Pit latrines and their impacts on groundwater quality: a systematic review.

BackgroundPit latrines are one of the most common human excreta disposal systems in low-income countries, and their use is on the rise as countries aim to meet the sanitation-related target of the Millennium Development Goals. There is concern, however, that discharges of chemical and microbial contaminants from pit latrines to groundwater may negatively affect human health.ObjectivesOur goals were to a) calculate global pit latrine coverage, b) systematically review empirical studies of the impacts of pit latrines on groundwater quality, c) evaluate latrine siting standards, and d) identify knowledge gaps regarding the potential for and consequences of groundwater contamination by latrines.MethodsWe used existing survey and population data to calculate global pit latrine coverage. We reviewed the scientific literature on the occurrence of contaminants originating from pit latrines and considered the factors affecting transport of these contaminants. Data were extracted from peer-reviewed articles, books, and reports identified using Web of ScienceSM, PubMed, Google, and document reference lists.DiscussionWe estimated that approximately 1.77 billion people use pit latrines as their primary means of sanitation. Studies of pit latrines and groundwater are limited and have generally focused on only a few indicator contaminants. Although groundwater contamination is frequently observed downstream of latrines, contaminant transport distances, recommendations based on empirical studies, and siting guidelines are variable and not well aligned with one another.ConclusionsIn order to improve environmental and human health, future research should examine a larger set of contextual variables, improve measurement approaches, and develop better criteria for siting pit latrines

A theoretical link between gradient and nonlocal elasticity models, including higher order boundary conditions

The paper presents a recently developed rational derivation of the strain gradient elasticity model from the nonlocal (or integral) model. This kind of derivations are generally recovered just by an expansion into a Taylor series of the nonlocal strain field up to a certain order, and then operating the integration (or averaging) over the spatial interaction domain. The latter procedure is fully consistent when the analysis is performed over an unbounded domain, but when a classical bounded domain is analyzed it lacks in reproducing the so-called higher-order boundary conditions. In the present contributions the complete derivation is achieved employing an extended version of the Principle of Virtual Power (PVP), written in a special form in order to comply with the nonsimple nature of the nonlocal material. Namely, extra terms are invoked in both internal and external virtual power

A symmetric BEM approach to strain gradient elasticity for 2D static boundary-value problems

The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 4 1/ r . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a research communication wherein a part of the results, being elaborated within a more general paper are reported

Symmetric Galerkin boundary element method.

This review concerns a methodology for solving numerically, to engineering purposes, boundary and initial-boundary value roblems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form; the discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager's sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions, some quadratic forms have a clear energy meaning, variational properties characterize the solutions and other results, invalid in traditional boundary element methods, enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, computer implementations. Areas and aspects which at present require further research are dentified and comparative assessments are attempted with respect to traditional boundary integral-element methods

Strain gradient elasticity within the symmetric BEM formulation

The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 1/ r 4 . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a research communication wherein some results, being elaborated within a more general paper [1], are reported

Incremental elastoplastic analysis for active macro-zones

In this paper a strategy to perform incremental elastoplastic analysis using the symmetric Galerkin boundary element method for multidomain type problems is shown. The discretization of the body is performed through substructures, distinguishing the bem-elements characterizing the so-called active macro-zones, where the plastic consistency condition may be violated, and the macro-elements having elastic behaviour only. Incremental analysis uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The nonlinear analysis does not use updating of the elastic response inside each plastic loop, but at the end of the load increment only. This is possible by using the self-stress matrix, both, in the predictor phase, for computing the stress caused by the stored plastic strains, and, in the corrector phase, for solving a nonlinear global system, which provides the elastoplastic solution of the active macro-zones. The use of active macro-zones gives rise to a nonlocal and path-independent approach, which is characterized by a notable reduction of the number of plastic iterations. The proposed strategy shows several computational advantages as shown by the results of some numerical tests, reported at the end of this paper. These tests were performed using the Karnak.sGbem code, in which the present procedure was introduced as an additional module