Optimization Methods

The paper presents an elasto-plastic model for unsaturated soils that takes explicitly into account the mechanisms with which suction affects mechanical behaviour as well as their dependence on degree of saturation. The proposed model is formulated in terms of two constitutive variables directly related to these suction mechanisms: the average skeleton stress, which includes the average fluid pressure acting on the soil pores, and an additional scalar constitutive variable, 

'csi', related to the magnitude of the bonding effect exerted by meniscus water at the inter-particle contacts. The formulation of the model in terms of variables closely related to specific behaviour mechanisms leads to a remarkable unification of experimental results of tests carried out with different suctions. The analysis of experimental isotropic compression data strongly suggests that the quotient between the void ratio, e, of an unsaturated soil and the void ratio es, corresponding to the saturated state at the same average soil skeleton stress, is a unique function of the bonding effect due to water menisci at the inter-particle contacts. The same result is obtained when examining critical states at different suctions. Based on these observations, an elastoplastic constitutive model is developed using a single yield surface the size of which is controlled by volumetric hardening. In spite of this simplicity, it is shown that the model reproduces correctly many important features of unsaturated soil behaviour. It is especially remarkable that, although only one yield surface is used in the formulation of the model, the irreversible behaviour in wetting–drying cycles is well captured. Because of the behaviour normalisation achieved by the model, the resulting constitutive law is economical in terms of the number of tests required for parameter determination.

The paper presents a collaborative piece of research undertaken by seven research teams from different universities within the ‘Mechanics of Unsaturated Soils for Engineering’ (MUSE) network. The objective is to benchmark different approaches to constitutive modelling of mechanical and water retention behaviour of unsaturated soils by comparing simulations of suction-controlled and constant water content laboratory tests. A set of 13 triaxial and oedometer laboratory tests, covering the mechanical and water retention behaviour of an unsaturated compacted silty soil under a variety of stress paths, has been provided by one of the seven participating teams. This data set has been used by the other six teams for calibrating a constitutive model of their choice, which has been subsequently employed for predicting strains and degree of saturation in three of the 13 tests used for calibration, as well as in one ‘blind’ test for which experimental results had not been previously disclosed. By comparing predictions from all teams among themselves and against experimental data, the work highlights the capability of some of the current modelling approaches to reproduce specific features of the mechanical and water retention behaviour of unsaturated soils helping to identify potential areas of weakness where future research should focus. It also demonstrates the dispersion of results to be expected when different constitutive models, independently calibrated by different teams of researchers, are used to predict soil behaviour along the same stress path.

Rainfall is the most frequent triggering factor for landslides and the development of early warning systems has to take account of this. It is suggested that direct measurement of pore pressure gives the most reliable prediction of failure of a slope. The amount of rainfall can be only a crude indicator of failure as the processes that occur between rain falling on a slope and the resulting pore water pressure change are complex, highly non-linear and hysteretic. The paper describes high capacity tensiometers developed within the EU-funded MUSE Research Training Network that have been used for measuring suctions in slopes. High-capacity tensiometers are capable of direct measurement of pore water pressure down to −2 MPa and are also able to record positive pore water pressures. Two methods of field installation are discussed; one developed by ENPC in France uses a single tensiometer per hole, and the second technique, developed by Durham University in the UK, allows multiple tensiometers to be used at different depths within a single borehole. Continuous monitoring of pore water pressure has been carried out over several months and shows the responses to climatic events.

A unique facility for engineering and biological research has been established with the aim of improving fundamental understanding of the effects of climate change on slopes. This paper describes the building and monitoring of a full-scale embankment representative of UK infrastructure, the planting and monitoring of representative vegetation, and the construction of a system of sprinklers and covers to control climate. A summary of the results of the first experiments simulating predicted future UK climate and the response of the embankment is also presented. The information that has begun to be gathered is providing data related to the failure modes anticipated as a result of climate change and hence on the sustainability of UK infrastructure slopes.

Spatial variability of material properties is inherent in both natural soil deposits and earth structures, yet it is often ignored during geotechnical design. With the objective of developing novel methods for assessing the effects of soil variability on groundwater flow, this study presents a stochastic finite element model of seepage through a flood defense embankment with randomly heterogeneous material properties. Stochastic modeling is undertaken by means of a Monte Carlo simulation which involves a large number of finite element analyses, each with randomly varied porosity at element level, which leads to a corresponding random variation of both permeability and water retention properties across the embankment domain. This provides a statistical distribution of responses, such as total flow rate and time to reach steady state, instead of a single deterministic result as in conventional studies of seepage through unsaturated heterogeneous soils. As the degree of heterogeneity increases, water tends to flow along the most permeable paths inside the soil mass, resulting in an irregular shape of the predicted wetting fronts and pore pressure contours. The mean and standard deviation of the computed quantities strongly depend on the statistics of the input porosity field. Simulations are also conducted to compare the statistical variation of flow rate with and without dependency of the water retention curve on porosity. With recent growth in computer speed, stochastic finite element models based on the Monte Carlo approach can become a powerful design tool, especially if a quantitative assessment of geotechnical risks is required. Copyright © 2011 John Wiley & Sons, Ltd.

