Daniel D. Kana

Influence of interface roughness on dynamic shear behavior in jointed rock

An interlock/friction model is used to predict the behavior of natural jointed rock specimens subject to static normal stress and dynamic shear. The friction part of the model is based on the simple Coulomb friction formulation. The interlock part of the model is shown to be related to the degree of interface matching that is present between two surfaces of a jointed rock pair. The interlock/friction model adequately predicts the offset phenomenon in the hysteresis results of well-matched jointed rocks. The offset phenomenon is recognized as an increase in shear stress required for shear displacement away from the naturally-aligned rock positions and a decrease in shear stress upon shear displacement back toward the naturally-aligned location. The parameters of the interlock/friction model are shown to be empirically related to rock interface roughness properties. Prediction of the shear stress vs shear displacement hysteresis including the offset phenomenon is possible for welded tuff specimen pairs using the measured interface roughness amplitude and the interface coherence between jointed rocks. Model parameters were verified by an experiment on molded mortar specimens. The data from the mortar specimens indicate that the empirically determined relations may be valid for jointed rock pairs that have dramatically different strength properties than welded tuff.

Interlock/friction model for dynamic shear response in natural jointed rock

A system identification approach is used to formulate a discrete element analytical model to predict the behavior of natural jointed rock specimens subject to static normal stress and dynamic shear in a compliant loading apparatus. Model parameters are synthesized to correspond to various low and high frequency physical phenomena that are observed to occur in available experimental data for welded tuff specimens subject to harmonic shear. An approximate interlock/friction model is postulated for the rock interface dynamics, while various spring/mass and damper systems represent the loading apparatus. Furthermore, it is found that primary and secondary asperities of the joint interface roughness must be characterized in order to provide an adequate model of the observed experimental behavior. It is found that the fundamental jointed rock behavior can be related to basic excitation frequency and primary joint asperities, while higher frequency phenomena are associated with compliant mode responses of the loading apparatus that are excited by secondary joint asperities. Recommendations are given for impact of the results on current joint friction model theories.

Validated spherical pendulum model for rotary liquid slosh

A combined spherical pendulum and linear pendulum system is developed to produce the same dynamic in-line and cross-axis reaction weight as liquid exhibiting rotary liquid slosh. An approximate solution of the dynamic equations for the spherical pendulum is used along with cross-axis weight measurements from slosh experiments to develop mass and damping parameters for the spherical pendulum. Similar measurements of in-line weight responses are used to develop the corresponding parameters for the linear pendulum solution. A verification of the spherical pendulum solution is accomplished by comparing the approximate solutions with those predicted by a time-step integration of the nonlinear governing equations. It is found that a constantparameter combined system model cannot be used to represent typical rotary slosh over the entire frequency range within which this type of liquid motion response occurs. Therefore, a model is developed with some parameters constant, and others are allowed to vary as necessary to match the force data.

Seismic response of flexible cylindrical liquid storage tanks

Abstract Liquid slosh and tank wall flexural vibrations are studied in a flexible model storage tank subject to simulated earthquake environments. Emphasis is placed on determining the influence of wall flexural vibrations on induced stresses. The approach is basically experimental, whereby similitude considerations are first presented. Then, a series of scale model experiments are conducted, and preliminary observations are evaluated. These evaluations allow formulation of an approximate analytical model for prediction of seismically induced stress. Validity range for this model is established by comparison of various predicted responses with observed results.

An iterative procedure for the generation of consistent power/response spectrum

Abstract An iterative procedure is presented that allows computation of spectrum-consistent parameters for the description of earthquake/transient motion. The procedure treats the strong motion portion of the earthquake event as being a stationary Gaussian random process, thereby allowing a mapping between the response spectrum and power spectral density function parameters. Several examples of the mapping procedure are presented with comparison to experimental results to demonstrate the validity and usefulness of the approach.

Distinguishing the transition to chaos in a spherical pendulum.

Complex responses are studied for a spherical pendulum whose support is excited with a translational periodic motion. Governing equations are studied analytically to allow prediction of responses under various excitation conditions. Stability for certain cases of damping is predicted by means of existing analysis and compared with experimental data. Numerical time-step integration of the governing equations is developed to predict responses for various types of excitation and damping conditions. Predicted results are compared with corresponding motions measured in an experimental spherical pendulum system. A data acquisition system is included whereby detailed digitized time histories of the pendulum motion can be established and various parameters can be computed to characterize the type of motion present. Two new vector spaces are defined for describing complex responses which occur for certain specified excitation conditions. It is shown in these parameter spaces that the transition from quasiperiodic to chaotic motions can be carefully quantified in systems with very light damping. This discovery provides a convenient means for comparison of complex motions in the numerical and experimental air pendulum systems. The implications of the results are important for dynamic response in various applications, including fluid motions in satellite tanks and other nonlinear time-dependent physical processes which include very light damping. (c) 1995 American Institute of Physics.

