Development of Comprehensive Subgrade Deflection Acceptance Criteria - Phase 3 Report

This report has presented the findings of Phase III of research conducted to aid in the development of subgrade deflection acceptance criteria for WisDOT. The reconfigured rolling wheel deflectomter (RWD), portable truck-mounted deflection measurement systems, and automated dynamic cone penetrometer (DCP) were utilized on subgrade construction projects throughout the 2000 construction season. Laboratory analysis of soil properties, including Proctor, CBR and unconfined compression tests, were also conducted. The research findings have validated the concept of using deflection testing results to identify areas of poor in-place stability within constructed subgrades. It is recommended that pilot implementations of deflection acceptance testing be conducted in conjunction with subgrade penetration testing and moisture controls until more data has been collected, especially in moisture sensitive fine grained soil types. The use of deflection acceptance testing, in conjunction with in-situ penetration tests, should provide the data necessary to determine if the in-place support capacity for a given soil is sufficient to provide a stable construction platform for subsequent paving operations. However, it is important to note that both the RWD and DCP test results are related to the moisture-density conditions at the time of testing. Soils that show acceptable results (i.e., low deflections) may subsequently weaken due to changes in moisture content, freezing/thawing, etc. In instances where subgrade acceptance is well in advance of base course application, subgrade moisture changes may result in decreased soil support

Comprehensive Subgrade Deflection Acceptance Criteria - Pilot Implementation Report

This report has presents the findings of implementations of pilot specifications for subgrade acceptance based on measured deflections. The reconfigured rolling wheel deflectomter (RWD), portable truck-mounted deflection measurement systems, and dynamic cone penetrometer (DCP) were utilized on four subgrade construction projects during the 2001 construction season. Comparative nuclear density readings were obtained at selected locations within each project. Comparative soil stiffness gauge readings were also obtained on 2 of the pilot projects The research findings from this and previous study phases indicate that deflection test results may be appropriate for identifying areas of poor in-place stability within constructed subgrades. However, deflection testing alone may not provide all of the data necessary to properly differentiate acceptable and non-acceptable subgrade stabilities. It is important to note that deflection test results are related to the moisture-density conditions at the time of testing. Soils that show acceptable results (i.e., low deflections) may subsequently weaken due to changes in moisture content, freezing/thawing, etc. In instances where subgrade acceptance is well in advance of base course application, subgrade moisture changes may result in decreased soil support. For those conditions where soil compaction has been conducted at a moisture state near optimum, surface deflections should be correlated to the achieved level of compaction. The overall objectives of this research have been met, particularly in the development of useful correlations between subgrade deflections and in-place subgrade stability as measured by the California Bearing Ratio (CBR). Deflection data collected to date using instrumentation on the axles of loaded quad-axle trucks indicates this data source should be adequate for acceptance testing. It is recommended that implementations of deflection acceptance testing be conducted during the 2002 construction season on selected projects using a deflection threshold of 1.50 inches to identify areas which would not provide sufficient stability for subsequent construction operations. For use within Year 2002 implementations, this threshold value is recommended for use to identify potentially “failed” test locations. The project engineer should retain the right to require corrective actions to improve subgrade conditions based on the magnitude and extent of failed readings

Hazardous Near Earth Asteroid Mitigation Campaign Planning Based on Uncertain Information on Asteroid Physical Properties

Given a limited warning time, an asteroid impact mitigation campaign would hinge on uncertainty-based information consisting of remote observational data of the identified Earth-threatening object, general knowledge on near-Earth asteroids (NEAs), and engineering judgment. Due to these ambiguities, the campaign credibility could be profoundly compromised. It is therefore imperative to comprehensively evaluate the inherent uncertainty in deflection and plan the campaign accordingly to ensure successful mitigation. This research demonstrates dual-deflection mitigation campaigns consisting of primary and secondary deflection missions, where both deflection performance and campaign credibility are taken into consideration. The results of the dual-deflection campaigns show that there are trade-offs between the competing aspects: the total interceptor mass, interception time, deflection distance, and the confidence in deflection. The design approach is found to be useful for multi-deflection campaign planning, allowing us to select the best possible combination of deflection missions from a catalogue of various mitigation campaign options, without compromising the campaign credibility

Towards Designing a Credible Hazardous NEA Mitigation Campaign of Dual-deflection Act

Given a limited warning time, an asteroid impact mitigation campaign would hinge on uncertainty-based information consisting of remote observational data of the identified Earth-threatening object, general knowledge on near-Earth asteroids, and engineering judgment. Due to these ambiguities, the campaign credibility could be profoundly compromised. It is therefore imperative to comprehensively evaluate the inherent uncertainty in deflection and plan the campaign accordingly to ensure successful mitigation. This research demonstrates dual-deflection mitigation campaigns consisting of primary and secondary deflection missions, where both deflection performance and campaign credibility are taken into consideration. The results of the dual-deflection campaigns show that there are trade-offs between the competing aspects: the total interceptor mass, interception time, deflection distance, and the confidence in deflection. The design approach is found to be useful for multi-deflection campaign planning, allowing us to select the best possible combination of deflection missions from a catalogue of various mitigation campaign options, without compromising the campaign credibility

Constructing minimum deflection fixture arrangements using frame invariant norms

This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method. Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented

Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray's impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.Comment: 22 pages, 5 figure

Consequences of asteroid fragmentation during impact hazard mitigation

The consequences of the fragmentation of an Earth-threatening asteroid due to an attempted deflection are examined in this paper. The minimum required energy for a successful impulsive deflection of a threatening object is computed and compared to the energy required to break up a small size asteroid. The results show that the fragmentation of an asteroid that underwent an impulsive deflection, such as a kinetic impact or a nuclear explosion, is a very plausible event.Astatistical model is used to approximate the number and size of the fragments as well as the distribution of velocities at the instant after the deflection attempt takes place. This distribution of velocities is a function of the energy provided by the deflection attempt, whereas the number and size of the asteroidal fragments is a function of the size of the largest fragment. The model also takes into account the gravity forces that could lead to a reaggregation of the asteroid after fragmentation. The probability distribution of the pieces after the deflection is then propagated forward in time until the encounter with Earth. A probability damage factor (i.e., expected damage caused by a given size fragment multiplied by its impact probability) is then computed and analyzed for different plausible scenarios, characterized by different levels of deflection energies and lead times

Mission Analysis For the Ion Beam Deflection of Fictitious Asteroid 2015PDC

A realistic mission scenario for the deflection of fictitious asteroid 2015PDC is investigated that makes use of the ion beam shepherd concept as primary deflection technique. The article deals with the design of a low thrust rendezvous trajectory to the asteroid, the estimation of the propagated covariance ellipsoid and the outcome of a slow-push deflection starting from three worst case scenarios (impacts in New Delhi, Dhaka and Teheran). Displacing the impact point towards very low populated areas, as opposed to full deflection, is found to be the simplest and most effective mitigation approach. Mission design, technical and political aspects are discussed.Comment: 19 pages, 19 figures, presented at the 2015 Planetary Defence Conferenc