Several microwave-assisted digestion methods were tested at the Centro de Estudios Aplicados en Química laboratory in Quito, Ecuador, to determine the accuracy and performance efficiency of the mineralization process for the determination of total mercury in fish tissue by cold vapor atomic fluorescence spectrophotometry. The use of MARSEasyPrep high-pressure vessels, low amounts of reagents (1 cm 3 HNO 3 , 1 cm 3 H 2 O 2 , and 1 cm 3 HClO 4), an irradiation temperature of 210 • C, and 35 min of mineralization time resulted in accurate performance, with recoveries of certified reference material DORM-4 between 90.1% and 105.8%. This is better than the Association of Official Analytical Chemists 2015.01 method, which has a reported accuracy of 81%. The repeatability precision and intermediate precision were established at three concentration levels (0.167, 0.500, and 0.833 mg·kg −1) and expressed as the percentage of the relative standard deviation ranging from 1.5% to 3.0% and 1.7% to 4.2%, respectively. Further, the method was satisfactorily applied to analyze fortified samples of tilapia (Oreochromis niloticus), with recoveries ranging from 98.3% to 104.3%. The instrumental limits of detection and quantification were 0.118 µg·dm −3 and 0.394 µg·dm −3 , respectively.

Although conventionally described as purely dip-slip, faults at caldera volcanoes may have a strike-slip displacement component. Examples occur in the calderas of Olympus Mons (Mars), Miyakejima (Japan), and Dolomieu (La Reunion). To investigate this phenomenon, we use numerical and analog simulations of caldera subsidence caused by magma reservoir deflation. The numerical models constrain mechanical causes of oblique-slip faulting from the three-dimensional stress field in the initial elastic phase of subsidence. The analog experiments directly characterize the development of oblique-slip faulting, especially in the later, non-elastic phases of subsidence. The combined results of both approaches can account for the orientation, mode, and location of oblique-slip faulting at natural calderas. Kinematically, oblique-slip faulting originates to resolve the following: (1) horizontal components of displacement that are directed radially toward the caldera center and (2) horizontal translation arising from off-centered or “asymmetric” subsidence. We informally call these two origins the “camera iris” and “sliding trapdoor” effects, respectively. Our findings emphasize the fundamentally three-dimensional nature of deformation during caldera subsidence. They hence provide an improved basis for analyzing structural, geodetic, and geophysical data from calderas, as well as analogous systems, such as mines and producing hydrocarbon reservoirs.

Satellite mission GRACE provides monthly models of the global gravity field with unprecedented accuracy showing temporal variations of the Earth’s gravity field, including those caused by large-scale coseismic and postseismic processes in the region of the Sumatra 26.12.2004 earthquake. The observed postseismic crustal displacements were fitted well by a viscoelastic relaxation model assuming Burgers body rheology for the asthenosphere (60-220 km deep) with a transient viscosity as low as 4·1017 Pa·s and constant ~1019 Pa·s steady state viscosity in the 60–660 km depth range. However, even the low viscosity asthenosphere provides the amplitude of strain which gravity effect does not exceed 50% of the GRACE gravity variations, thus additional localized slip of about 1 m was suggested at downdip extension of the coseismic rupture. Postseismic slip at coseismic rupture or its downdip extension has been suggested by several authors but the mechanism of the postseismic fault propagation has never been investigated numerically. Depth and size of localized slip area as well as rate and time decay during the postseismic stage were either assigned a priory or estimated by fitting real geodesy or gravity data. In this paper we investigate postseismic rupture propagation by modelling two consequent stages. First we run a long-term, geodynamic simulation to self-consistently produce the initial stress and temperature distribution. At the second stage we simulate a seismic cycle using results of the first step as initial conditions. The second short-term simulation involves three substeps, including additional stress accumulation after part of the subduction channel was locked; spontaneous coseismic slip; formation and development of damage zones producing afterslip. During the last substep postseismic stress leads to gradual ~1 m slip localized at three faults around ~100 km downdip extension of the coseismic rupture. We used displacement field caused by the slip to calculate pressure and density variations and to simulate gravity field variations. Wavelength of calculated gravity anomaly fits well to the real data and its amplitude provides about 60 % of the observed GRACE anomaly. Importantly that surface displacements caused by estimated afterslip are much smaller than those registered by GPS networks. As a result cumulative effect of Burgers rheology viscoelastic relaxation (which explains registered GPS displacements and about a half of gravity variations) plus postseismic slip predicted by damage rheology model (which causes much smaller surface displacements but provides another half of the GRACE gravity variations) fits well to both sets of real data. Hence presented numerical modelling based on damage rheology supports postseismic downdip rupture propagation previously hypothesized from the GRACE gravity data.

