Carl E. Renshaw

On the relationship between mechanical and hydraulic apertures in rough‐walled fractures

Accurate analyses of the hydrogeology of fractured rock require an understanding the flow characteristics of single fractures. It is well known that these flow characteristics are strongly controlled by fracture apertures. Recent investigations on the distribution of apertures in natural fractures suggest that the cubic law can accurately predict the fluid flux through rough-walled fractures as long as the appropriate average fracture aperture is used. Combining the stochastic cubic law with a simple deformation model results in a nonlinear relationship between fracture hydraulic and mechanical aperture. This relationship is shown to be consistent with published experimental and numerical data above a critical minimum aperture. Below this minimum aperture, the transmissivity of the fracture is approximately constant. Results have implications for the interpretation of laboratory fracture flow data and raise important questions pertaining to the mechanics of fracture deformation below the critical minimum aperture.

Isotopic evolution of a seasonal snowpack and its melt

The study of isotopic variation in snowmelt from seasonal snowpacks is useful for understanding snowmelt processes and is important for accurate hydrograph separation of spring runoff. However, the complex and variable nature of processes within a snowpack has precluded a quantitative link between the isotopic composition of the original snow and its melt. This work studies the isotopic composition of new snow and its modification by snow metamorphism and melting. To distinguish individual snowstorms, we applied solutions of rare earth elements to the snow surface between storms. The snowmelt was isotopically less variable than the snowpack, which in turn was less variable than the new snow, reflecting isotopic redistribution during metamorphism and melting. The snowmelt had low d 18 O values early in the season and became progressively enriched in 18 O as the pack continued to melt. On a given day, meltwater d 18 O was systematically lower whenever melt rates were low than when melt rates were high. The progressive enrichment in d 18 O of snowmelt and the dependence of d 18 O on melt rates can be explained by isotopic exchange between liquid water and ice. A one-dimensional (1-D) model of the melting process, including advection and water-ice isotopic exchange kinetics, reproduces the observed progressive 18 O enrichment of snowmelt.

Universal behaviour in compressive failure of brittle materials

Brittle failure limits the compressive strength of rock and ice when rapidly loaded under low to moderate confinement. Higher confinement or slower loading results in ductile failure once the brittle–ductile transition is crossed. Brittle failure begins when primary cracks initiate and slide, creating wing cracks at their tips. Under little to no confinement, wing cracks extend and link together, splitting the material into slender columns which then fail. Under low to moderate confinement, wing crack growth is restricted and terminal failure is controlled by the localization of damage along a narrow band. Early investigations proposed that localization results from either the linkage of wing cracks or the buckling of microcolumns created between adjacent wing cracks. Observations of compressive failure in ice suggest a mechanism whereby localization initiates owing to the bending-induced failure of slender microcolumns created between sets of secondary cracks emanating from one side of a primary crack. Here we analyse this mechanism, and show that it leads to a closed-form, quantitative model that depends only on independently measurable mechanical parameters. Our model predictions for both the brittle compressive strength and the brittle–ductile transition are consistent with data from a variety of crystalline materials, offering quantitative evidence for universal processes in brittle failure and for the broad applicability of the model.

On the initiation of shear faults during brittle compressive failure: A new mechanism

Brittle materials loaded under compression generally fail by shear faulting. This paper addresses the initiation of the fault. It presents direct observational evidence from ice, which is used as a model material for rock, and shows that wing cracking and “splay cracking” are important processes in the localization of deformation, both prior to and during fault initiation. Wing cracks develop at the tips of sliding intergranular cracks and tend to align with the maximum principal stress. Splay cracks emanate from one side of the sliding parent crack. The theme of the paper is that the splay cracks play the dominant role in triggering the fault. The central idea is that the slender columns between the splay cracks are more likely to buckle and fail than are the columns between adjacent wing cracks because they do not have two fixed ends; instead, the end stemming from the inclined parent crack is free. A moment is then applied by frictional sliding of the parent inclined crack, and this causes the fixed-free columns to break at a much lower stress than the fixed-fixed columns. Columns created near a free surface are more likely to fail than those created elsewhere, and this explains the observation that shear localization tends to initiate near free surfaces. A first-order calculation shows that the failure stress of the splay-created columns is of the same order of magnitude as the terminal failure stress.

Propagation velocity of a natural hydraulic fracture in a poroelastic medium

The propagation rate of a natural hydraulic fracture is limited by the rate that fluid flows from the saturated rock into the void space created by fracture growth. Unlike induced hydraulic fractures, natural hydraulic fractures can not be modeled by specifying rates of fracture growth or fluid flow into the fracture as boundary conditions. Numerical solutions of the governing equations for natural hydraulic fracture growth in a poroelastic medium indicate that growth rates are primarily controlled by the hydraulic conductivity κ, the storage Sp′ and the initial flaw length 2αo. Computationally more efficient models which partially and completely decouple material stresses from fluid pressures give similar results. Results for several rock types indicate that, although the rate of fracture propagation is limited by fluid flow, fracture growth still accelerates. Results are generalized in dimensionless plots of fracture length versus time for various values of the dimensionless parameter ϕ = (1-ν)/(GSp′), where G is the shear modulus and ν is the drained Poissons ratio.

