Non-unique Estimates Research Articles

Determination of load combination factors for code calibration

Semi-probabilistic methods are widely used for structural engineering design and assessment. In such methods, the safety and performance adequacy of structures are typically tied to partial safety factors for load and resistance, and load combination factors. There exist some heuristic strategies for estimating these partial factors, such as the design value method and first order reliability coefficient method. However, when adopted for the estimation of load combination factors, these strategies are either inaccurate or have non-unique estimates. Excessive conservatism in factor estimates is not desirable, particularly for the performance assessment of existing structures. In this study we propose a method for estimating load combination factors using a matrix linear algebra approach. Specifically, we develop a closed-form analytical expression to estimate unique load combination factors for typical code calibration problems. A comparative study of the existing heuristic approaches with the new approach is presented and demonstrated on two case studies. It is shown that the proposed method offers a valuable means of deriving load combination factors: one that avoids hueristics, and conservatism.

Special Issue on Toxics and Pathogens in the Environment

Special Issue on Toxics and Pathogens in the Environment

Field Experiment and Data Analysis of a Constant-Head Injection Test with Skin Effects in a Low-Transmissivity Aquifer

In a confined, silty sand aquifer of low transmissivity, constant-rate pumping can rapidly dewater the pumping well without creating measurable drawdown at nearby observation wells. To overcome this difficulty, a constant-head test is performed by overflowing the test well by water injection. The difference between the injection rate and the overflow rate directly gives the cumulative volume Vw(t) entering the aquifer, which is characteristic of the aquifer hydrogeologic properties and can be used for parameter estimation. The field experiments include two constant-head injection tests, CHIT1 and CHIT2, performed at two different wells, respectively. Semilog plot of t/Vw(t) of CHIT2 indicates little or no skin, and the two unknown parameters of the storage coefficient and transmissivity can be uniquely determined in a similar way by the well-known Jacob semilog method. Semilog plot of t/Vw(t) of CHITl, however, shows the ex istence of well skin, and a curve matching method is developed for estimatiog the four pertinent parameters. Among them, the aquifer transmissivity can be uniquely determined while the skin transmissivity, the skin thickness, and the storage coefficient are obtained in appropriate ranges. To avoid non-unique estimates of aquifer parameters, therefore, the test well should be carefully constructed with complete and thorough well development to prevent skin region from happening. Due to the limitation of the site hydrogeology, only slug tests can be performed for the sake of validating transmissivity. The transmissivity values determined from the CHITs and from the slug tests are in good agreement, supporting the usefulness of the CHIT. The aquifer transmissivities estimated from CHITl and CHIT2 are within 14% difference, indicating that the aquifer is relatively homogeneous in the neighborhood of the two test wells.

A Method for Differentiating Nonunique Estimates of Membrane Transport Properties: Mature Mouse Oocytes Exposed to Glycerol

Measurement of the osmotic response of a cell in the presence of cryoprotectant facilitates the determination of permeability coefficients which, in turn, can be used to design cryopreservation protocols which minimize osmotic stress. One problem encountered in determining permeability coefficients, using the Kedem–Katchalsky (K-K) model of membrane permeability, is that several combinations of the three passive coupled transport coefficients, namely, hydraulic permeability (Lp, μm min−1 atm−1), solute permeability (Pgly, μm s−1), and the reflection coefficient (ς), can give a similar fit to the measured data. A method for determining the “correct” set of coefficients is suggested. The osmotic response of 10 metaphase II mouse oocytes was measured on perfusion with 1.5 mol L−1 glycerol at 24°C. For 8 of 10 oocytes perfused, two combinations of Lp, Pgly, and ς gave a predicted response which closely matched the measured osmotic response, depending upon the initial estimates supplied to the software for these parameters. For the remaining two oocytes, similar values for the permeability coefficients were generated regardless of the initial estimates. To determine the correct set of parameters, the K-K equations were used to predict experimental conditions for which volumetric histories would be distinctly different for the two sets of “best-fit parameters,” and then additional experimental data were compared to these predictions. Thus a further three oocytes were perfused with 0.2 or 0.5 mol L−1 glycerol in the absence of nonpermeating solute. In the presence of both 0.2 and 0.5 mol L−1 glycerol, Lp = 2.11 ± 0.69, Pgly = 0.0016 ± 0.0015, and ς = 0.44 ± 0.11 yielded a very poor fit to the measured response while Lp = 0.98 ± 0.70, Pgly = 0.0031 ± 0.0021, and ς = 0.91 ± 0.15 yielded a close fit to the measured response. Thus the latter combination of coefficients was taken to be correct.

Estimation of near‐surface elastic parameters using multicomponent seismic data

In multicomponent seismic reflection surveys, surface and near‐surface effects can severely deteriorate the quality of reflection data. Such effects are more pronounced on shear‐wave than on compressional‐wave profiles. Amplitude anomalies, statics, and strong coherent source‐generated noise (i.e., surface waves) are often associated with inhomogeneous, poorly compacted near‐surface sediments of the weathering layer. The magnitude of such effects increases when sources and receivers are deployed at or near the surface in proximity to such inhomogeneities. Near‐surface effects can be investigated with respect to their depth of occurrence by burying seismic sources and/or receivers at various depths below the inhomogeneous weathering layer. In this context, an experiment was conducted to collect multicomponent seismic field data on a borehole‐controlled test site in east Texas. Data were recorded on three‐component surface and buried receivers using a full‐vector wavefield surface source. Although the geology appears simple, results of modeling one or two components of the field data with synthetics yields nonunique estimates of elastic parameters. Effects of anisotropy and heterogeneities are better identified and estimated with full‐wavefield surface and buried receiver observations. Single fold data from buried receivers yield reflection events with higher signal‐to‐noise ratio than 30‐fold CDP surface data previously acquired in the same area.