فرمول های ساده شده برای ظرفیت تحمل لرزه ای فونداسیون نواری کم عمق
Abstract
1- Introduction
2- Problem definition and theoretical framework
3- Cohesive-frictional soil (γ ≠ 0, c ≠ 0, ϕ ≠ 0)
4- Purely cohesive soil (γ ≠ 0, c = cu, ϕ = 0)
5- Summary of results and ultimate failure envelopes
6- Conclusions
References
Abstract
The seismic bearing capacity of shallow foundations is affected by inertia forces acting both on the structure and in the supporting soil. Even though the former have been recognised to play often the major role, by increasing the horizontal load and the overturning moment transferred to the foundation, both of them must be taken into account in the seismic design of foundations. Using a pseudostatic approach and based on the upper bound theorem of limit analysis, a comprehensive set of formulas is derived for the computation of the seismic bearing capacity of strip footings resting on cohesive-frictional and purely cohesive soils. Results are given in terms of: (i) reduction coefficients for the Terzaghi's equation of the vertical bearing capacity and (ii) ultimate failure envelopes in the space of normalised loading variables. These formulas extend to more general conditions other literature results, allowing to take into account easily the effects of inertia forces acting both on the superstructure (load inclination and eccentricity) and into the foundation soil. The reliability of the proposed equations, suitable for the design practice, is verified through a thorough comparison with other rigorous and approximate solutions.
Introduction
Many studies on the seismic bearing capacity of shallow foundations have shown that inertia forces acting on the structure and in the supporting soil tend to reduce the bearing capacity under seismic conditions. Most works on this topic have been carried out with a pseudostatic approach [18,22,23,25,3,29,30,32,34,35,5,6,9], by adopting: (i) different methods (numerical or theoretical) and theories (limit equilibrium, limit analysis or method of characteristics); (ii) different constitutive assumptions for the soil (purely frictional, purely cohesive or cohesive-frictional); (iii) different hypotheses on the inertia forces on the soil (with or without the vertical component) and (iv) on the structure (equal to or a fraction of those acting on the soil). Despite the fact that structure inertia has been recognised to play often the major role in reducing the seismic bearing capacity of shallow foundations, recent studies have highlighted possible situations in which even the effects associated to soil inertia can have a significant relevance, in the case of either frictional [22,6] or purely cohesive [24] soils. Moreover, most design codes recommend to take into account the effects of soil inertia in the seismic design of such systems (e.g.: [10]). Going to the design practice, the bearing capacity of shallow foundations under general loading is usually evaluated by means of simple approaches, neglecting any possible soil-structure interaction effect. In this context, codes and guidelines make use of closed form expressions for the bearing capacity, given in the form of either the classical Terzaghi's formula [1,17] or complete three-dimensional failure envelopes [10]. With this respect, only few works in the literature provide empirical formulas including inertia forces both on the structure and into the soil. As far as spread footings on cohesive-frictional soils are concerned, Budhu and Al-Karni [3], Paolucci & Pecker [23] and Cascone et al. [5] provide reduction factors for the vertical bearing capacity. However, Budhu and Al-Karni [3] consider the same accelerations into the soil and the structure; Paolucci & Pecker [23] do not contemplate the effects of the structure inertia on the Nc and Nq bearing capacity factors, while Cascone et al. [5] refer only to the effects of the seismic action on the Nγ term, thus resulting in a limited applicability of the proposed formulas. Only very recently, Cascone & Casablanca [6] proposed empirical expressions for the reduction coefficients, derived from the best fit of numerical results.