crack propagation on desert surface clasts by differential insolation of cracks

1. abstract In the Southwest US, cracks in surface clasts have a preferred orientation independent of rock fabric, rock shape and local conditions. Differential insolation of incipient cracks of random orientations provides an explanation of this preferred orientation through removal of moisture held in the crack. A study of differential insolation of cracks of different orientations at 35°N was undertaken using a numerical radiative transfer code and idealized crack geometry. The amount of energy reaching the bottom of each crack was calculated at five minute intervals over the day for several days of the year to determine hourly, daily, seasonal and annual deposition of energy depending only on crack orientation and depth. By assuming that only crack orientations which effectively shield their interiors and minimize their water loss are able to grow, the pattern of cracks produced, including both expressed modes and their deviations from pure North-South and East-West behavior are consistent with observations in the field. Given this formulation, the important timescale for water retention is the annual average insolation which is associated with both modes of the aligned cracks while the effect of daily recharge by summer monsoon rains is consistent with the observed deviations of these modes. This suggests that both the annual average insolation and the daily pattern of rainfall could be recorded in the cracking patterns of surface rocks in the Southwest. timescales The timescales over which water enters and exits cracks is important to the analysis. For instance, if more then a year is required to discharge a crack, then only the annual average insolation is significant. Similarly, the timescale of the recharge of cracks is also important. As such, the nature of water movement through rock and the microstructure of the rock itself must be considered to determine the mechanisms by which water enters and exits the rock in the vicinity of cracks. This is analyzed using an order of magnitude approach. Equations [1] and [2] can be plotted for the pore size range of interest (Figure 3) using values for the various constants taken at 20°C. The most significant feature of this plot is the observed roll off in the discharge rate for pores larger then a few tens of nm. This means that for the largest pores which represent the largest volume of water and the major pathways into the smaller pores and microcracks, recharge can happen very quickly, on the order of hours, and occurs much more rapidly then crack discharge. As a result, unlike ponded water in a macroscopic crack which will evaporate quickly due to direct contact with the atmosphere, water in these pores and microcracks is stable on long timescales and will continue to recharge smaller microcracks and pores during this period. The characteristic timescale of discharge is of the order of 2x107 seconds or about two thirds of a year. crack propagation on desert surface clasts by differential insolation of cracks the role of water in thermal cycling The breakdown mechanism of surface clasts in arid environments has been a topic of debate for almost a century. Unlike in other environments where physical and chemical weathering by the action of plentiful liquid water is clearly the primary mechanism, arid environments largely lack sufficient water in the form of precipitation for typical weathering processes to dominate [2]. Instead rocks may remain on the surface for very long periods, in excess of 30 Ma in the most arid of deserts [3]. As a result, it has been suggested that rocks may be broken down by thermal insolation cycling. However, this has been difficult to show in experimental tests. The situation changes once water is added. Griggs [4] found that samples of rock which had survived 244 years of diurnal cycling unchanged when the cooled with dry air disintegrated noticeably within ten days of cycling (equivalent to about 2-3 years of exposure) when cooled with a mist of water. Barton also observed this effect in the field, noticing a correlation between the presence of moisture and degree of disintegration of monuments in Egypt [5,6]. Even so, additional evidence of the role of insolation is provided by recent work by McFadden et al. [1] in which a meticulous survey of a great many rocks at various sites in the United States Southwest found that there is a net preferred orientation to all the crack population once the effects of rock fabric and shape have been removed. This preferred orientation is reproduced, after McFadden et al., in Figure 1, and demonstrates that some regional or possibly global actor is affecting how rocks breakdown on a very small scale. It seems highly likely, as suggested by McFadden et al., that this actor is the sun. How can the role of water be reconciled with the crack preferred orientation observed by McFadden et al. which suggests that the sun is primarily responsible for rock failure? One possible solution is that the cracks themselves, by offering partial shielding from solar insolation, can act as locations of enhanced water retention by the rock. In this way, crack orientations which offer the best shielding from solar insolation will retain the most water and grow at the expense of other orientations of cracks. Figure 3 – Recharge and Discharge rates from convoluted capillary pores of length 10cm according to