Seismic safety of reinforced concrete members and structures

Based on cyclic load tests of large-scale reinforced concrete elements and assemblages, a probabilistic model of member failure is developed. The model gives the probability of survival at time t as a functional of damage ratio and dissipated energy up to t. After extension to multivariate survival of several members with correlated resistance, the model is used to calculate the safety of reinforced concrete frames subjected to given input motions. Results are in terms of the probability of local failure and of no failure anywhere in the system.     

Flexural uplift of a lithospheric slab near the Vema transform (Central Atlantic): Timing and mechanisms

The Vema Transverse Ridge (VTR) is a prominent, long and narrow topographic anomaly that runs for over 300 km along a sea floor spreading flow line south of the Vema transform at 11° N in the Atlantic. It rises abruptly about 140 km from the axis of the Mid-Atlantic Ridge (MAR) in 10 Myr old crust and runs continuously up to 25 Myr old crust. It reaches over 3 km above the predicted lithospheric thermal contraction level. It is absent in crust younger than 10 Myr; thus, the uplift of the VTR must have ended roughly 10 Ma. The VTR is interpreted as the exposed edge of a flexured and uplifted slab of oceanic lithosphere that was generated at an 80 km long MAR segment. Based on satellite gravimetry imagery this MAR segment was born roughly 50 Ma and increased its length at an average rate of 1.6 mm/yr. Multibeam data show that the MAR-parallel sea floor fabric south of the VTR shifts its orientation by 5° to 10° clockwise in 11–12 Myr old crust, indicating a change at that time of the orientation of the MAR axis and of the position of the Euler rotation pole. This change caused extension normal to the transform, followed between 12 and 10 Ma by flexure of the edge of the lithospheric slab, uplift of the VTR at a rate of 2 to 4 mm/yr, and exposure of a lithospheric section (Vema Lithospheric Section or VLS) at the northern edge of the slab, parallel to the Vema transform. Ages of pelagic carbonates encrusting ultramafic rocks sampled at the base of the VLS at different distances from the MAR axis suggest that the entire VTR rose vertically as a single block within the active transform offset. A 50 km long portion of the crest of the VTR rose above sea level, subsided, was truncated at sea level and covered by a carbonate platform. Subaerial and submarine erosion has gradually removed material from the top of the VTR and has modified its slopes. Spreading half rate of the crust south of the transform decreased from 17.2 mm/yr between 26 and 19 Ma to 16.9 mm/yr between 19 and 10 Ma, to 13.6 mm/yr from 10 Ma to present. The slowing down of spreading occurred close in time to the change in ridge/transform geometry, suggesting that the two events are related. A numerical model relates lithospheric flexure to extension normal to the transform, suggesting that the extent of the uplift depends on the thickness of the brittle layer, consistent with the observed greater uplift of the older lithosphere along the VTR.     

A model for silicate melt viscosity in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8

Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi₂O₆ (Di)-CaAl₂Si₂O₈ (An)-NaAlSi₃O₈ (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660-2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: log η = A + B/(T − C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is −5.06, which implies a high-temperature limit to viscosity of 10^-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (b_i=1,2.6, c_j=1,2..6) representing linear (e.g., b_i=1:3) and higher order, nonlinear (e.g., b_i=4:6) contributions. Our results suggest a near-linear compositional dependence for B (<10% nonlinear) and C (<7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of T_g for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have T_g values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.     

Stability of Al- and F-rich titanite in metacarbonate: petrologic and isotopic constraints from a polymetamorphic eclogitic marble of the internal Sesia Zone (Western Alps)

Al- and F-rich titanite (3.862O₃ <9.33 wt%, 0.931(F, OH)₁Ti_-1O_-1 substitution within single crystals, particularly at grain boundaries with omphacite and/or phengite. In-situ ion microprobe U-Pb analysis of titanite domains that have various Al and F contents yielded apparent ²⁰⁶Pb/²³⁸U ages scattering between 283 and 153 Ma. Chemical and petrological data are indispensable to interpret this complex age distribution, and the good correlation between ²⁰⁶Pb/²³⁸U ratios and Al content indicates that the Al- and F-rich titanite was formed during pre-Alpine metamorphism (𔕑ᆟ Ma). Progressively younger ages are obtained in domains with decreasing Al and F content, suggesting that partial chemical re-equilibration was responsible for the incomplete isotopic resetting during Alpine metamorphism. Petrological and U-Pb data show that Al- and F-rich titanite should be used with caution to infer high-pressure conditions in polymetamorphic carbonate systems.     

