Journal of Engineering Mechanics

Motivated by the growing interest in suppressing vibrations with supplemental rotational inertia, this paper examines and constructs the basic frequency-response functions and subsequently derives the corresponding causal time-response functions of elementary mechanical networks that involve the inerter, a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This is achieved by extending the relationship between the causality of a time-response function and the analyticity of its corresponding frequency-response function to the case of generalized functions. This paper shows that all frequency-response functions that exhibit singularities along the real frequency axis need to be enhanced with the addition of a Dirac delta function or with its derivative, depending on the strength of the singularity. It is shown that because of the inerter, some basic time-response functions exhibit causal oscillatory response, in contrast to the decaying exponentials that originate from dashpots. Most importantly, the inerter emerges as an attractive response-modification element because in some cases it absorbs the singular response of the solitary spring or dashpot.

This paper investigates a new and simplified nonlinear approach considering the softening effect of the soil–pile interface to predict the settlement of a single pile and a pile group. The approach adopts a nonlinear model described by a piecewise function to simulate the relationship between skin friction and soil–pile relative displacement. The relationship between the pile-bottom load and the settlement also is addressed in a piecewise function. A simplified calculation approach is proposed to predict the settlement on pile head. The results of the proposed approach and those of the published literature and the field test data are compared. Correction made by the proposed approach also is validated. Numerical results show that the proposed approach generates a reasonable settlement prediction on pile head. Parametric analysis compares the influence of different parameter values on the load-settlement curve on the pile head.

In this paper, a new fuzzy distance index is proposed to measure the effect of the fuzzy distribution parameters of random model inputs on the statistical characteristics of model output. First, the definition of the distance of fuzzy numbers is introduced. The effect of fuzzy distribution parameters is measured by using the average distance between the unconditional membership function of the statistical characteristics of output and the conditional membership function with one fixed distribution parameter. Second, to reduce the computational cost of the proposed index, the extended Monte Carlo simulation (EMCS) and unscented transformation-based Kriging surrogate model method (UT-Kriging) are adopted. Finally, four examples are used to verify the accuracy and the efficiency of the proposed methods.

In the dispersion theory of solute transport in groundwater flow, the dispersion coefficient is regarded as proportional to the $n$th power of groundwater velocity, where $n$ varies from 1 to 2. The present study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport for any permissible value of $n$. For a nonhomogeneous medium, groundwater velocity is considered as a linear function of space and analytical solutions are obtained for $n=1$, 1.5, and 2.0. For $n=1$, the dispersivity (ratio of dispersion coefficient and velocity) remains uniform, representing a homogeneous medium, while it varies with position in the finite domain (aquifer) for any other permissible value of $n$ representing the heterogeneity of the medium. From a hydrological point of view, the derived solutions are of significant interest and are of value in the validation of numerical codes. A generalized integral transform technique (GITT) with a new regular Sturm-Liouville problem (SLP) is used to derive analytical solutions in a finite domain. The analytical solutions elucidate the important features of solute transport with Dirichlet-type nonhomogeneous and homogeneous conditions assumed at the origin and at the far end of the finite domain, respectively. The first condition expresses a uniform continuous source of the dispersing mass. The analytical solutions are also compared with numerical solutions and are found to be in perfect agreement. The effect of a Peclet number on the solute concentration pattern is also investigated.

A mechanistic-cum-stochastic theory describing the sediment transport phenomenon from the particle scale of entrainment to the continuum scale of bedload flux under a steady unidirectional flow over a compact sediment bed is developed. The sediment particles, considered as discrete spherical particles, are subjected to hydraulically smooth, transitional, and rough wall-shear flows. At the particle scale, the hydrodynamic forces acting on a sediment particle resting over three closely packed bed particles are analyzed. The criteria for entrainment threshold in rolling, sliding, and lifting modes are determined introducing the velocity fluctuations. Comparison of the computed threshold curves with the experimental data reveals that the entrainment threshold primarily belongs to the transition of the sliding to the lifting modes. Then, at the particle scale, the entrainment probabilities in rolling, sliding, and lifting modes for a given median size of sediment particles are obtained. The rolling and sliding probabilities increase with an increase in Shields parameter, and after attaining their individual peak values, they decrease, while the lifting probability increases. Finally, the bedload flux, in a continuum scale, is obtained using the lifting probability.

