End-use forecasting in the context of building adaptive water services

Water resource managers are faced with planning for an uncertain future constrained by limited knowledge of how demands will change in future and what supplies will be available to match them. By adopting an adaptive management approach, flexible and robust responses can be developed as new information comes to hand. A transparent approach has been developed that avoids complicated probabilistic approaches and encourages planners to consider investment policies to accommodate a range of potential scenarios. Integrated resource planning (IRP) principles are key to this approach and requires that both supply and demand side options are considered. Whilst much focus has been on the supply side, end user interventions have received less attention as a longer term approach. Restrictions have to date been the fall back option to deal with impending droughts, but this is not likely to be acceptable under reduced trending supplies. By focusing on end-use planning, savings through suppressed customer demand can free up further water thereby delaying the introduction of large expensive supply options. By disaggregating the end uses by residential customers into for example, showers, toilets, baths, washing machines, outdoor use, etc., a richer understanding of where residential water actually gets used and therefore where the potential for demand reduction lie. This paper firstly presents a framework for adaptive planning for urban water supplies and secondly, introduces the notion of end-use modelling and planning as a means to reduce consumption. Real examples from work conducted in Australia will be used to illustrate these approaches

Variation of hydraulic properties due to dynamic fracture damage: Implications for fault zones

High strain rate loading causes pervasive dynamic microfracturing in crystalline materials, with dynamic pulverization being the extreme end-member. Hydraulic properties (permeability, porosity, and storage capacity) are primarily controlled by fracture damage and will therefore change significantly by intense dynamic fracturing—by how much is currently unknown. Dynamic fracture damage observed in the damage zones of seismic faults is thought to originate from dynamic stresses near the earthquake rupture tip. This implies that during an earthquake, hydraulic properties in the damage zone change early. The immediate effect this has on fluid-driven coseismic slip processes following the rupture, and on postseismic and interseismic fault zone processes, is not yet clear. Here, we present hydraulic properties measured on the full range of dynamic fracture damage up to dynamic pulverization. Dynamic damage was induced in quartz-monzonite samples by performing uniaxial high strain rate (> 100 s−1) experiments in compression using a split-Hopkinson pressure bar. Hydraulic properties were measured on samples subjected to single and successive loadings, the latter to simulate cumulative damage from repeated rupture events. We show that permeability increases by 6 orders of magnitude and porosity by 15% with dissipated energy up to dynamic pulverization, for both single and successive loadings. We present damage zone permeability profiles induced by earthquake rupture and how it evolves with repeated ruptures. We propose that the enhanced hydraulic properties measured for pulverized rock decrease the efficiency of thermal pressurization, when emplaced adjacent to the principal slip zone

Fault reactivation and strain partitioning across the brittle-ductile transition

The so-called “brittle-ductile transition” is thought to be the strongest part of the lithosphere, and defines the lower limit of the seismogenic zone. It is characterized not only by a transition from localized to distributed (ductile) deformation, but also by a gradual change in microscale deformation mechanism, from microcracking to crystal plasticity. These two transitions can occur separately under different conditions. The threshold conditions bounding the transitions are expected to control how deformation is partitioned between localized fault slip and bulk ductile deformation. Here, we report results from triaxial deformation experiments on pre-faulted cores of Carrara marble over a range of confining pressures, and determine the relative partitioning of the total deformation between bulk strain and on-fault slip. We find that the transition initiates when fault strength (σ_{f}) exceeds the yield stress (σ_{y}) of the bulk rock, and terminates when it exceeds its ductile flow stress (σflow). In this domain, yield in the bulk rock occurs first, and fault slip is reactivated as a result of bulk strain hardening. The contribution of fault slip to the total deformation is proportional to the ratio (σ_{f} − σ_{y})/(σ_{flow} − σ_{y}). We propose an updated crustal strength profile extending the localized-ductile transition toward shallower regions where the strength of the crust would be limited by fault friction, but significant proportions of tectonic deformation could be accommodated simultaneously by distributed ductile flow