equations [1] and [2] respectively for a constant crack temperature of 20°C and a relative humidity of 0%. The rates of recharge and discharge are similar for small pores, but drastically different for large pores due to the transition between the Knudsen and Molecular Diffusion regimes. results There are three different regimes in insolation for the annual average depending upon the depth of the crack. The first regime (Fig 4, panel A) is a monotonic increase with E-W oriented cracks receiving the most insolation. This is the result of a domination of the summer months in the insolation curve in which E-W cracks receive more insolation then the N-S cracks. This regime extends from the shallow end to relative depths of 1 to 1.2 units. At large crack depths, greater then 2.5 to 2.8 units in depth, the opposite relationship is true (Fig 4, panel C) with N-S cracks receiving more insolation as the ‘winter’ regime dominates. However, there is an interesting crossover region between these two in which latitudinal effects dominate and a minimum is observed at about 35° N of E-W (Fig 4, panel B). To highlight the possible resulting crack directionality, a threshold in energy has been added beyond which cracks are considered to be baked out. The effect of the evaporation threshold (Fig 5) is to cause N-S oriented cracks to propagate when the incipient cracks are themselves shallow as E-W cracks are permanently baked out due to the large amounts of insolation received in the summer. If the incipient cracks are deeper then 1.2 units, a second population of cracks with ENE-WSW and ESE-WNW orientations can be produced. Finally for deep incipient cracks (3 units or more) E-W orientations are favored. The secondary mode is exhibited only along an ENE-WSW axis in Figure 1 instead of being symmetric around a north-south axis (i.e. there is no WNW-ESE mode represented) as seen in the results from section 4.3 and in Figure 6. Since the position of the sun in the sky is symmetric about a N-S axis, it cannot be an insolation effect on an annual time scale and must instead be a diurnal effect. As such, it is necessary to determine whether there is any orientation bias in the amount of available recharge.During most of the year, there is no hourly preference for rainfall, however, in the summer months, at weather stations near the New Mexico cluster studied by McFadden et al. [1] there is a strong peak at 2PM [9,10].This will favor those orientations which receive most of their insolation in the morning, before 2PM. Since these cracks will typically be shielded after precipitation has fallen, they should be able to retain this water for a longer amount of time (potentially overnight) which will allow more water to diffuse into the rock for these orientations. Figure 1 – 10° binned rose diagram of crack orientations unrelated to local conditions or rock fabric after McFadden et al, 2005 using the frame of reference as described in this publication with North indicated at 0°. The cracks are oriented with two major modes represented, a primary N-S mode and a weaker ENE-WSW mode. John E. Moores, Jon D. Pelletier and Peter H. Smith Lunar and Planetary Laboratory, University of Arizona 1629 E University Blvd Tucson, AZ 85721-0092 Email: jmoores@lpl.arizona.edu Figure 4 (left) – Annual insolation on cracks divided into three regimes. Cracks with a minimum in insolation at N-S orientations (A), cracks with a minimum in insolation away from E-W or N-S (B) and cracks with a minimum at E-W orientations (C). Open squares and circles indicate the identity of the line, resolution is 1°. Figure 5 (right) – Rose diagrams of preferred orientations for water retention corresponding to the three regimes shown in Figure 6. Depending upon the depth, cracks may be produced with any of the three forms. Panel A corresponds to a crack depth of 0.2, Panel B to 1.5 and Panel C to 4.0. The energy thresholds used were 1.65x109J yr-1 m-², 4.70x108 J yr-1 m-² and 1.12x108 J yr-1 m-² for each panel respectively. Cracks which receive more energy then this threshold are considered baked out and are not shown. hydration weathering and differential insolation model Cracks, in general, represent areas of a rock in which water can be retained for longer times then directly on the surface (1) because of their concave geometry provides a low point in which water can accumulate, (2) because they shield their interiors from solar insolation and (3) if they are deep enough, they can shield their interiors from the daily thermal wave penetrating down from the surface. As such, orientations which receive more insolation will evaporate more water from their interiors and will bake out entirely before other orientations of cracks. This means that if water is required for a crack to grow, those cracks which preserve their internal water for the longest period will grow preferentially. These preferential cracks will be those with the lowest amount of insolation over the timescale relevant to crack formation. The solar insolation within the cracks is modeled using a plane-parallel radiative transfer code originally designed by Martin Tomasko to perform calculations in the atmosphere of Titan [7].The cracks themselves are modeled as linear troughs with flat bottoms and sides, as in Moores et al. [8] and shown schematically in Figure 2. The assumption has been made that the cracks are found on a flat, horizontal surface, both for simplicity and because this