Seismic failure mechanisms for loaded slopes with associated and nonassociated flow rules

Seismic failure mechanisms were investigated for soil slopes subjected to strip load with upper bound method of limit analysis and finite difference method of numerical simulation,considering the influence of associated and nonassociated flow rules.Quasi-static representation of soil inertia effects using a seismic coefficient concept was adopted for seismic failure analysis.Numerical study was conducted to investigate the influences of dilative angle and earthquake on the seismic failure mechanisms for the loaded slope,and the failure mechanisms for different dilation angles were compared.The results show that dilation angle has influences on the seismic failure surfaces,that seismic maximum displacement vector decreases as the dilation angle increases,and that seismic maximum shear strain rate decreases as the dilation angle increases.

Influences of nonassociated flow rules on seismic bearing capacity factors of strip footing on soil slope by energy dissipation method

Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient concept was adopted for seismic bearing capacity calculations. A multi-wedge translational failure mechanism was used to obtain the seismic bearing capacity factors for different seismic coefficients and various inclined angles. Employing the associated flow rule, numerical results were compared with the published solutions. For bearing capacity factors related to cohesion and equivalent surcharge load, the maximum difference approximates 0.1%. However, the difference of bearing capacity factor related to unit weight is larger. With the two flow rules, the seismic bearing capacity factors were presented in the form of design charts for practical use. The results show that seismic bearing capacity factors related to the cohesion, the equivalent surcharge load and the unit weight increase greatly as the dilatancy angle increases, and that the nonassociated flow rule has important influences on the seismic bearing capacity.

Influences of nonassociated flow rules on three-dimensional seismic stability of loaded slopes

The influences of soil dilatancy angle on three-dimensional （3D） seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-static coefficient concept. Extended Bishop method and Boussinesq theorem were employed to establish the stress distribution along the rupture surfaces that are required to obtain the rate of internal energy dissipation for the nonassociated flow rule materials in rotational collapse mechanisms. Good agreement was observed by comparing the current results with those obtained using the translational or rotational mechanisms and numerical finite difference method. The results indicate that the seismic stability of slopes reduces by decreasing the dilatancy angle for nonassociated flow rule materials. The amount of the mentioned decrease is more significant in the case of mild slopes in frictional soils. A nearly infinite slope under local loading, whether its critical failure surface is 2D or 3D, not only depends on the magnitude of the external load, but also depends on the dilataney angle of soil and the coefficient of seismic load.

AN APPLICATION OF NONSYMMETRIC LAX-MILGRAM LEMMA TO NONASSOCIATED PLASTICITY

Based on a general assumption for plastic potential and yield surface, some properties of the nonassociated plasticity are studied, and the existence and uniqueness of the distribution of incremental stress and displacement for work-hardening materials are proved by using nonsymmetric Lax-Milgram lemma, when the work-hardening parameter

Slope stability analysis considering joined influences of nonlinearity and dilation

The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.

Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties

The generating function for generating integer sequence of Aunu numbers of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator on the function for where the operation induces addition or subtraction on the pairs of ai, aj elements which are consecutive pairs of elements obtained from a generating set of some finite order. The paper identifies that the set of the generated pairs of integer sequence is non-associative. The paper also presents the graph theoretic applications of the integers generated in which subgraphs are deduced from the main graph and adjacency matrices and incidence matrices constructed. It was also established that some of the subgraphs were found to be regular graphs. The findings in this paper can further be used in coding theory, Boolean algebra and circuit designs.

Influence of Nonassociativity on the Bearing Capacity Factors of a Circular Footing

Numerical computations using the finite difference code FLAC (fast Lagrangian analysis of continua) are presented to evaluate the soil bearing capacity factors Nc,Nq and Nγ for circular smooth and rough footings. The influence of nonassociative flow rule on the ultimate bearing capacity of a circular footing is investigated. The footing rests on the surface of a homogeneous soil mass and a Mohr-Coulomb yield criterion have been assumed for the soil behavior. The values of ultimate bearing capacity factors Nc,Nq and Nγ are obtained for a wide range of values of the friction angle for five different values of the dilation angle. The values from the numerical simulation are found to decrease significantly with the increase of nonassociativity of the soil. The results are compared with those derived from existing classical solutions.

On Free Pre-Lie Algebras

In this paper, we find Hall-Shirshov type bases for free pre-Lie algebras. We show that Segal＇s basis of a free pre-Lie algebra is a type of these bases. We give a nonassociative GrSbner-Shirshov basis S for a free pre-Lie algebra such that Irr（S） is a monomial basis （called normal words） of a free pre-Lie algebra, where Irr（S） is the set of all nonassociative words, not containing maximal nonassociative words of polynomials from S. We establish the Composition-Diamond lemma for free pre-Lie algebras over the basis of normal words and the degree breadth lexicographic ordering.