncertainty.

Example 1: StrengthMohr-Coulomb strength theory is widelyadopted by engineers.In this theory, total stress or effective stress isthe only variable to control soil strength.The influences of many other factors are ignoredin the theory, which have been contained by theparameters c and φ. Therefore, the experimentalresults of c and φ have lost their physicalmeaning of cohesion and friction angle,respectively. These parameters actually includethe effects of other factors, which leads to theirdiscreteness.

Triaxial shear instrument is considered to be an perfectgeotechnical laboratory equipment. The effective stress in asoil sample usually can be accurate controlled in the triaxialtest. However, the other influence factors, such as soil internalstructure, physical-chemical effect of pore water, void ratio,etc., are difficult to control by triaxial shear instrument, whichleads to errors and uncertainties.

It is well known that for the same person, using the sametriaxial instrument and method, applying the same effectivestress and doing the same experiment. But the experimentalresults are different with some errors for different samples .

In the past, those error have been attributed to thedisturbance of soil samples. But in fact, there are someinfluential factors that are difficult to be controlled in thetriaxial instrument, which cause errors.

Example 2: Deformation

Conclusion

At present, the soil mechanics theory isoverly simplified. It is difficult to reflectthe impact of many important factors,which leads to the prediction result bysoil mechanics to have very largeuncertainty.

2. Discussions onEffective Stress Principle

Soil mechanics is the study of soil deformation and strengthin the framework of mechanics.As mentioned above, soil deformation and strength dependon many factors.Continuum mechanics mainly studies the relationshipamong stress , deformation and strength in single-phasematerials.The soil is multiphase mixture, where the saturated soil isthe simplest two phase mixture. The large error willproduce if the total stress is adopted for saturated soil.Therefore, the influence of the liquid phase should beconsidered.An equivalent stress approach was adopted by Terzaghi toconsider the effects of liquid phase.

This method is a simplified approach, just asadopting the temperature stress to deal with thetemperature problems.The two forms of effective stress were exploredfrom two perspectives of strength and deformationby Skempton (1960).

An effective stress formula considered the physical-chemical action was given by Mitchell (1976).

The effects of other factors are converted to theformulas of equivalent stress in these approach.

wij ij ijku

wij ij ij iju A R

The above approach is a simplified method, inwhich the stress in continuous mediummechanics is replaced by the effective stress.Then the models of deformation and strength forsaturated soils can be established in the sameway as that of single-phase continuous mediummechanics.Why the approach of effective stress is asimplified method?It is because that the multi-phase, multi-variable,complex multi-field problem is simplified as asingle-phase mechanical problem by using theapproach of effective stress . It should be notedthat a multi-field problem is not a single phasemechanics problem.

Unsaturated soil is a three-phase mixture. Adopting theeffective stress of saturated soil to deal with the problem ofcomplex unsaturated soil is incomplete and unsatisfied,and it can’t be accepted by engineers, which exist largeerror.Similar to the case of saturated soil, the three-phase, multi-variable, complex three field problem is simplified as asingle-phase mechanics problem by using the approach ofeffective stress , when the equivalent unsaturated soileffective stress is adopted.The corresponding deformation and strength models wereestablished by using the effective stress for unsaturatedsoil. Owing to lack enough independent variable, thedeformation model is still unsatisfied.The theory of unsaturated soil mechanics will be difficultto make substantial progress, if the effective stressprinciple is still hold.

The effective stress principle tells us thatthe soil strength and deformation aredetermined by the effective stress.But the principle does not say that thesoil strength and deformation aredetermined only by the effective stress ,and it does not say that the effectivestress is the only independent variable todetermine the strength and deformationof soils.

Therefore, for the strength anddeformation of unsaturated soils, adoptingtwo variables, e.g. net stress and suction, issuperior to the use of a single effectivestress for unsaturated soil .

The limitations of effective stressAs discussed above, the soil is a kind of easyvariable material. Therefore, there are manyfactors affected its strength and deformation.It is a simplified approach to consider thevarious influencing factors (e.g. pore waterpressure, suction, degree of saturation,physico-chemical effect, etc.) into some formsof effective stress, i.e. reducing a multi-fieldcomplex problem into a single-phasemechanical problems by using the effectivestress.

Soil is a kind of friction material. Its deformation andstrength depend mainly on the skeleton stress (effectivecompressive stress), friction coefficient and contact areaamong soil particles, connection strength.The connection strength among soil particles is determinedby the soil internal structure and its variation, which maybe related to changes in the external environment (e.g.,temperature and humidity), but may not be directly relatedto the effects of external forces or stress.In other words, the soil deformation and strength are notonly depend on the skeletal stress or effective stress.Other factors affected the connection strength of soil grainwill also affect its deformation and strength, such asphysico-chemical action, suction and degree of saturation.

To suggest a study method from a multi-field perspective

Under the framework of classical theory, it is difficult tobreak through the shackles of the theory, and it isdifficult to obtain a comprehensive and in-depthunderstanding of the shortcomings and limitations ofclassical theory.Only by jumping out of the framework of the classicaltheory, getting rid of its influences, and re-examining theclassic theory with a broader perspective, we cancomprehensively and deeply understand itsshortcomings and limitations.This report is intended to rethink the effective stressprinciple from a broader perspective.

Therefore the researchers should not only pay attentionto the effect of effective stress (this is certainly correct),but also consider the effects of other factors to be as theindependent state variables rather than to be someparameters or some conditions.Because the constitutive models of deformation andstrength are change with these variables. For example,the deformation and strength formulas at lowtemperature or low degree of saturation conditions aredifferent from that at high temperature or high degree ofsaturation.From the perspective of multi-field coupling to examinethe classical soil mechanics problems, a lot of newproblems and knowledge growth point will be produced,and the knowledge and understanding of the originalproblem will broaden and deepen.

Therefore, the soil deformation and strengthshould be studied from the multi-fieldperspective.Others factors are treated as independentvariables (or independent field variables),rather than are simplified as the effectivestress.Besides, the coupling in multiple fields can beconsidered.It is clear that the study of soil deformationand strength from a multi-field perspective is amore complete and scientific approach.

Thanks