Colored Non-Crossing Euclidean Steiner Forest

Given a set of $k$-colored points in the plane, we consider the problem of finding $k$ trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For $k=1$, this is the well-known Euclidean Steiner tree problem. For general $k$, a $k\rho$-approximation algorithm is known, where $\rho \le 1.21$ is the Steiner ratio. We present a PTAS for $k=2$, a $(5/3+\varepsilon)$-approximation algorithm for $k=3$, and two approximation algorithms for general~$k$, with ratios $O(\sqrt n \log k)$ and $k+\varepsilon$

Influence of gouge thickness and grain size on permeability of macrofractured basalt

Fractures allow crystalline rocks to store and transport fluids, but fracture permeability can also be influenced significantly by the existence or absence of gouge and by stress history. To investigate these issues, we measured the water permeability of macrofractured basalt samples unfilled or infilled with gouge of different grain sizes and thicknesses as a function of hydrostatic stress and also under cyclic stress conditions. In all experiments, permeability decreased with increasing effective pressure, but unfilled fractures exhibited a much greater decrease than gouge-filled fractures. Macrofractures filled with fine-grained gouge had the lowest permeabilities and exhibited the smallest change with pressure. By contrast, the permeability changed significantly more in fractures filled with coarser-grained gouge. During cyclic pressurization, permeability decreased with increasing cycle number until reaching a minimum value after a certain number of cycles. Permeability reduction in unfilled fractures is accommodated by both elastic and inelastic deformation of surface asperities, while measurements of the particle size distribution and compaction in gouge-filled fractures indicate only inelastic compaction. In fine-grained gouge this is accommodated by grain rearrangement, while in coarser-grained gouge it is the result of both grain rearrangement and comminution. Overall, sample permeability is dominated by the gouge permeability, which decreases with increasing thickness and is also sensitive to the grain size and its distribution. Our results imply that there is a crossover depth in the crust below which the permeability of well-mated fractures (e.g., joints) becomes lower than that of gouge-filled fractures (e.g., shear faults)

Scaling relationship between the wavelength of longitudinal ridges and the thickness of long runout landslides on the moon

The formation mechanism of longitudinal ridges in long runout landslides has been proposed to require ice and/or clay minerals, as low friction materials would allow the spreading of the deposit, causing the development of longitudinal ridges by tensile deformation of the slide. The necessity of ice in the formation of longitudinal ridges has been challenged by the finding that the wavelength of longitudinal ridges is 2 to 3 times the thickness of the deposit in both ice-free laboratory experiments on rapid granular flows and in a martian and terrestrial long runout landslide, suggesting a scale- and environment-independent mechanism. We conduct morphometric analysis of the longitudinal ridges in two landslides on the Moon, considered ice-free throughout its geological history: the Tsiolkovskiy crater landslide; and the Light Mantle avalanche in Taurus-Littrow Valley. We show that Tsiolkovskiy crater landslide exhibits a scaling relationship between the wavelength of its longitudinal ridges and the thickness of its deposit that is consistent with previous studies, supporting the idea that ice is not a necessary condition for the development of longitudinal ridges. As the Tsiolkovskiy crater landslide is laterally confined, it demonstrates that neither the development of longitudinal ridges nor the occurrence of the scaling relationship between the wavelength of the ridges and the thickness of the deposit depend on the lateral spreading of the deposit. Finally, we use the Light Mantle to test the use of the scaling relationship as a tool to estimate the thickness of the deposit when classical geomorphological methods are not applicable

Direct Evidence for Fluid Pressure, Dilatancy, and Compaction Affecting Slip in Isolated Faults

Earthquake instability occurs as a result of strength loss during sliding on a fault. It has been known for over 50 years that fault compaction or dilatancy may cause significant weakening or strengthening by dramatically changing the fluid pressure trapped in faults. Despite this fundamental importance, we have no real understanding of the exact conditions that lead to compaction or dilation during nucleation or rupture. To date, no direct measurements of pore pressure changes during slip in hydraulically isolated faults have been reported. We show direct examples of fluid pressure variations during nucleation and rupture using a miniature pressure transducer embedded in an experimental fault. We demonstrate that fluids not only are significant in controlling fault behavior but can provide the dominant mechanism controlling fault stability. The effect of fluid pressure changes can exceed frictional variations predicted by rate‐ and state‐dependent friction laws, exerting fundamental controls on earthquake rupture initiation

