Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasi-empirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth's brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori's law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.     

Organic matter quality in reclaimed boreal forest soils following oil sands mining

Following surface mining of the Athabasca Oil Sands deposits in northeastern Alberta, Canada, land reclamation entails the reconstruction of soil-like profiles using salvaged soil materials such as peat and mining by-products. The overall objective of this research was to assess soil organic matter (SOM) quality in different reclamation practices as compared to undisturbed soils found in the region. Soil samples (0–10 cm) were taken from 45 plots selected to represent undisturbed reference ecosites and reclamation treatments. Soil OM pools were isolated using a combination of acid hydrolysis and physical separation techniques. Chemical composition of the low density fractions was characterized using ramped cross polarization (RAMP-CP) ¹³C nuclear magnetic resonance (NMR). Differences between disturbed and undisturbed sites reflected the influence of different botanical inputs (peat vs. forest litter) to SOM composition. Reconstructed soils were characterized by significantly lower alkyl over O-alkyl carbon (ALK/O-ALK) ratios (0.3) than undisturbed sites (0.5). For these reconstructed soils, a significantly higher proportion of soil carbon was present in the sand associated (Heavy sand) pool (49.2 vs. 37.3) and in the acid-unhydrolyzable residue (AUR) fraction (61.3 vs. 54.7). These SOM parameters were significantly related to time since reconstruction, with the AUR (p value = 0.012) and Heavy sand (p value = 0.05) fractions decreasing with time since reconstruction, while the ALK/O-ALK ratio increased (p value = 0.006). These findings suggest that the ALK/O-ALK, AUR, and Heavy sand parameters are suitable indicators for monitoring SOM quality in these reconstructed soils following oil sands mining.     

Correlations in aftershock and seismicity patterns

Correlations in space and time play a fundamental role in earthquake processes. One direct manifestation of the effects of correlations is the occurrence of aftershocks due to the stress transfer in the vicinity of a main shock. Less obvious and more speculative changes in correlations may occur in the background seismicity before large earthquakes. Using statistical physics it is possible to introduce a measure of spatial correlations through a correlation length. This quantity characterizes how local fluctuations can influence the occurrence of earthquakes over distances comparable with the correlation length. In this work, the physical basis of spatial correlations of earthquakes is discussed in the context of critical phenomena and the percolation problem. The method of two-point correlation function is applied to the seismicity of California. Well defined variations in time of the correlation length are found for aftershock sequences and background seismicity. The scaling properties of our obtained distributions are analyzed with respect to changes in several scaling parameters such as lower magnitude cutoff of earthquakes, the maximum time interval between earthquakes, and the spatial size of the area considered. This scaling behavior can be described in a unified manner by utilizing the multifractal fit. Utilizing the percolation approach the time evolution of clusters of earthquakes is studied with the correlation length defined in terms of the radius of gyration of clusters. This method is applied to the seismicity of California.     

The weathering of stones due to dissolution

We hypothesize that the weathering of building stones can be attributed to surface dissolution processes. We assume that chemical interactions occur on grain boundaries and/or microcracks and that diffusion is the controlling process. A dissolution layer (rind) develops adjacent to the weathering surface. We quantify the extent of dissolution by introducing a damage variable f; f=0 for pristine rock, and when f=1 the rock disintegrates. We assume that the variations of the damage variable are given by the diffusion equation. We solve two problems. The first is for the structure of the transient dissolution boundary layer prior to surface disintegration. We find an incubation time t_i, before active weathering (disintegration) begins. The second is the solution for steady-state weathering with a constant weathering velocity v_w. Our results are entirely consistent with weathering studies on Carrara marble gravestones in the United Kingdom. Typical incubation times are t_i=20–30 years, and typical steady-state weathering velocities are v_w=5–50 m year^–1.     

Magma migration beneath an ocean ridge

Basaltic volcanism which forms the oceanic crust at mid-ocean ridges is the result of pressure release melting associated with ascending mantle convection. We present a model that gives the distribution of melting beneath the ridge and the subsequent migration of magma through the asthenosphere. In order to produce the degree of partial melting associated with the basaltic rocks making up the ocean crust, melting must extend to a depth of at least 70 km. Small degrees of partial melting are expected to result in an interconnected permeability along grain intersections. Due to the differential buoyancy of the magma relative to the residual solid the magma will be rapidly driven upwards. Solid-state creep allows the solid matrix to collapse as the magma migrates upwards and the lithostatic pressure in the matrix is nearly equal to the fluid pressure in the magma. The percentage partial melt present is only slightly greater than that necessary for the development of interconnected permeability and is much less than the degree of partial melting. The first partial melt fraction produced at the greatest depths migrates upwards and mixes with the later partial melt fractions produced at shallower depths. The uniformity of this mixing will have a profound effect on the chemistry of the basalts of the oceanic crust.     

An elastic-perfectly plastic analysis of the bending of the lithosphere at a trench

A number of authors have modelled the flexure of the lithosphere at an oceanic trench using a thin elastic plate with a hydrostatic restoring force. In some cases good agreement with observed topography is obtained but in other cases the slope of the lithosphere within the trench is greater than that predicted by the elastic theory. In this paper the bending of a thin plate is considered using an elastic-perfectly plastic rheology. It is found that the lithosphere behaves elastically seaward of the trench, but that plasticity decreases the radius of curvature within the trench. The results are compared with a number of observed trench profiles. The elastic-perfectly plastic profiles are in excellent agreement with those profiles that deviate from elastic behavior.     

Aftershock Statistics

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Båths law for the magnitude of the largest aftershock, and (3) the modified Omoris law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Båths law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omoris law.     

The mid-ocean ridge axial valley as a steady-state neck

In this paper the mid-ocean ridge axial valley is modelled as a steady-state lithospheric neck in which lithospheric stretching balances lithospheric accretion. Conversely, the axial high is a steady-state lithospheric bulge. The lithosphere is modelled as a thin plate with a Newtonian rheology. It is shown that an axial valley will occur if the rate of viscosity increase away from the ridge axis is faster than the rate at which accretion decreases. An axial high will occur if the opposite condition holds. This is consistent with the observation that axial valleys occur at low spreading rates and axial highs at high spreading rates. By fitting our model to profiles across the Mid-Atlantic Ridge and the East Pacific Rise and assuming the lithospheric thickness at the ridge axis to be 5 km, we find accretion widths of 6–8 km. We find the width over which there is a significant increase in lithospheric viscosity to be also 6–8 km.