Stress and Strain:
Squashing Rocks in the Muav Gorge

(Continued from page 1)

   gently up a few degrees as you approach the river. Bedding on the other side of the river mirrors this fold: rising from the opposite direction to meet the main canyon walls.

   These faults and folds occur within a twenty-five mile stretch of the canyon that begins near Fishtail and ends somewhere below Tuckup. The folds are exposed from river level to perhaps two or three hundred feet up the walls. They are petite in comparison to other folds within the canyon like the East Kaibab Monocline. Their expression is restricted entirely to the Muav, and they are persistently aligned with the canyon no matter which way the walls twist and turn. Since the faults and folds so faithfully follow the river, they can only be reached by boat. Voila: three research permits for four people to spend twenty-one days simply messing about in boats during April, July, and October.

   Pat Tierney rowed a boat on the first of those three research trips. At the foot of the Bass Trail, Pat and I came around a corner and saw a naked old man standing knee-deep in the river. As we pulled up, Pat whispered that I wasn’t going to believe this. The man- George- bellowed out: “Have you got any women?” Pat said no. George, a true gentleman, was relieved not to embarrass anyone as he took his bath. George was once an Indiana mason; since retirement he had tried his hand at rock-climbing, sky-diving, kayaking (Pat had taught him on Westwater the year before), and most recently hiking. He had been in the canyon for six months now, hiking for three weeks at a shot.

   George rode with us the next morning. We spent the day dawdling in upper Elves. Story by story, without self-consciousness, he outlined a life led in honor. At day’s end, I was sorry to leave him but we had to push on. Five days later, working at Olo, we watched a Georgie White flotilla blast by, boat after boat after boat. Georgie drove the last triple rig, wearing that leopard-skin get-up. George stood next to her in the motor well.

   Geologists frequently get away with wildly waving their arms as they describe “tremendous stresses” that cause rocks to fold and mountains to grow. Excuse me, but how much stress? “Hard to say, but certainly a lot.” Larry Stevens once treated us to his wonderful analogy of 69,000 elephants pouring through Crystal hole every minute. He was putting his money where his oars were, not just waving his arms about “lots of water.” Most geologists are loathe to be so precise.

   Peter Huntoon had ascribed the presence of the Muav folds to the underlying Bright Angel Shale being squeezed up like toothpaste by the weight of the adjacent canyon walls. A nice analogy, but one with some shortcomings: its vertical orientation of force could not explain the thrust faults and kink folds that are intimately associated with other, more gentle folds found in this exposure of the Muav. I suspected that Huntoon was on to something with his toothpaste metaphor, but that the driving force behind the folds would turn out to be a bit more complicated.

   The beauty of studying the Muav river-level folds was that the stress that caused the folding was quantifiable: gravity, all 32-feet-per-second-squared of it. Regional stresses of the arm-waving ilk can be discounted because the folding so perfectly follows the river as it snakes southwest past Matkat, south toward Sinyala, and northwest toward Ledges. I idealized that section of the canyon into a flat-bottomed gash with vertical walls (not far from the truth); plugged in the specific gravity of the Muav, Redwall, and Supai; and ground the numbers through a finite-element model in order to relate force to deformation, stress to strain.

   The mathematics suggested that the most significant stress on bedrock just under the river would be horizontal, not vertical. This is because rock beneath the canyon walls exerts a horizontally directed pressure on its neighbors as it tries to flatten in response to gravity. Rock just beneath the river, on the other hand, is not vertically compressed; the greatest stress it feels is the laterally directed force derived from rocks beneath the canyon walls.

   My father was on the second trip. At the outset, I had discouraged him from bringing a transistor radio; I knew that he would just listen to the Albuquerque traffic reports on KOB. At Nevills on night five, I cooked dinner and yelled to come get it. Nothing happened. I couldn’t find Dad, and Jimmy Hendrick was missing too. I yelled again. Still nothing. Ten minutes later on that October night in 1977, Dad and Jimmy erupted up from behind a boulder fifty yards away, whooping and hollering as Reggie Jackson hit his third home run in that year’s World Series.

   Folds that follow canyon walls are not common. The Meander Anticline in Cataract does parallel the Colorado River, but it has no kink folds and can probably best be explained by Huntoon’s toothpaste model. The underlying Paradox salts are squeezed up by the differential loading of canyon walls, bending rock along the way, oozing out along the crest as small salt volcanoes in Red Canyon. Beyond Cataract, examples of other river-oriented folds become difficult to find. Even within the Grand Canyon, the folds are expressed in one place (Fishtail to Tuckup) where the Muav is at river level, but not at another (36-Mile to Saddle). Why are the folds so rare?