A new suction probe, the WF-DU tensiometer, has been developed by Wykeham Farrance in collaboration with Durham University. The performance of the new suction probe is assessed in terms of the minimum negative value of pressure that can be measured by the probe before cavitation. A series of tests performed on four different units of the same design of tensiometer is presented and the results are discussed in relation to the procedure adopted for the saturation of the probe prior to the tests. Other aspects of the tensiometer response are interpreted by making reference to similar experiments published in the literature. All tensiometers used in this work are calibrated in the positive range of pressure. The extrapolation of such calibration to the domain of negative pressures is validated by using the tensiometer to measure known values of suction.

Loose particles in moist granular materials, such as unsaturated soils, are held together by capillary forces acting at the interparticle contacts. The magnitude of these capillary forces depends on the surface tension and on the radius of curvature of the menisci, which in turn depends on the contact angle of the air/water interface against the surface of the solid particles. Menisci are usually assumed to be predominantly concave on the side of the air with negative water pressure (relative to the atmosphere). Evidence for this comes from direct bservations at the millimetre scale or from theoretical assumptions. This note presents data from environmental scanning electron microscopy of particles at the micrometre scale that contradict this assumption and show for the first time that, for a given water content, the contact angle between air/water interfaces and grains can give rise to a variety of meniscus shapes, with curvatures not all concave on the side of air. It was found that the curvature of water menisci, in both idealised and natural granular materials with variable particle sizes, shapes and nature, could vary along the border of a single meniscus or differ from one point to another separated at the micrometre scale, and is also dependent on the nature of materials and wetting history. Menisci can have both predominantly convex shapes (corresponding to compressive capillary pressure) and predominantly concave shapes (corresponding to tensile capillary water pressure). These observations confirm the importance of surface tension in the air/water interfaces (often also referred to as ‘contractile skin’) in holding particles together.

The paper presents a benchmarking study carried out within the ‘Mechanics of Unsaturated Soils for Engineering’ (MUSE) network aimed at comparing different techniques for measurement and control of suction. Techniques tested by the eight ‘Mechanics of Unsaturated Soils for Engineering’ research teams include axis-translation (pressure plate and suction-controlled oedometer), high capacity tensiometer and osmotic technique. The soil used in the exercise was a mixture of uniform sand, sodium bentonite (active clay) and kaolinite (non-active clay), which were all commercially available. Samples were prepared by one team and distributed to all other teams. They were normally consolidated from slurry under one-dimensional conditions (consolidometer) to a given vertical stress. The water retention characteristics of the initially saturated specimens were investigated along the main drying path. Specimens were de-saturated by applying suction through the liquid phase when using an axis-translation technique or osmotic method and de-saturated by air-drying, when suction was measured using high-capacity tensiometers. In general, the same technique was tested by at least two teams. The water retention curves obtained using the different techniques are compared and discrepancies are discussed in the paper.

In this article, multi-objective optimization of braced frames is investigated using a novel hybrid algorithm. Initially, the applied evolutionary algorithms, ant colony optimization (ACO) and genetic algorithm (GA) are reviewed, followed by developing the hybrid method. A dynamic hybridization of GA and ACO is proposed as a novel hybrid method which does not appear in the literature for optimal design of steel braced frames. Not only the cross section of the beams, columns and braces are considered to be the design variables, but also the topologies of the braces are taken into account as additional design variables. The hybrid algorithm explores the whole design space for optimum solutions.
Weight and maximum displacement of the structure are employed as the objective functions for multi-objective optimal design. Subsequently, using the weighted sum method (WSM), the two objective problem are converted to a single objective optimization problem and the proposed hybrid genetic ant colony algorithm (HGAC) is developed for optimal design. Assuming different combination for weight coefficients, a trade-off between the two objectives are obtained in the numerical example section. To make the final decision easier for designers, related constraint is applied to obtain practical topologies. The achieved results show the capability of HGAC to find optimal topologies and sections for the elements.

Soil-water retention curves (SWRCs) can be determined using high-suction tensiometers (HSTs) following two different procedures that involve either continuous or discrete measurement of suction. In the former case, suction measurements are taken while the sample is permanently exposed to the atmosphere and the soil is continuously drying. In the latter case, the drying or wetting process is halted at different stages to ensure equalization within the sample before measuring suction. Continuous drying has the advantage of being faster; however, it has the disadvantage that the accuracy of mass measurements (necessary for the determination of water content) is affected by the weight and stiffness of the cable connecting the HST to the logger. To overcome this problem, an alternative continuous drying procedure is presented in this paper in which two separate but nominally identical samples are used to obtain a single SWRC; one sample is used for the mass measurements, while a second sample is used for suction measurements. It is demonstrated that the new continuous drying procedure gives SWRCs that are similar to those obtained by discrete drying.