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This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary K0${{K}_0}$ values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with K0=1${K}_{0}=1$. It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between 5π3$\frac{{5\pi }}{3}$ and 11π6$\frac{{11\pi }}{6}$ or on the specific line of θ=11π6$\theta = \frac{{11\pi }}{6}$. The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils. [ABSTRACT FROM AUTHOR]

In this work, an approximate analytical solution (AS) is presented to evaluate the radiative thermal exchange through a gaseous participating medium composed of H2O, CO2, and CO, which is valid for the product values of pressure path‐length (PL) from 0.06 to 20 atm m and temperatures (T) from 300 K to 2100 K. The Spence root weighting method is used to approximate the exact solutions. For each set of PL;T $\mathrm{PL}{\rm{;}}T$, the value of exact spectral emissivity and absorptivity ελ ${\varepsilon }_{\lambda }$ and aλ ${a}_{\lambda }$ for the gas mixture is calculated using the AS, the Hottel graphical method (HGM) and the proposed approximate solution. The weaker adjustment was achieved in the modeling of the HGM, with a mean deviation obtained of ±15% and ±20% for 43.8% and 56.3% of the data evaluated, respectively, while the best indices were obtained in the estimation of the proposed method, with a mean deviation obtained of ±10% and ±15% for 81.3% and 98.1% of the available data, respectively. In all cases, the agreement of the proposed model with the available experimental data is good enough to be considered satisfactory for practical design. [ABSTRACT FROM AUTHOR]

This paper presents analytical solutions for the finite expansion problems of a spherical or cylindrical cavity, using a simple yet novel graphical approach recently proposed by Chen & Abousleiman in 2022, in both original Cam Clay (OCC) and modified Cam Clay (MCC) soils under undrained conditions. It is shown that, for a soil mass subjected to isotropic in situ stress conditions, the stress paths in the deviatoric plane for the spherical and cylindrical cavity expansions turn out to be two straight lines, which correspond to Lode angles equal to 11π6$\frac{{11\pi }}{6}$ and 5π3$\frac{{5\pi }}{3}$, respectively. The desired limiting cavity pressure therefore can be directly and accurately evaluated through simple numerical integration with respect to the mean effective stress, while the relationship between the internal cavity pressure and the cavity radius, the cavity expansion curve, may be equally conveniently determined. Numerical results obtained from the current graphical method, for a range of the values of over consolidation ratio considered, compare extremely well with those from the conventional semianalytical formulations of the undrained cavity problem that involve solving a system of coupled governing differential equations. It is interesting to note that the representative and approximate solution developed by Collins & Yu in 1996 indeed is a correct one for the spherical cavity expansion problem, and, with minor modifications, will be applicable for the accurate calculation of the responses of the cylindrical cavity as well. [ABSTRACT FROM AUTHOR]

Gardner's (1956, https://doi.org/10.2136/sssaj1956.03615995002000030006x) transient method of measuring the hydraulic conductivity function of unsaturated media has been largely used, together with the improved graphical method proposed by Kunze and Kirkham (1962, https://doi.org/10.2136/sssaj1962.03615995002600050006x) to account for the impedance effect resulting from using a low hydraulic conductivity ceramic disk in porous plate testing. These methods are nowadays seldom used, since they have been replaced by numerical back analysis and methods for parameter optimization. Based on tests carried out on a specific device allowing to determine the water retention and transport properties of water in a coarse granular media at low suctions (up to 50 kPa), it was found necessary to account (i) for impedance effects and (ii) for the effects of nonconstant suction increments, as is often the case when using the hanging column technique. A new method is proposed to account for impedance effects, based on an analytical solution of the equations governing water transfer. The validity of this method is tested by considering experimental data from three distinct materials: a coarse green roof volcanic substrate, poorly graded sand, and undisturbed silty clay. Compared to the graphical method Kunze and Kirkham's method, it is less operator‐dependent and hence more objective. It is also simpler than numerical back analysis methods, since it does not require any use of numerical code or parameter optimization algorithm, providing a more direct and reliable access to the hydraulic conductivity. An analytical solution is also proposed to solve the problem resulting from the application of a nonconstant suction increment. Key Points: Gardner developed the first analytical method for determining the hydraulic conductivity function based on transient outflow dataKunze and Kirkham developed a graphical method to account for impedance effects, that is nowadays replaced by numerical back analysisThe new proposed analytical method appears to be more reliable than Kunze and Kirkahm's method and simpler than numerical back analysis [ABSTRACT FROM AUTHOR]

Lossy mode resonance (LMR) is an optical resonance phenomenon developed in the past decade, which has been researched for sensors and filters due to its high sensitivity, low loss, and broad tunable range. As a novel technology, if an analytical mathematical model for some fundamental questions like how to design the resonance wavelength, surrounding sensitivity, resonance width, and resonance depth, it will be guiding significance to its development. Herein, this paper develops a generalized Fabry–Perot resonance theory for LMR, where the oblique incidence, cavity loss, and dispersion of substrate and cavity are comprehensively considered, and the consistency of this model and a more rigorous guided wave optics model have been verified. Then, analytical mathematical models are established and analyzed, and the designing criterion for LMR‐based optical devices is proposed. After intensive reviewing the work of predecessors, the previous experimental results are consistent with the prediction of this model, and this model can also provide some new ideas that have not been researched yet. As an assistant to wave optics theory, this paper provides a second perspective to understand LMR phenomenon, and it is hoped the analytical solutions for LMR can be a guide for designing optical devices. [ABSTRACT FROM AUTHOR]

Thermal conductivity is an essential parameter in heat transfer models including soil‐water systems. Herein, an Internet of Things (IoT) tool and a computational method are advanced for vertically resolving in situ thermal conductivity values in soil‐groundwater systems. A demonstrative application of this approach at a former petroleum refinery is presented. A line heat source is co‐located with a vertical string of in situ temperature sensors. Five‐minute multiple level temperature data were collected before, during, and after a 100‐min long heating period. Vertically distributed temperature data are transformed into vertically discretized thermal conductivity values using an analytical solution. Results fall in the range of thermal conductivity values reported in the literature. Specifically, estimated thermal conductivity values from 0.3 to 7.3 m below ground surface range between 0.7 and 5.4 (W/m/C) with the highest values occurring in media with greater water content. Overall, the advanced method in this study provides a pragmatic approach for vertically resolving subsurface thermal conductivity values applicable for many scientific disciplines. [ABSTRACT FROM AUTHOR]

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (Ss) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and Ss of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test. [ABSTRACT FROM AUTHOR]