This study is comprised of three major parts. The first part involved the development of a multi-measurement, confined, free-free resonant column device. This device was developed to improve upon traditional manually excited, vacuum-confined, free-free methods. The device is capable of testing specimens with diameters up to 6-in., under confinements upwards of 50 psi. The device is composed of a seismic-source system, a data acquisition system and a specimen support and confinement system. The seismic source system is used to induce small-strain constrained compression waves, and longitudinal and torsional stress waves in the specimen. The data acquisition system is used to measure: (1) direct travel time of constrained compression waves, (2) longitudinal resonance in unconstrained compression, and (3) torsional resonance. From these measurements, constrained compression wave velocity, Vp, unconstrained compression wave velocity, Vc, and shear wave velocity, Vs, can be determined. With these wave velocities, small-strain, constrained modulus, Mmax, Young’s modulus, Emax, and shear modulus, Gmax can be determined. Poisson’s ratio is also calculated with the wave velocities. Finally, from the resonance measurements, small-strain material damping in unconstrained compression, DCmin, and in shear, DSmin, can be evaluated. The second part of this study involved verification tests with materials of known dynamic properties. The tests were performed with a manufactured aluminum specimen, ASTM graded Ottawa sand, and crushed rock aggregate base. The results compared well with previous results from similar tests. The third part of this study involved testing artificially cemented ASTM graded Ottawa sand. Cement contents (by weight) of 0.0, 0.5, 1.0 and 2.0%, were used to observe the effect of cementation with curing time at a constant confining pressure of 5 psi. The overall effect of cementation was: (1) a large increase in stiffness, and (2) an increase in material damping. The key effects related to cementation versus curing time are: (1) the increase in wave velocities are reasonably proportional to an increase in cement content up to a curing time of about 5 to 7 days, and (2) after a curing time of 5 to 7 days time the velocity increase with time seems to be similar for all cemented specimens. Additionally, the 2% cemented specimen was tested to observe the effect of confining pressure. The stiffness of this specimen was quite insensitive to confining pressure as was the material damping. / text

The time-independent and -dependent damage characteristics of brittle rocks inside the pre-failure range have been investigated using numerical simulations and lab testing. Grain-based discrete element models have been developed to simulate both, time-independent and -dependent damage evolution leading to ultimate failure of sandstone and granite, respectively. The models take into account elastic grain and elasto-plastic contact deformation, inter- and intra-granular fracturing and lifetime prediction on the basis of subcritical crack growth. The time-independent mechanical behavior of Coconino sandstone and Lac du Bonnet granite during uniaxial compression tests, Brazilian splitting tests and fracture toughness tests was simulated. Triaxial compression tests and fracture toughness tests for Kirchberg II granite and fracture patterns tests for Eibenstock II granite were carried out in laboratory to perform time-independent damage and failure criterion analysis. The corresponding simulations showed reasonable damage phenomena compared with experimental results. Damage indices were deduced and were applied for different time-independent simulations. Based on calibrations of the time-independent damage simulations of selected brittle rocks, Charles equation and Hillig-Charles equation, which are generally used to describe subcritical crack growth, were implemented into the numerical code to simulate time-dependent damage. One-edged crack growth in Coconino sandstone specimen due to stress corrosion has been analyzed theoretically and numerically. Uniaxial compressive creep tests for Lac du Bonnet granite were simulated and time-dependent behavior in terms of the damage process during primary, secondary and tertiary creep until final failure characterized by macroscopic fracturing was discussed in detail. Subsequent to this, the time-dependent Mode-I crack growth tests and uniaxial compressive creep tests for Kirchberg II granite were carried out and the corresponding simulations were performed. Simulation results are in good agreement with experimental observations. In addition, damage indices and time-dependent fracture development were monitored and illustrated. The developed approach was applied to two potential practical applications: the damage analysis of a sandstone landscape arch and a tunnel. Finally, the results are summarized and recommendations for future work are proposed.

The time-independent and -dependent damage characteristics of brittle rocks inside the pre-failure range have been investigated using numerical simulations and lab testing. Grain-based discrete element models have been developed to simulate both, time-independent and -dependent damage evolution leading to ultimate failure of sandstone and granite, respectively. The models take into account elastic grain and elasto-plastic contact deformation, inter- and intra-granular fracturing and lifetime prediction on the basis of subcritical crack growth. The time-independent mechanical behavior of Coconino sandstone and Lac du Bonnet granite during uniaxial compression tests, Brazilian splitting tests and fracture toughness tests was simulated. Triaxial compression tests and fracture toughness tests for Kirchberg II granite and fracture patterns tests for Eibenstock II granite were carried out in laboratory to perform time-independent damage and failure criterion analysis. The corresponding simulations showed reasonable damage phenomena compared with experimental results. Damage indices were deduced and were applied for different time-independent simulations. Based on calibrations of the time-independent damage simulations of selected brittle rocks, Charles equation and Hillig-Charles equation, which are generally used to describe subcritical crack growth, were implemented into the numerical code to simulate time-dependent damage. One-edged crack growth in Coconino sandstone specimen due to stress corrosion has been analyzed theoretically and numerically. Uniaxial compressive creep tests for Lac du Bonnet granite were simulated and time-dependent behavior in terms of the damage process during primary, secondary and tertiary creep until final failure characterized by macroscopic fracturing was discussed in detail. Subsequent to this, the time-dependent Mode-I crack growth tests and uniaxial compressive creep tests for Kirchberg II granite were carried out and the corresponding simulations were performed. Simulation results are in good agreement with experimental observations. In addition, damage indices and time-dependent fracture development were monitored and illustrated. The developed approach was applied to two potential practical applications: the damage analysis of a sandstone landscape arch and a tunnel. Finally, the results are summarized and recommendations for future work are proposed.:1 Introduction 2 State of the art 3 Time-independent damage analysis 4 Time-dependent damage analysis 5 Applications of numerical models . 6 Conclusions and outlook References