Time Dependent Mechanical Crack Closure as a Potential Rapid Source of Post-Seismic Wave Speed Recovery: Insights From Experiments in Carrara Marble

Seismological observations indicate strong variations in wave velocities around faults both co-seismically during earthquakes, and post-seismically. Recovery is commonly associated with a reduction in crack damage. Here, we explore the recovery associated with time-dependent mechanical closure of cracks. We report results from laboratory experiments conducted on dry cores of Carrara marble at room temperature. We deformed cylindrical samples in the semi-brittle regime to induce crack damage before subjecting them to hydrostatic and triaxial stress conditions for extended periods of time while recording dilatancy and wave speeds repeatedly. We report wave speed increases of up to 40% of the damage-induced wave speed drop in samples subject to hydrostatic loading. Moreover, we report the occurrence of significant wave speed increases contemporaneously with time-dependent creep in triaxially loaded samples. Wave speed recovery during creep is only observed below a threshold creep strain rate, a result we interpret as a transition from brittle to plastic creep with decreasing strain rate. We interpret the wave speed increase in terms of reduced crack density and increased contact area within the crack array, and show that around 40% of the total crack surface has to be closed to justify the observed wave speed recoveries. We propose that mechanical crack closure is driven by the viscous relaxation of the bulk rock under the influence of locked-in stresses at low confining pressure, and of the external stresses at higher confining pressure. Our study shows that mechanical crack closure is a significant source of time-dependent wave speed recovery

Compactive Deformation of Sandstone under Crustal Pressure and Temperature Conditions

The transition from macroscopically brittle to macroscopically ductile deformation in porous sandstones is known to be pressure dependent, with compactive, ductile behavior occurring only once significant effective pressures have been reached. Within the crust, such effective pressures are associated with burial depths in the range 0.5 to 6 km, where the temperature is likely 35 ◦C to 200 ◦C. To test the importance of such elevated temperature on the strength and deformability of sandstone, a series of constant strain rate, triaxial deformation experiments were performed on three different water saturated sandstones at either ambient temperature or 150 ◦C. For each sandstone, an effective pressure range was used which spanned both the brittle and ductile deformation regimes, up to a maximum of 120 MPa. In the brittle regime, we observed a temperature‐dependent lowering of the yield stress of between 8 and 17%. Within the ductile regime, we observed an even greater reduction in the yield stress of between 9 and 37%. A further notable observation is that the transition from dilatant, brittle behavior to compactive, ductile behavior tends to occur at a lower effective pressure at elevated temperature. The weakening observed at elevated temperature can be explained by a reduction in fracture toughness, which is shown mathematically to cause greater weakening in the ductile regime than in the brittle regime. The apparent reduction in toughness at elevated temperature is potentially driven by a combination of a reduction in surface energy and, to a minor extent, an increase in subcritical crack growth rate

Longitudinal ridges imparted by high-speed granular flow mechanisms in martian landslides

The presence of longitudinal ridges documented in long runout landslides across our solar system is commonly associated with the existence of a basal layer of ice. However, their development, the link between their occurrence and the emplacement mechanisms of long runout landslides, and the necessity of a basal ice layer remain poorly understood. Here, we analyse the morphometry of longitudinal ridges of a martian landslide and show that the wavelength of the ridges is 2–3 times the average thickness of the landslide deposit, a unique scaling relationship previously reported in ice-free rapid granular flow experiments. We recognize en-echelon features that we interpret as kinematic indicators, congruent with experimentally-measured transverse velocity gradient. We suggest that longitudinal ridges should not be considered as unequivocal evidence for presence of ice, rather as inevitable features of rapid granular sliding material, that originate from a mechanical instability once a kinematic threshold is surpassed