**7. Conclusions**

d*ε* p

soil considering particle breakage.

from the generalized Hook's law:

expressed as

form,

<sup>s</sup> <sup>¼</sup> *m C*ð Þ <sup>t</sup> � *<sup>C</sup>*<sup>e</sup> *pm* a

> ð Þ <sup>2</sup>*n*þ<sup>1</sup> *<sup>p</sup>*2*n*þ<sup>1</sup> *M*<sup>2</sup> c

*M*<sup>4</sup> f *M*<sup>4</sup> c

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

d*ε*<sup>e</sup>

d*ε*<sup>e</sup>

where E is the elastic modulus and v is the Poisson's ratio.

d*ε*<sup>e</sup>

d*ε*<sup>e</sup>

<sup>v</sup> <sup>¼</sup> *m C*ð Þ <sup>t</sup> � *<sup>C</sup>*<sup>e</sup> *pm* a

*<sup>η</sup>*<sup>2</sup> <sup>þ</sup> *<sup>p</sup>*<sup>2</sup>*n*þ<sup>1</sup> h i*<sup>m</sup>*�2*n*�<sup>1</sup> <sup>2</sup>*n*þ<sup>1</sup>

> <sup>s</sup> <sup>¼</sup> *m C*ð Þ <sup>t</sup> � *<sup>C</sup>*<sup>e</sup> *pm* a

*<sup>η</sup>*<sup>2</sup> <sup>þ</sup> *<sup>p</sup>*<sup>2</sup>*n*þ<sup>1</sup> h i*<sup>m</sup>*�2*n*�<sup>1</sup> <sup>2</sup>*n*þ<sup>1</sup>

*n* can be obtained by consolidated drained triaxial test.

shear strain are, respectively, expressed as

<sup>v</sup> þ d*ε* p

ð Þ <sup>2</sup>*n*þ<sup>1</sup> *<sup>p</sup>*2*n*þ<sup>1</sup> *M*<sup>2</sup> c

<sup>s</sup> þ d*ε* p

ð Þ <sup>2</sup>*n*þ<sup>1</sup> *<sup>p</sup>*2*n*þ<sup>1</sup> *M*<sup>2</sup> c

considering particle brakeage.

<sup>d</sup>*ε*<sup>v</sup> <sup>¼</sup> <sup>d</sup>*ε*<sup>e</sup>

<sup>d</sup>*ε*<sup>s</sup> <sup>¼</sup> <sup>d</sup>*ε*<sup>e</sup>

**162**

*M*<sup>2</sup> <sup>c</sup> <sup>þ</sup> *<sup>η</sup>*<sup>2</sup> � �2*<sup>η</sup> M*<sup>4</sup>

Equations (26) and (27) are the plastic strain expression of weathered granite

In three-dimensional axisymmetry, the following expressions can be obtained

<sup>v</sup> <sup>¼</sup> 3 1ð Þ � <sup>2</sup>*<sup>v</sup>*

<sup>s</sup> <sup>¼</sup> 2 1ð Þ <sup>þ</sup> *<sup>v</sup>*

After taking the derivative of *p* in Eq. (15), the elastic volumetric strain can be

<sup>v</sup> <sup>¼</sup> *mC*e*pm*�<sup>1</sup> *pm* a

Combining Eqs. (29)–(31), the elastic shear strain is obtained in the following

<sup>s</sup> <sup>¼</sup> 2 1ð Þ <sup>þ</sup> *<sup>v</sup> mC*e*p<sup>m</sup>*�<sup>1</sup> 9 1ð Þ � 2*v pm*

According to elastoplastic mechanics, the total volumetric strain and the total

*M*<sup>4</sup> <sup>c</sup> � *<sup>η</sup>*<sup>4</sup> � � *M*<sup>4</sup>

*<sup>p</sup>*<sup>2</sup>*<sup>n</sup>* � *<sup>p</sup>*<sup>2</sup>*<sup>n</sup> M*<sup>2</sup> c *η*2

*M*<sup>2</sup> <sup>c</sup> <sup>þ</sup> *<sup>η</sup>*<sup>2</sup> � �2*<sup>η</sup> M*<sup>4</sup>

*<sup>p</sup>*<sup>2</sup>*<sup>n</sup>* � *<sup>p</sup>*<sup>2</sup>*<sup>n</sup> M*<sup>2</sup> c *η*2

!