The anisotropic behavior of a rock mass with persistent and planar joint sets is mainly governed by the geometrical and mechanical characteristics of the joints. The aim of the study is to develop a continuum-based approach for simulation of multi jointed geomaterials. There are two available numerical techniques for the strain-stress analysis of rock masses: continuum-based methods and discontinuum based methods. Joints are simulated explicitly in discontinuous methodology. This technique provides a more accurate description for the behavior of a rock mass. However, in some projects, the explicit definition becomes impractical, especially with increasing number of joints. Besides, the calculation efficiency will be significant reduced as the number of joints increases within the model. Considering the above mentioned shortcomings of the discontinuous method, the continuum-based approach is widely used in rock mechanics. Within the continuum methods, the discontinuities are regarded as smeared cracks in an implicit manner and all the joint parameters are incorporated into the equivalent constitutive equations. A new equivalent continuum model, called multi-joint model, is developed for jointed rock masses which may contain up to three arbitrary persistent joint sets. The Mohr-Coulomb yield criterion is used to check failure of the intact rock and the joints. The proposed model has solved the issue of multiple plasticity surfaces involved in this approach combined with multiple failure mechanisms. The multi-joint model is implemented into FLAC and is verified against the distinct element method (UDEC), analytical solutions, and experimental data. Uniaxial compression tests with artificial rock-like material (gypsum) are carried out in the laboratory in order to verify the developed constitutive model and to investigate the behavior of jointed specimen. Samples with two crossing joints covering more than 20 angle configurations and two different property sets were prepared and tested. Simulation results are in good agreement with experimental observations. The developed model is applied to two potential practical applications: the stability analysis of a slope and a tunnel under different stress conditions. Finally, the main achievements of the whole PhD study are summarized and future research work is proposed.

<p>With rising temperatures, urbanization, population growth, improving economic wellbeing, decarbonization and electrification efforts, the demand for space cooling and heating equipment is continuously increasing around the world. To counteract the effect of rising demand for air conditioners and heat pumps on total energy consumption, peak electricity demand, and emissions, it is crucial to promote the development and market penetration of energy-efficient systems. Establishing minimum energy performance standards (MEPS), energy labeling and utility programs are some of the effective and tested methods for achieving this goal. The technical basis for these energy efficiency standards is a testing and rating procedure for estimating equipment seasonal performance from laboratory tests. Although the current rating procedures provide standardized metrics to compare different equipment performances, they fail to appropriately characterize the field representative performance of systems by not considering the effects of: 1) test unit embedded controls, thermostat, and realistic interactions with the building load and dynamics; 2) different climate zones and building types; and 3) and other integrated accessories for improving energy efficiency such as economizer for rooftop units (RTUs). Therefore, current approaches for performance ratings neither incentives the development and implementation of improved system and control designs nor consumers with a metric that represents the advanced systems' actual energy savings. To address this, a load-based testing methodology that enables dynamic performance evaluation of equipment with its integrated controls, thermostat, and other accessories was recently proposed. The test methodology is based on the concept of emulating the response of a representative building conditioned by the test unit in a test lab using a virtual building model. </p> <p>In this work, the proposed load-based testing methodology was further extended, evaluated, and validated for residential heat pumps to integrate it into next-generation energy efficiency testing and rating procedures and to serve as a tool for engineers to develop and validate improved control algorithms in a laboratory setting. Further, a load-based testing method for evaluating the dynamic performance of RTUs with integrated economizers was also developed and demonstrated.</p> <p>A load-based testing approach previously developed for residential cooling equipment is extended for heat pump heating-mode and demonstrated for a variable-speed system. The heat pump's typical dynamic behaviors are captured along with controller imperfections that aren't reflected in current testing approaches. Further, a comprehensive comparison was performed between the proposed load-based testing approach to the current steady-state testing approach in the U.S., AHRI 210/240, based on performance evaluation of three residential variable-speed heat pumps to understand the differences and their significance for the next-generation rating procedure. For cooling mode, steady-state testing estimates higher seasonal performance, but for heating mode, the steady-state testing approach estimates higher seasonal performance for warmer climates and is comparable for colder climates. The load-based testing methodology was validated by comparing the laboratory performance of a heat pump to that of a residential building in a controlled environment. The virtual building modeling approach for building loads and thermal dynamics effectively captured these characteristics of the house. The heat pump's cycling rate response with run-time fraction, which represents the unit's overall dynamic response, matched well between lab load-based tests and house tests. The test unit's COP difference for cooling and heating tests was within 3% between the two facilities, except for 9% in 95°F and 6% in 104°F cooling dry-coil test intervals. To evaluate the applicability of the developed load-based testing methodology as next-generation rating standards, its repeatability and reproducibility were assessed based on multiple heat pump round-robin tests conducted in two labs. Overall, reasonable to good repeatability was observed in load-based test results in both labs, however, poor reproducibility was observed except for one heat pump heating mode results. A root cause analysis of the observed differences along with recommendations for a next-generation rating approach are presented. This work aided in the development of a CSA (Canadian Standards Association) standard EXP07:19 and its subsequent revision for equipment rating based on load-based testing.</p> <p>The application of the load-based testing methodology as a tool for the development and evaluation of a residential heat pump controller design was demonstrated. Further, a load-based testing methodology was developed and demonstrated for the dynamic performance evaluation of RTUs with integrated economizers in a test laboratory setting. Recommendations for future work to further develop and improve the repeatability, reproducibility, and representativeness of the load-based testing and rating approach for residential and commercial air conditioners and heat pumps are summarized at the end of the dissertation. </p>