Contrasting styles of Mount Vesuvius activity in the period between the Avellino and Pompeii Plinian eruptions,and some implications for assessment of future hazards

Intense explosive activity occurred repeatedly at Vesuvius during the nearly 1,600-year period between the two Plinian eruptions of Avellino (3.5 ka) and Pompeii (79 A.D.). By correlating stratigraphic sections from more than 40 sites around the volcano, we identify the deposits of six main eruptions (AP1-AP6) and of some minor intervening events. Several deposits can be traced up to 20 km from the vent. Their stratigraphic and dispersal features suggest the prevalence of two main contrasting eruptive styles, each involving a complex relationship between magmatic and phreatomagmatic phases. The two main eruption styles are (1) sub-Plinian to phreato-Plinian events (AP1 and AP2 members), where deposits consist of pumice and scoria fall layers alternating with fine-grained, vesiculated, accretionary lapilli-bearing ashes; and (2) mixed, violent Strombolian to Vulcanian events (AP3-AP6 members), which deposited a complex sequence of fallout, massive to thinly stratified, scoria-bearing lapilli layers and fine ash beds. Morphology and density variations of the juvenile fragments confirm the important role played by magma-water interaction in the eruptive dynamics. The mean composition of the ejected material changes with time, and shows a strong correlation with vent position and eruption style. The ranges of intensity and magnitude of these events, derived by estimations of peak column height and volume of the ejecta, are significantly smaller than the values for the better known Plinian and sub-Plinian eruptions of Vesuvius, enlarging the spectrum of the possible eruptive scenarios at Vesuvius, useful in the assessment of its potential hazard.     

A multi-arc approach for chaotic orbit determination problems

Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter.     

Single-point position estimation in interplanetary trajectories using star trackers

This study provides a single-point position estimation technique for interplanetary missions by observing visible planets using star trackers. Closed-form least-squares solution is obtained by minimizing the sum of the expected object-space squared distance errors. A weighted least-squares solution is provided by an iterative procedure. The weights are evaluated using the distances to the planets estimated by the least-squares solution. It is shown that the weighted approach only requires one iteration to converge and results in significant accuracy gains compared to simple least squares approach. The light-time correction is taken into account while the star-light aberration cannot be implemented in single-point estimation as it requires knowledge of the observer velocity. The proposed method is numerically validated through a statistical scenario as follows. A three-dimensional grid of test cases is generated: two dimensions sweep through the ecliptic plane and the third dimension sweeps through time from January 1, 2018 to January 1, 2043 in 5-year increments. The observer position is estimated at each test case and the estimate error is recorded. The results obtained show that a large majority of positions are well suited to position estimation by using star trackers pointing to visible planets, and reliable and accurate single-point position estimations can be provided in interplanetary missions. The proposed approach is suitable to be used to initiate a filtering technique to increase the estimation accuracy.     

S-wave splitting intensity analysis and inversion

Analysing S-wave splitting has become a routine step in processing multicomponent data. Typically, this analysis leads to determining the principal directions of a transversely isotropic medium with a horizontal symmetry axis, which is assumed to be responsible for azimuthal anisotropy, and to the time delays between the fast and slow S-waves. These parameters are commonly estimated layer-by-layer from the top. Errors in layer stripping occurring in shallow layers might propagate to deeper layers. We propose a method for S-wave splitting analysis and compensation that consists of inverting interval values of splitting intensity to obtain a model of anisotropic parameters that vary with time and/or depth. Splitting intensity is a robust attribute with respect to structural variations and is commutative, which means that it can be summed along a ray (or throughout a sensitivity kernel volume) and can be linearly related to anisotropic perturbations at depth. Therefore, it is possible to estimate anisotropic properties within a geological formation (e.g. the reservoir) by analysing the differences of splitting intensity measured at the top and at the bottom of the layer. This allows us to avoid layer stripping, in particular, for shallow layers where anisotropic parameters are difficult to estimate due to poor coverage, and it makes S-wave splitting analysis simpler to apply. We demonstrate this method on synthetic and real data. Because the splitting intensity attribute shows usefulness in S-wave splitting analysis in transversely isotropic media, we extend the splitting intensity theory to lower symmetry classes. It enables the characterization of tilted transversely isotropic and tilted orthorhombic media, opening new opportunities for anisotropic model building.     

Mapping river bathymetries: Evaluating topobathymetric LiDAR survey

Advances in topobathymetric LiDARs could enable rapid surveys at sub-meter resolution over entire stream networks. This is the first step to improving our knowledge of riverine systems, both their morphology and role in ecosystems. The Experimental Advanced Airborne Research LiDAR B (EAARL-B) system is one such topobathymetric sensor, capable of mapping both terrestrial and aquatic systems. Whereas the original EAARL was developed to survey littoral areas, the new version, EAARL-B, was also designed for riverine systems but has yet to be tested. Thus, we evaluated the ability of EAARL-B to map bathymetry and floodplain topography at sub-meter resolution in a mid-size gravel-bed river. We coupled the EAARL-B survey with highly accurate field surveys (0.03 m vertical accuracy and approximately 0.6 by 0.6 m resolution) of three morphologically distinct reaches, approximately 200 m long 15 m wide, of the Lemhi River (Idaho, USA). Both point-to-point and raster-to-raster comparisons between ground and EAARL-B surveyed elevations show that differences (ground minus EAARL-B surveyed elevations) over the entire submerged topography are small (root mean square error, RMSE, and median absolute error, M, of 0.11 m), and large differences (RMSE, between 0.15 and 0.38 m and similar M) are mainly present in areas with abrupt elevation changes and covered by dense overhanging vegetation. RMSEs are as low as 0.03 m over paved smooth surfaces, 0.07 m in submerged, gradually varying topography, and as large as 0.24 m along banks with and without dense, tall vegetation. EAARL-B performance is chiefly limited by point density in areas with strong elevation gradients and by LiDAR footprint size (0.2 m) in areas with topographic features of similar size as the LiDAR footprint. © 2018 John Wiley & Sons, Ltd.