In most cases it is justified to regard pipelines as lumped capacitances when hydraulic systems are simulated. In some cases, however, when the system is widely distributed the wave propagation effects in lines may become important and there exists very good models today to simulate these effects. The price to be paid is that of a much larger computational effort. In this paper, a numerically highly efficient model is presented which is just slightly more demanding than a model to represent a pure capacitance, yet it captures all the essential characteristics of a line, the finite wave propagation speed and the distributed frequency dependent friction. The model only calculates state variables at the ends of a line and not in any internal nodes as most models do. Despite this, the model gives good results both in the time and frequency domain which compared to more elaborate models. If for some reason internal state variables are wanted they can be obtained by representing a line with several line elements. The model is integrated in the library of the HOPSAN simulation package and has been used successfully for simulation of oil hydraulic systems as well as the human cardiovascular system.
In this investigation, experiments were carried out in order to determine the mechanical properties of Bohus granite considering the influence from pre-existing cracks and defects. The experimental investigation aimed at a complete material characterization, for the purpose of mechanical analyses using advanced constitutive models, based on a variety of tests. In doing so, direct tensile and compression tests were performed to evaluate the stiffness and strength; quasi-oedometric tests were carried out in order to obtain the deviatoric and volumetric behavior of the material at different levels of hydrostatic pressure (up to 860 MPa); three-point bend tests were performed to evaluate the quasi-static strength of the rock and its distribution. Weibull statistics was then employed to describe the strength distribution. The intact specimens indicated a rather low scatter in the mechanical properties such as Young’s modulus and tensile strength. However, specimens with large initial defects behaved differently. The failure mechanism in these specimens was not as brittle as the intact ones. The crack was opened on the tensile surface of such specimens during the three-point bend test at an early stage during loading, as demonstrated by digital image correlation results.
The inelastic behavior of Bohus granite is investigated based on experimental and numerical results. The yield surface and related dilation angle are determined based on quasi-oedometric tests performed in an earlier work. It is shown how to obtain the yield surface and dilation angle from this test for hydrostatic pressure levels up to 750 MPa. In the constitutive modeling, a Drucker-Prager law is employed together with a variable dilation angle. The constitutive model is first applied to simulate the quasi-oedometric test and the stress and strain fields are obtained. Furthermore, the validation of the model is investigated by simulation of the spherical indentation test. The results are compared with corresponding experimental data and a good agreement is found.
SUMMARYThe aim of this study is to investigate the effect of pre-existing, or structural, cracks on dynamic fragmentation of granite. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are chosen based on previous experiments. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. The pre-existing cracks are introduced in the model by considering sets of elements with negligible tensile strength that leads to their immediate failure when loaded in tension even though they still carry compressive loads as crack closure occurs because of compressive stresses. Previously performed edge-on impact tests are reconsidered here to validate the numerical model. Percussive drilling is simulated, and the influence of the presence of pre-existing cracks is studied. The results from the analysis with different crack lengths and orientations are compared in terms of penetration stiffness and fracture pattern. It is shown that pre-existing cracks in all investigated cases facilitate the drilling process.
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