A New Method for Evaluating the Bearing Capacity of the Bridge Pile Socketed in the Soft Rock

Aiming at the rock-socketed pile in the soft rock area, this paper studies the inherent constitutive relationship between the vertical restraint stiffness at the pier bottom and the bearing capacity of the pile foundation. A new method to evaluate the bearing capacity of the pile foundation is proposed. Based on the Rayleigh energy method and the Southwell frequency synthesis method, the analytical expression of the vertical vibration fundamental frequency of the pier was calculated, and the constraint stiffness expression of the pier bottom was derived. By investigating the impact of parameters on the bearing capacity coefficient of the pile foundation, the fitting formula of the bearing capacity coefficient was obtained by multiple linear regression. Then, with this method, the vertical fundamental frequency of the pier was obtained through a field dynamic test to calculate the vertical constraint stiffness and evaluate the bearing capacity of the rock-socketed pile in the soft rock area. This method can overcome the shortcomings of the traditional static load test method, such as the high cost, long cycle, and poor representativeness. Finally, this method’s accuracy was verified by comparing field measurements and finite element simulation results. The results show that the difference between the code design constraint stiffness and the constraint stiffness by the frequency synthesis method was about 0.7%, and the bearing capacity difference between the analytical solution and the numerical simulation was small. The new method is accurate and effective.

Wave Power Extraction from a Dual Oscillating-Water- Column System Composed of Heave-Only and Onshore Units

With the aim of broadening the wave-frequency bandwidth of high-efficiency, a small-scaled dual oscillating-water-column (OWC) system consisting of two heave-only and onshore units was numerically investigated by a well-validated computational fluid dynamics (CFD) model. Based on the popular open source package OpenFOAM, the volume of fluid (VOF) method was employed to track the transformation of the air–water interface under the excitation of regular waves. The six degree of freedom (6DOF) solver was applied to duplicate the heaving motion of the floating device. The effects of the two chamber widths b 1 and b 2 , the vertical restraint force (represented by the dimensionless stiffness coefficient K), the back-lip draught d 2 of the floating device, and the gap Δ L between the two OWCs on the hydrodynamic characteristics and the wave energy conversion efficiencies were examined. The numerical results show that a larger width ratio b 2 / b 1 with a relatively shallow back-lip draught is more conducive to the high-performance over a broader frequency range. The floating device with a stronger vertical restraint force is more satisfactory for the high-performance of the system. Moreover, a relatively small gap is more recommended in the stage of design and construction.

Poroelasticity During Fluid Injection in Confined Geological Reservoirs: Incorporating Effects of Seal-Rock Stiffness

Summary This paper presents a new poroelastic solution to describe the time-dependent response of a confined geological reservoir to fluid injection through a fully penetrating vertical well treated as a point source. Unlike previous studies, vertical-confinement effects of seal rocks are incorporated in the solution. To facilitate analytical description of a fully coupled poroelastic behavior within the reservoir, the stiffness of surrounding rocks is described by the Winkler model, simplifying the response of seal rocks in the direction perpendicular to the reservoir plane. Analytical expressions are obtained for axisymmetric stress and strain components in the reservoir and for the vertical reaction stress. The latter is essential for evaluation of integrity of seal rocks during injection. Solutions are also obtained for the magnitude and location of the maximum-induced radial displacement as a function of time during injection. The effects of poroelastic coupling are articulated through the equivalent diffusion constant of the reservoir-seal rocks system. The latter is expressed through traditional poroelastic parameters as well as the relative stiffness of reservoir and seal rocks. The Winkler modulus of seal rocks, which is involved in all analytical relationships presented in this paper, is empirically linked to elastic characteristics of surrounding strata by comparing their response with the same pressure change in the reservoir according to the ideally elastic and Winkler models. The derived solutions are compared with previous studies, and verified against fully coupled numerical simulations. A comprehensive sensitivity analysis is conducted to assess the effects of the stiffness of the confining strata on the response of a uniform reservoir to injection. The vertical component of stress and the radial and vertical displacements are found to be substantially sensitive to the magnitude of the vertical restraint. The findings note the significance of incorporating seal-rock characteristics to attain a realistic assessment of the geomechanics of injection, specifically in formations with lower elastic moduli.

The Use of Full-Line Forcing Contracts in the Video Rental Industry

Bundling is at the forefront of many policy debates as new technologies allow firms to implement more complex bundling arrangements. Realistic analyses of bundling—particularly between suppliers and retailers—require detailed data on both supply arrangements and consumer demand. We analyze firms' use of bundling as a vertical restraint (known as full-line forcing) using extensive supply and demand data from the video rental industry. Our model captures key details of the market that determine firms' contractual choices, and sheds light on the implications of these decisions. The empirical approach provides a model for how to analyze bundling when detailed data are available. (JEL D86, L14, L81, L82)