A Model for Nonlinear Rotary Slosh in Propellant Tanks

A compound pendulum model is developed to predict rotary slosh of liquid in a scale model Centaur propellant tank at low fill level. A portion of the liquid behaves as a spherical pendulum that experiences rotary motion throughout a frequency range below, at, and above first mode resonance. The remainder of the fluid behaves as an ordinary linear pendulum. Phasing of the rotary motion is such that it subtracts from the effects of normal slosh below resonance and adds to the effects above resonance. The compound pendulum experiences analogous responses to that observed experimentally for the liquid, including bivalued states and jump phenomena, in a range just above resonance. Its responses are used to predict the effective weight response of the liquid by assigning pendulum mass, frequency, and damping parameters based on experimental measurements. An especially important result is that a significant magnitude cross-axis force exists for the rotary motion. This force is predicted by the compound pendulum model, but it is not predicted by the usual linear theory models.

Synthesis of shuttle vehicle damping using substructure test results

An empirical method is developed for predicting the modal damping of a combined parallel-stage Shuttle model by means of damping measurements performed on the individual substructures. Correlations are first determined for each component in terms of damping energy as a function of peak kinetic energy and modal amplitude. The results are then used to predict component damping energies corresponding to the respective kinetic energies and amplitudes that occur for the new modes of the combined System. Modal characteristics for the System, other than damping, are obtained by a real eigenvalue solution of dynamic equations developed by thirtys procedure of substructures . System equations, which include component modal damping, are also solved by a complex eigenvalue approach for comparison with results of the empirical method. Experimental model components are tested in pin-slip and free-free support conditions, and a combined model is tested in the free-free condition. A variety of damping and mass configurations are included. The empirical method is found to provide damping predictions within 10 % to 20 % error, while the complex eigenvalue results deviate by as much as 300%, when based only on component modal damping values.

Status and research needs for prediction of seismic response in liquid containers

Abstract Current methods for seismic design of liquid storage tanks and steam suppression pools are reviewed to establish requirements for future research. The use of a transfer function and response spectrum method is emphasized for prediction of slosh response and impulsive loading. The method is also applicable to operating transient loads that occur in nuclear power plants. Direct applicability is noted for much of the available design data that had previously been developed for aerospace launch vehicles.

Experimental study on dynamic behavior of rock joints

Abstract A comprehensive evaluation of the dynamic behavior of rock joints based on both experimental studies in the laboratory on natural and simulated rock joints as well as an actual underground case study is presented. The laboratory single jointed dynamic tests made use of natural rock joints in a welded tuff, and were tested under both harmonic and earthquake loading conditions at various frequencies under displacement control. Experimental results showed that the shearing resistance could be markedly different between the forward and reverse shearing directions depending on the joint roughness and interlocking nature of the mated joint surfaces. It was also found that the joint dilation that takes place during foward shearing is fully recovered during shear reversal, with a small offset due to -gouge buildup within the joint. A laboratory-scale model experiment was also conducted to study the dynamic behavior of a system of interconnected (artificial) joints around a circular opening in a scaled down rock mass when subjected to earthquake shear wave motion at the base. Results showed that the primary mode of deformation of the rock mass around the tunnel was due to stick-slip behavior along the joints. This type of stick-slip behavior was confirmed during an actual 3 year underground seismic field experimental program designed to study the effect of relatively low-magnitude, repetitive seismic motion (i.e., mining induced) on the behavior of mined excavations. This stick-slip behavior as evidenced in both the field and laboratory seems to explain quite well the phenomenon of the excavations responding to some seismic events but being unresponsive to others. It is believed that the joint stick-slip behavior forms a basis for the progressive accumulation of joint permanent deformation and, consequently, rock mass fatigue. Since materials are normally weaker under fatigue conditions, it is suggested that similar, or even more, damage to an excavation may be realized through a number of seismic events with relatively smaller magnitudes, as opposed to the damage due to a single seismic event with a strong motion.