orientation of crack can retain the largest amount of water. As the sun moves in the sky, the model determines if it can be seen from each of 200 individual area elements located on the bottom of the trench. If the sun is not seen, the incident flux on that panel is zero for that configuration of the sun in the sky. The rock surface is considered sufficiently dark that reflections from the trench walls are not significant. The energy variations to be presented in section 3 describe the total energy received at the trench bottom. As such, this can be considered as characteristic of the amount of down-welling radiation at a characteristic depth. Trough deepening is accomplished by deepening the floor of such a trench while keeping the cross section constant. These trenches will be described by their aspect ratios in the manner of length:width:depth. The final piece of information required to plot the path of the sun on each day of interest is the latitude of the observer. Since this model will be tested against the orientations shown in McFadden et al. [1], a latitude of 35°N, a typical value for the sites surveyed in this study was chosen.In order to build up diurnal, seasonal and yearly variations, the model tracks the sun in the sky at 5-minute intervals during the day for 8 values of the solar longitude equally spaced over the year (LS=0° or vernal equinox, LS=45°, LS=90° or northern summer solstice, LS=135°, LS=180° or autumnal equinox, LS=215°, LS=270° or northern winter solstice, and LS=315°). Intermediate values, when necessary, are obtained by interpolating between these points. Figure 6 (above) – Cumulative Insolation by 13:20 at Los Alamos, NM by crack orientation. ENE-WSW cracks receive less insolation by the early afternoon compared to WNW-ESE trending cracks at all depths of the initial crack. The differential is more extreme for the variation shown in Figure 6, panel C (120° vs 60°) then for panel B (20° vs 170°). Open squares and circles indicate the identity of the line, resolution is 1°. Figure 2 – Geometry of the simulated cracks with aspect ratios of 8:1:1 (A) and 8:1:3 (B). Both cracks are shown in an E-W configuration corresponding to a rotation angle of 90°. The direction of increasing rotation angle is shown in both panels and is consistent with the frame of reference shown in Figure 1. Background Image A surface clast in Southern Iceland broken by freeze-thaw weathering (a form of hydration weathering) along a preferred direction. Photo by Till Niermann (1989), used under the GNU Free Documentation Licence v1.2 conclusions Simulations of different orientations of cracks show that certain orientations of cracks can receive more insolation then other cracks on all timescales. The pattern of orientations that are favored changes for different depths of crack under the same conditions. By assuming that crack growth is proportional to moisture content in a crack which is itself inversely proportional to the received insolation on the crack bottom, it was possible to determine which orientations would propagate most easily. For the US Southwest, three different modes were exhibited, a north-south population when the initial crack was shallow, an ESE-WNW and ENE-WSW population when initial cracks were of intermediate depth and an east-west population when initial cracks were deep. The first two modes correlate well to the data retrieved by McFadden et al. [1] for cracked rocks at several sites in the US Southwest. Thus, the pattern of yearly average insolation in selecting certain orientations for growth and not others correlates well with the observed data. The east-west mode predicted by the simulation is not seen and could result from a lack of deep initial cracks compared to shallow cracks and an inability of the discharge of moisture to respond to variations in insolation shorter then a year. This relative lack of east-west cracks compared to ENE-WSW cracks which are themselves less common then north-south oriented cracks correlates well with the idea that these modes are associated with progressively shallower initial cracks which are progressively more common in the initial surface cracking of rocks. The apparent offset in the north-south mode and the lack of an ENE-WSW mode in the dataset of McFadden et al. is also correlated with the diurnal cycle of rainfall in the summer which promotes recharge of certain crack orientations and not others. This suggests that a record of both the annual variation in insolation and the daily pattern of rainfall could be preserved in the orientations of cracks on rocks in the US Southwest. references [1] McFadden, L.D., Eppes, M.C., Gillespie, A.R., and Hallet, B. 2005. Physical weathering in arid landscapes due to diurnal variation in the direction of solar heating. GSA Bulletin, 117 1, 161-173 [2] Mabbutt, J.A. 1977. Rock Weathering in Deserts in Desert Landforms. MIT Press, Cambridge, Mass. [3] Dunai, T. J., Gonzáles-Lòpez, G.A. and Juez-Larré, J. 2005. Oligocene-Miocene age of aridity in the Atacama Desert revealed by exposure dating of erosion-sensitive landforms. Geology., 33 4, 321-324 doi: 10.1130/G21184.1 [4] Griggs, D.T. 1936. The factor of fatigue in rock exfoliation. Geology, 44, 783-796 [5] Barton, D.C. 1916. Notes on the disintegration of granite in Egypt. Geology 24, 382-393. [6] Barton, D.C. 1938. Discussion: The disintegration and exfoliation of granite in Egypt. 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