   The recipe for river-oriented folds first calls for steep walls (lie on your back at Upset Hotel: you’re looking two thousand feet straight up to the Esplanade). Add a limestone with just the right consistency: solid beds separated by thin silt layers. The silt, if wet, would allow the limestone layers to slide over one another, much like the pages in a bending telephone book. Imagine trying to flex a single piece of three-inch-thick wood. Maybe Dan Dierker could do it if Brian were holding the other end; I sure can’t. But anyone can easily bend a telephone book of the same thickness because the pages are free to slide past one another. Similarly, the Muav limestone (in lots of layers separated by silt) is much more easily bent than a massive limestone like the Redwall. The direction of force acting upon the rock is critical. If the force is perpendicular to bedding, it will tend to lock up the layers, and prevent them from sliding relative to one another while bending. But if the force is directed not-quite-parallel to bedding, then the layers don’t lock up and the limestone is more likely to bend.

   Back in the office, I fussed and doodled, crumpling a lot of paper along the way. Engineering equations gradually emerged that related stress to strain.

   I remember a time during graduate school when I lived, breathed, and ate those sort of equations. I once looked groggily out the back seat of a car at snow swirling past the window. For a millisecond, I clearly visualized the snow’s movement in terms of the differential equations with which I had been struggling in a dream. Then the circuit breakers blew, smoke poured out my ears, and I fell back asleep. It is fascinating to reflect on those days from this vantage point fifteen years down the road. Did all those variables really make sense to me? Did I speak such a different language then than I do now?

  To complete the recipe for these folds, add a dash of raw imagination. Basalt flows plugged up the canyon in the vicinity of Lava Falls about a million years ago, to depths of at least seven hundred feet. Could this lake have had anything to do with formation of the Muav folds? The river, with its depth measured in tens of feet, is able to wet only superficial horizons of bedrock. Pressures at the bottom of the lake would have been much higher, capable of driving water much deeper into the pores of the Muav. The lake would have been much deeper at Kanab Canyon than back upstream at Buck Farm. This difference in depth and pore pressure might explain the presence of folds in one place and not the other.

   The added pore pressure may have been enough to adequately moisten the Muav, and to allow the layers of limestone to glide over one another in response to laterally compressive stresses transmitted from the weight of the nearby canyon walls. In geologic terms, the folding could have occurred in a relatively short time; the mathematics and field observations both point to an “elastic,” not “plastic,” type of deformation which theoretically occurs at a rate independent of time. According to this “lake” hypothesis, the folding happened a million years ago, before the river eroded down to its current level; subsequent erosion has exposed the folds where we now see them in the canyon walls.

   Hugh Rieck and I each rowed a boat on my third research trip. I had already written the thesis, but my research trip. I had already written the thesis, but my advisor hadn’t gotten around to reviewing it before our departure from the Ferry. I was resigned to field checking the work without his comments. Two motor boats pulled alongside near Bedrock, to gab and to ogle the two ladies who were working with us. One of the boatmen was distracted from his ogling by a small plane flying at Redwall level (legal if ill-advised in those days). His distraction turned to downright orneriness when the plane returned and skimmed by at river level. As it passed, a package popped out and a parachute blossomed. I rowed over and fetched the tupperware container: my advisor approved. I jumped up and down, yelling incomprehensibly something that sounded like, “I have a master’s degree! I have a master’s in Science!”

   Wesley Smith, using a bright flashlight and an even brighter imagination, once treated us to a remarkably pornographic shadow show, projected onto the wall across from Ledges. The passengers howled. That same wall brought many of my thoughts about the Muav folds into sharper focus. My equations had predicted that the limestone ought to fold when units about a meter thick were able to slide past one another. Look at that wall next time you drive by: the Kanab Canyon Member of the Muav does indeed seem to have parted into slabs separated by silty planes about a meter apart. Well, about a meter. Whose imagination was more fertile, mine or Wesley’s?

   Equations do not define the Muav folds; they are not a substitute. Instead, I think of them as a light held inside the rock, an illumination that allowed me to inspect the edges, ponder the details, and conjecture about the origin of one tiny aspect of the Grand Canyon.

Michael Collier