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In this paper, the dynamic response of an infinite beam resting on a Pasternak foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The mechanical resistance of the Pasternak foundation is modeled using two parameters, that is, one accounts for soil resistance due to compressive strains in the soil and the other accounts for the resistance due to shear strains. Because the Winkler model only represents the compressive resistance of soil, comparatively, the Pasternak model is more realistic to consider shear interactions between the soil springs. The governing equation of the beam is simplified into an algebraic equation by employing integration transforms, so that the analytical solution for the dynamic response of the beam can be obtained conveniently in the frequency domain. Both inverse Laplace and inverse Fourier transforms combined with convolution theorem are applied to convert the solution into the time domain. The solutions for several special cases, such as harmonic line loads, moving line loads, and travelling loads are also discussed and numerical examples are conducted to investigate the influence of the shear modulus of foundation on the beam responses. The proposed solutions can be an effective tool for practitioners.

In previous studies, two conflicting conclusions existed, which were: (a) the isobutane/n-butane ratio of natural gas increases with the increasing maturity (Ro) of source rocks and (b) decreases with the increasing Ro. In this paper, the correlations between the isobutane/n-butane ratios, dryness of natural gases, and the Ro values of source rocks of 77 gas samples from Cretaceous and Tertiary in Kuqa Depression, Tarim Basin, Triassic Xujiahe Formation in central Sichuan Basin, Carboniferous–Permian in Sulige and Yulin gas field, Ordos Basin, China, and 80 shale gas samples from Mississippian Barnett Shale in the Fort Worth Basin, the United States are analyzed to reveal the evolution of the isobutane/n-butane ratios, then mathematical models of the isobutane/n-butane ratios and Ro are attempted to be established. Results show that the isobutane/n-butane ratio initially increases and then decreases with increasing Ro, both coal-derived gas and oil-type gas. Diverse types of kerogens may be responsible for the different corresponding Ro values when the isobutane/n-butane ratios of gases reach their maximum values. The initial increase in the isobutane/n-butane ratios with increasing Ro is the reason that isobutane is mainly generated at a higher rate by carbonium ion reaction of α-olefins with protons during kerogen primary cracking at lower maturity, whereas free radical reactions to form n-butane relatively quickly during oil cracking at higher maturity and isobutane cracked at a higher rate during the wet gas cracking stage may result in the terminal decreases in the isobutane/n-butane ratios. Besides, mathematical models of the isobutane/n-butane ratios of different types of natural gas and maturity are established. Therefore, the maturity of gas source rock can be obtained quickly based on the models using the isobutane/n-butane ratio combined with other component information (such as dryness, wetness, etc.), which is of great significance to the characterization of natural gas maturity and gas source rock correlation.

The development of the highway traffic has promoted the construction of increasing numbers of river-crossing bridges, but at the same time, large-size ship causes serious threat to structural safety of the bridge. The probability of bridge-ship collision increases, water safety accidents have happened frequently in the recent years. Arch bridge is easier to be subjected to the threat of ship collision because of small navigation clearance on both sides. However, study on the destructive consequences by ship impact on arch bridge is seldom. This paper takes reinforced concrete arch bridge as an example, on the basis of the forecast of the water-level frequency, flow velocity and long-term navigation density of the ship, the ship collision probability on different parts of the arch ring at different water levels are analyzed to deduce the annual collapse frequency of the grand bridge. The risk matrix evaluation result shows that there is medium risk in longterm. The establishment of finite element numerical model concludes the energy absorption and the change process when the arch ring suffers from collision from the ship under different working conditions as well as the relationship among the impact force, crown displacement and collision depth along with time change. According to the result of simulated analysis, the maximum collision force of the main arch ring suffered from the ship is 25.9MN, and the resistance of the main arch ring is 33.6 MN, so the existing structure basically meets the requirement for fortification against the ship collision. The numerical simulation results are qualitatively consistent with the risk of evaluation. The results of the analysis can provide scientific foundation to the maintenance and management of the arch bridge.

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