Recent work has shown the applicability of Bayesian inference techniques, which use a physics-based representation of the structure of interest, to structural health monitoring (SHM) tasks, such as damage identification. This paper focuses on Bayesian filtering algorithms that provide a way to detect, localize, and identify damage in an online fashion. These algorithms aim to identify the states and parameters of the structure, and take into account noise in the system and measurements, and are thus well fitted to quantify uncertainties. In this paper, a thorough review of these algorithms is provided, primarily the particle filter and the unscented Kalman filter. Estimates of the posterior probability-density functions (PDFs) obtained with these filters are compared for three nonlinear mechanical systems, thus providing an insight into the filters’ behavior and their ability to quantify uncertainties. Furthermore, novel techniques are introduced to take into account non-Gaussian noise and non-Gaussian posterior PDFs by means of a novel framework that expands the nonlinear Kalman filtering theory to non-Gaussian baseline distributions.

A description of yield surfaces in the axial-torsional-hoop stress space, which is able to capture the yield surface expansion/contraction, translation, rotation, affine deformation, and distortion, is constructed under a three-dimensional point of view. Starting from the yield surface theory of cubic polynomials in two-dimensional spaces, the authors first clarify the relations between it and the Kurtyka and Życzkowski theory which exhibits excellent performance of fitting the experimental data of yield points in two-dimensional stress space. Because an arbitrary cubic polynomial does not guarantee that its zero-level locus is closed, the authors apply projective transformation of the Weierstrass normal form of cubic curves in the two-dimensional space in order to obtain closed cubic yield loci. Following the derivation of closed cubic yield loci, the authors investigate the convexity of the yield loci. Then the two-dimensional theory is extended into a standard formulation of convex closed cubic polynomial in the three-dimensional stress space with consideration of preserving the closure and the convexity of yield surface, and the orthotropic and isotropic symmetry of the convex closed cubic polynomial is explored. Furthermore, a geometrically meaningful identification with three stages is proposed to estimate the values of coefficients of the polynomials from the experimental data of yield points in the axial-torsional-hoop stress space. Validation is performed by checking the estimated results of yield surface and experimental yield points and shows that almost all probed yield points are located directly on or near the estimated evolving yield surfaces. Therefore the convex closed cubic polynomial and three-stage identification provides reliable visualization of the yield surfaces which unite individual yield points to present the global information.

Water-driven hydraulic fractures with high flow rates are more common now than ever in the oil and gas industry. Although these fractures are small, the high injection rate and low viscosity of the water lead to high Reynolds numbers and potential turbulence in the fracture. This paper presents a semianalytical solution for a blade-shaped [Perkins-Kern-Nordgren (PKN)] geometry hydraulic fracture driven by a turbulent fluid in the limit of zero fluid leak-off to the formation. Turbulence in the PKN fracture is modeled using the Gaukler-Manning-Strickler parametrization, which relates the flow rate of the water to the pressure gradient along the fracture. The fully turbulent limit is considered with no transition region anywhere at any time, but the effect of fracture toughness on crack propagation is not considered. The key parameter in this relation is the Darcy-Weisbach friction factor for the roughness of the crack wall. Coupling this turbulence parametrization with conservation of mass allows a nonlinear partial differential equation (PDE) to be written for the crack width as a function of space and time. By way of a similarity ansatz, a semianalytical solution is obtained using an orthogonal polynomial series. Very rapid convergence is found by embedding the asymptotic behavior near the fracture tip into the polynomial series; a suitably accurate solution is obtained with two terms of the series. This closed-form solution facilitates clear comparisons between the results and parameters for laminar and turbulent hydraulic fractures. In particular, it resolves one of the well-known problems whereby calibration of models to data has difficulty simultaneously matching the hydraulic fracture length and wellbore pressure.