The Eqs. (33) and (34) are the constitutive relation of the weathered granite soils

The seven parameters in the constitutive model of weathered granite soil are *C*e, *C*t, *m*, *M*, *p*c, *n*, and *ν.* Except for Poisson's ratio *ν*, the other six parameters can be obtained by conventional triaxial test. The value of *ν* is assumed to be 0.3. *C*e, *C*t, and *m* can be obtained by isotropic compression and unloading test, and *M*, *p*c, and

!

*M*<sup>4</sup> f *M*<sup>4</sup> c

*M*<sup>4</sup> f *M*<sup>4</sup> c

a

<sup>f</sup> � *<sup>η</sup>*<sup>4</sup> � � <sup>d</sup>*<sup>p</sup>* <sup>þ</sup>

<sup>f</sup> � *<sup>η</sup>*<sup>4</sup> � � <sup>d</sup>*<sup>p</sup>* <sup>þ</sup>

þ

þ

*<sup>η</sup>*<sup>2</sup> <sup>þ</sup> *<sup>p</sup>*2*n*þ<sup>1</sup> h i*<sup>m</sup>*�2*n*�<sup>1</sup> <sup>2</sup>*n*þ<sup>1</sup>

<sup>f</sup> � *<sup>η</sup>*<sup>4</sup> � � <sup>d</sup>*<sup>p</sup>* <sup>þ</sup>

2*η M*<sup>2</sup>

!

*<sup>p</sup>*2*<sup>n</sup>* � *<sup>p</sup>*2*<sup>n</sup> M*<sup>2</sup> c *η*2

<sup>c</sup> � *<sup>η</sup>*<sup>2</sup> <sup>d</sup>*<sup>q</sup>*

*<sup>E</sup>* <sup>d</sup>*<sup>p</sup>* (29)

<sup>3</sup>*<sup>E</sup>* <sup>d</sup>*<sup>p</sup>* (30)

d*p* (31)

d*p* (32)

2*η M*<sup>2</sup>

> 2*η M*<sup>2</sup>

2 1ð Þ <sup>þ</sup> *<sup>v</sup> mC*e*p<sup>m</sup>*�<sup>1</sup> 9 1ð Þ � 2*v pm*

!

!

*mC*e*pm*�<sup>1</sup> *pm* a

<sup>c</sup> � *<sup>η</sup>*<sup>2</sup> <sup>d</sup>*<sup>q</sup>*

d*p*

<sup>c</sup> � *<sup>η</sup>*<sup>2</sup> <sup>d</sup>*<sup>q</sup>*

a

�

�

d*q:*

(33)

(34)

! (28)

�

In this chapter, routine physical and mechanics tests and large-scale triaxial tests were conducted to investigate the compaction, bearing, strength and shearingdilatancy characteristics, and constitutive model of compacted weathered granite soil. The main conclusions obtained from the study in this chapter are summarized as below:


Given that wet conditions may influence the evolution of embankments after construction, future extensive research should be focused on dynamic measurement methods of particle breakage and long-term behavior degradation analysis of subgrade as a result of further weathering and particle breakage [7, 11, 30, 31]. It is very difficult to entirely understand the road performance of weathered granite soil due to its special mechanical properties. Further research needs to be performed for assessing the unique mechanical behaviors of compacted weathered granite soil considering particle breakage and the mechanical properties of different types of weathered granites soils (e.g., coarse-grained weathered granite soil and finegrained weathered granite soil). Given that measuring particle breakage and its variations during triaxial compression tests are still a challenging task [32], future extensive research should be focused on the dynamic measurement methods, the mathematical description of particle breakage, and the long-term behavior degradation owning to particle breakage [33].