A study of solute transport mechanisms using rare earth element tracers and artificial rainstorms on snow

Rare earth element (REE) tracers and three artificial rain-on-snow storms at the Central Sierra Snow Laboratory, California indicate that (1) tracers applied to the snow surface immediately prior to the storm quickly appear at the bottom of the pack, with the tracer traversing the pack faster when the snowpack is wetter; (2) unlike most previous studies in which low solute concentrations were observed at high flow in diurnal cycles, the concentrations of the REE tracers in the outflow are positively related with input water flux; and (3) at a constant input flux the concentrations of all the REE tracers decreased exponentially with time, and the rate of this decrease was greater at high flow than at low flow. These observations can be qualitatively simulated by partitioning liquid water in the snowpack into mobile and immobile phases. Transport of the mobile water phase is governed by the advection-dispersion equations, while the immobile water only moves by exchanging with the mobile water. The rate of exchange between mobile and immobile waters follows first-order kinetics. Unlike previous mobile-immobile models for snow, the exchange rate coefficient is assumed to increase exponentially with the effective water saturation. The model successfully simulates the positive concentration dependency on input water flux. However, it remains unclear how the exchange rate coefficient varies with the nature of the medium and with hydrological conditions. These observations suggest that tracer concentrations in the outflow are largely dominated by solute transport via fast flow channels. This surprising result implies that a spatially averaged flow rate may not be adequate for modeling solute transport properties in unsaturated media.

Impact of Computer-Assisted Instruction in Hydrogeology on Critical-Thinking Skills

Although studies demonstrate that computer-assisted instruction (CAI) can be effective for enhancing basic cognitive skills such as rote memory, the role of CAI in developing higher-order critical-thinking skills such as problem solving remains uncertain. Using principles from cognitive psychology, the impact of a hydrogeological CAI laboratory on student problem-solving skills is assessed. Problem-solving skill is measured by statistical analyses of the ability to transfer concepts across disciplinary domains. Results suggest that in comparison to traditional instruction, the CAI laboratory focuses student attention on fundamental principles and is effective in developing problem-solving skills, particularly for students with stronger backgrounds in math and science.

Gradients in stream power influence lateral and downstream sediment flux in floods

Locations of landslides, bank failures, and floodplain deposition during recent intense flooding in Vermont and Colorado (USA) were spatially nonuniform, indicating that some reaches are more prone to these types of geologic hazards. These three key flood effects signal redistribution of sediment across landscapes, reflecting hillslope-channel coupling and the sources and/or sinks of material. We show that spatial gradients in total stream power (Ω) provide critical additional information beyond at-a-point Ω magnitudes for predicting which reaches are likely to be susceptible to these hazards during floods. Field tests in four rivers (watershed areas 0.8–180 km 2 ) indicate that downstream increases in Ω coincide with erosion and mass wasting into channels, and downstream decreases in Ω are associated with floodplain deposition. Our analytical approach, supported by field evidence, predicts geologic hazards and, more broadly, sources and sinks of material along rivers. These are critical concerns from a practical and theoretical standpoint.

Surficial redistribution of fallout 131iodine in a small temperate catchment

Isotopes of iodine play significant environmental roles, including a limiting micronutrient (127I), an acute radiotoxin (131I), and a geochemical tracer (129I). But the cycling of iodine through terrestrial ecosystems is poorly understood, due to its complex environmental chemistry and low natural abundance. To better understand iodine transport and fate in a terrestrial ecosystem, we traced fallout 131iodine throughout a small temperate catchment following contamination by the 11 March 2011 failure of the Fukushima Daiichi nuclear power facility. We find that radioiodine fallout is actively and efficiently scavenged by the soil system, where it is continuously focused to surface soils over a period of weeks following deposition. Mobilization of historic (pre-Fukushima) 137cesium observed concurrently in these soils suggests that the focusing of iodine to surface soils may be biologically mediated. Atmospherically deposited iodine is subsequently redistributed from the soil system via fluvial processes in a manner analogous to that of the particle-reactive tracer 7beryllium, a consequence of the radionuclides’ shared sorption affinity for fine, particulate organic matter. These processes of surficial redistribution create iodine hotspots in the terrestrial environment where fine, particulate organic matter accumulates, and in this manner regulate the delivery of iodine nutrients and toxins alike from small catchments to larger river systems, lakes and estuaries.

A Laboratory Exercise on Determining Dinosaur Speeds Using Dimensional Analysis

Measurements from a dinosaur trackway are used to estimate how fast the dinosaur track makers were moving. The exercise, which is appropriate for any introductory earth-science course at the secondary-school or college level, introduces students to dimensional analysis by having them construct an empirical graph of dimensionless stride length versus dimensionless velocity. The students then estimate the dimensionless stride length from the trackway data and use the dimensionless graph to determine the speeds of the dinosaurs. Experience with the exercise indicates that even students with little quantitative background are motivated by the challenge of determining whether they could outrun the dinosaurs and often begin to appreciate the power of dimensional analysis, a concept not usually presented in introductory courses.