The time-variant system reliability analysis is a challenging and significant topic, which also faces the common obstacles of traditional system reliability methods such as combination explosion and unclear correlation information. In this paper, the probability density evolution method (PDEM) for two types of time-variant system reliability analysis is proposed. First, the system reliability is classified into two types, and the corresponding equivalent performance functions are given, which are further extended to time-variant structural systems. Second, based on the single equivalent performance function, the generalized density evolution equation (GDEE) for time-variant structural system is derived in two different ways. Third, the GDEE is solved by the Dirac sequence method and the time-variant system reliability is evaluated. Finally, several numerical examples are investigated to illustrate the accuracy and effectiveness of proposed method.

Semiactive devices offer the opportunity to customize the device response, and thus to customize the overall structural hysteretic response. However, they are actively controlled and thus entail a significant addition of complexity and potentially cost for the added performance. This study introduces the concept, design, and experimental validation of a direction- and displacement-dependent (D3) device using viscous damping. D3 devices provide viscous damping in any individual or multiple quadrants of the force-displacement response. Previously only achievable using semiactive devices, this research presents an entirely passive and thus more robust and lower cost device. The D3 device design concept is presented and experimental tests are undertaken on a prototype device. Sinusoidal displacement inputs provide a range of velocity inputs and device forces used to characterize the damping behavior of the prototype and illustrate the ability to provide controllable viscous damping in any single or multiple quadrant(s) of the force-displacement response. Performance is characterized by device design parameters. The overall results provide a proof of concept for a new class of relatively low-cost passive devices that enable customized hysteretic behavior for any given structural application.

This paper presents a semianalytical solution for drained expansion of a cylindrical cavity in $K_0$-consolidated clay. The solution is derived based on the $K_0$-based anisotropic modified Cam-clay model ($K_0$-AMCC), which can properly consider the initial stress anisotropy and the initial stress-induced anisotropy of natural soils. Parametric studies are carried out to investigate the effects of different overconsolidation ratios on the growth of plastic zone and cavity pressure, the distributions of the stress components and the specific volume around the cavity, and the effective stress path. The results are compared with the published solution based on the modified Cam-clay model to study the effects of the initial stress anisotropy and the initial stress-induced anisotropy on the cylindrical cavity expansion. The present solution provides a more realistic interpretation for practical geotechnical engineering problems such as pressuremeter tests and cone penetration tests.

An energy-based solution is developed for the lateral torsional buckling analysis of wooden beams with a midspan lateral brace subjected to uniformly distributed loads or midspan point load. The predicted critical moments and mode shapes are shown to agree with results based on three-dimensional finite-element analysis. The study indicates that such beams are prone to two buckling patterns: a symmetric mode and an antisymmetric mode. Whether the symmetric or the antisymmetric mode governs the critical moment capacity is shown to depend on the bracing height. A technique is developed to determine the threshold bracing height required to maximize the critical moment. A parametric study is conducted to investigate the effect of lateral bracing and load height effects on the critical moments. Simple design equations are developed to predict critical moments for a practical range of cases. The limitations of the simplified procedure are discussed. For cases outside the scope of the simplified procedure, designers are recommended to adopt the more detailed energy-based solution. Design examples are provided to illustrate the merits and applicability of the proposed procedure in practical situations.

The resistance of the soil inside a pipe-pile’s cavity to the horizontal dynamic response of the pipe pile is quantified by extending a well-established analytical model from the literature for the soil surrounding solid piles. Accordingly, the derived solution is used to investigate the differences in the dynamic resistance mechanisms associated with the inner soil and outer soil surrounding the pipe pile.