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A novel soil strength criterion is proposed based on the shear stress ratio on a new spatially mobilized plane, where the cube root of principal stresses is constant. The strength failure surface depicted in the principal stress space by this criterion was smoothly conical, with a curved triangle shape on the octahedral plane. A comparative analysis of the strength failure surfaces of the Mohr-Coulomb (M-C), the Drucker-Prager (D-P), the Matsuoka-Nakai (M-N), the Lade-Duncan (L-D), the new criteria, and the shear strength laws of different criteria with parameter b on the π plane showed that the L-D criterion and the new spatially mobilized plane strength criterion were comparable, which revealed the physical essence of the L-D criterion. Comparing the new strength criterion with the measured results of true triaxial tests of 4 kinds of intact loess under conditions of consolidation and drain, the strength law of loess could be described by the new strength criterion under complex stress conditions, and the rationality and reliability of the strength criterion were verified by the correspondence between the criterion and experimental values.

Four criterion models have been used extensively in rock and soil mechanics, including the Mohr-Coulomb (M-C) [

The D-P strength criterion model is based on the assumption that the octahedral shear stress at failure depends linearly on an octahedral normal stress through material constants. The octahedral shear plane forms the same angle with each plane on which every 2 of the principal stress axes fall (

Based on the M-C criterion’s geometrical description of the shear failure plane, the M-N failure criterion takes into account the intermediate principal stress, leading to the concept of the spatially mobilized plane [

considered to be spatially mobilized planes as well, the axis intersection points that can be derived from the M-C criterion would be

In addition to all the models above demonstrating that shear stresses on spatially mobilized planes are in a linear relationship with normal stress, the L-D criterion established the nonlinear relationship between shear stress and mean normal stress described by a power function. However, the L-D criterion does not establish a corresponding spatially mobilized plane. A nonlinear strength criterion was established by Yangping Yao et al. [

To better describe the strength of loess, this paper introduces a new spatially mobilized plane model that generates the axis intersections as

Similar to the M-N proposal of a spatially mobilized plane, the new model is called the

The spatially mobilized plane could be determined by

According to the geometric relationship shown in

The cosine of the normal direction of the spatially mobilized plane relating to the axis I is

The cosine of the normal direction of the spatially mobilized plane relating to axes II and III are respectively:

Or, the equations could be combined as

From which the component of stress on the

The resultant force on the

Also, the normal stress

and

Since shear stress to normal stress on the spatially mobilized plane is a constant value

Under triaxial compression

With Formula (13), the strength failure envelope in the principal stress space and the strength failure curve on the octahedral plane could be plotted as in

The failure criteria are related only to the internal friction angle for noncohesive soil. After testing soil samples with internal friction angles φ of 5˚, 15˚, 25˚, 35˚, and 45˚, the authors plotted the corresponding strength failure circle on the π plane as shown in

Generalizing the

and

and the strength criterion would be

while

The D-P criterion can be generated by changing the circumcircle in the M-C criterion. It is also known as a generalized von Mises criterion:

The M-N criterion’s criterion is

The L-D criterion generated the fitting curve of the failure points, which formed a curved triangle on the octahedral plane, based on the true triaxial test result. The strength curve is in a linear relationship with the average spherical stress on the meridional plane that can be described as

or

According to the strength failure criterion

A comparison of the L-D and the

very similar to that of the

Further, a comparison between the L-D and

The strength failure surface on the principal stress plane and the strength failure circle on the π plane can be derived from the L-D criterion. While the soil internal friction angle increases at 5˚, 10˚, 15˚, 20˚, 25˚, 30˚, 35˚, and 40˚, the strength failure surface and strength failure circle increase their radius at the same time, as shown in

Similarly, for the

The following study reveals how soil shearing resistance changes along with the change of principal stress ratio b under different combinations of soil internal friction angles φ and spherical stresses on the π plane. As shown in

Loess soil structure strength is highly correlated with the soil’s outstanding physical and structural properties. However, its strength stability drops significantly when it loses its protogenic structure. With the support of data from the Yichuan Xing et al. true triaxial test [

In this study, the authors conducted true triaxial tests of 4 kinds of intact loesses under conditions of consolidation and drain. Tests were completed with the newly developed true triaxial apparatus, with 70 mm × 70 mm × 140 mm specimens, from the Xi’an University of Technology [

Three confining pressures were applied, 100 kPa, 200 kPa, and 300 kPa, and the intermediate principal stress ratios were controlled at 0.00, 0.25, 0.50, 0.75, and 1.00 (

Four sets of test results were plotted for each type of loess sample.

The normal stress plane intersected with each of the major, intermediate, and minor normal stress axes at points

Loess Type | Loess Type | |||
---|---|---|---|---|

Intact loess ① | Intact loess ② | Intact loess ③ | Intact loess ④ | |

Moisture content (%) | 5.0 | 10.0 | 14.2 | 24.2 |

Dry density (g/cm^{3}) | 1.273 | 1.273 | 1.55 | 1.65 |

Liquid limit (%) | 35.3 | 35.3 | 37.8 | 40.0 |

Plastic limit (%) | 16.9 | 16.9 | 22.6 | 23.0 |

Loess Type | Loess Type | |||
---|---|---|---|---|

Intact loess ① | Intact loess ② | Intact loess ③ | Intact loess ④ | |

Confining pressure (σ^{3}/kPa) | 100, 200, 300 | |||

Intermediate principal stress ratio (b) | 0.0, 0.25, 0.50, 0.75, 1.0 |

The

On the octahedral plane, the shearing resistances of the L-D criterion and the

True triaxial test results verified the linear relationship between shear stress and normal stress on the

This research was supported by National Natural Science Foundation of China and the Shaanxi Key Laboratory of Loess Mechanics and Engineering of China.

Shao, S., Shao, S.J., Zhang, Y. and Chen, C.L. (2017) Novel Soil Strength Criterion Compared with Conventional Criteria. Geomaterials, 7, 25-39. http://dx.doi.org/10.4236/gm.2017.71003