Topic 13: WHEN PUSH CAME TO SHOVE: Mountain Chains of the World 1. The Paradox of Rock Strata on Bedding-Plane Faults The assignment was this: Given, a large block of rock resting on a horizontal slab of another rock. The block is 30,000 ft long and 10,000 ft high. I don't say how wide. The unit weight (w) is 150 pcf (lbf/cu ft). The block is pushed by a force T until it moves. By definition, the friction coefficient f is equal to T/N, where N is normal force acting between block and slab beneath. In this case N = W, the full weight of block, since the slab is horizontal. So, we can write T = fN, where N = W = (abc) w = volume X unit weight. But I want the push in terms of stress S, where stress = force/area. In this case, S = T/ac = [f (abc) w]/ac = bwf Now, calculate the stress needed to slide the block. OK, i did not give you f!! Are you really stuck? I don't think so! -- You could (1) assume a few values of f, and plot S against f to generalize all possible values (linear plot); you could (2) look a typical value up, using the library, searching for any text on structural geology, engineering geology, rock engineering, rock mechanics, or a handbook like the Handbook for Chemistry and Physics; or (3) use the internet search; or, (4) look in your class text (!!). Or, you could make your own test, as we did in class (see digression below) Having now made the calculation for the push S required to move the block, will it slide? Or will the edge of the block break off, before the required S for block sliding can actually be applied? To answer this, ask if S is greater than the compressive strength C of the rock block. How to get C? See (1) through (4), above. You also have a set of triaxial strength data that could be used for this example. If S > C, the block withstands the stresses, and the whole block slides. If C > S, the block breaks (a thrust or reverse fault) before the stress is big enough to slide the block. WHICH IS IT? Can the block slide, or not? The dimensions and unit weight used above are compatible with a cross-section in the Jura Mountains, Switzerland, but similar (and even larger) lengths b could be chosen from the Appalachians, Alps etc. Since these are accurate cross-sections, evidently the movement in question DID occur. If the analysis above suggests that it could not move, something must be wrong with the analysis! Can you solve this dilemma? (see also below) [digression from above: MAKE YOUR OWN FRICTION TEST Place a rock block on a rock slab. Tilt the slab carefully, increasing its angle A to the position where the block just begins to move. Have a friend measure this critical angle, A = A*, with a protractor. The critical dip angle A* of the slab is equal to the friction angle P (for Phi). The friction coefficent f = tanA*. It works out like this: The block has weight W, and the sliding force is T = W sinA. The resisting force R = k(area) + [W cosA] tanP, which is just Coulomb's strength law expressed in terms of forces. In this general case, the cohesion k is multiplied by the contact area of the block. For simple sliding, k is zero, so the term drops out. So, at the moment of sliding, angle A = A*, and T = T*. T* = W sinA* = [W cosA*] tanP sinA*/cosA* = tanP tanA* = tanP So, A* = P, and its tangent is the coefficient of friction. When we tried it out on a smooth sandstone block, we measured about 28 degrees for A*, suggesting f = ? Carefully repeating the test and averaging results gives a mean value accurate to about a degree. The above value is a typical one for rock materials, as you can verify by looking in suitable textbooks. (end of digression)] The above stuff applies to the topics below, particularly for the Valley and Ridge ranges as discussed below. 2. Kinds of Mountains The formation of mountain ranges (orogenesis) is one of the key ways the continental crust maintains its average elevation, relief, and aerial extent. From early in its development, the Earth's surface has been characterized by mountain ranges. It has become clear that mountains go through long cycles, during which they first are uplifted, then gradually waste by erosion, and finally cease to exist in the traditional sense of the word. Their former presence is recorded in the eroded remnants of gigantic batholiths and belts of highly deformed metamorphic rocks. Perhaps all continental rocks were parts of mountains at one time or another. Mountains worldwide differ is age, history, origin, and size. Although in a loose sense, we can define "mountains", it is difficult to classify them in a systematic way because they display a great variety of rocks and structures; no two mountain ranges are identical. About the only thing mountains have in common is the fact that they are (or were) higher than the surrounding terrain. There are certain characteristics of mountain groups which are of importance in understanding the process of orogenesis. Mountain belts are commonly characterized by a "hinterland" and a "foreland". The hinterland is usually closer to the edge of the continent, where deformation is has been more severe and involved deeper lithosphere. The foreland is found nearer to the craton (interior) of continents. The most severe deformation occurs where continent-continent collision has taken place. Some features of most continental and oceanic mountain systems: - Mountains tend to occur in elongate or "sub-linear" associations. When a group of mountains so aligned are clearly related with respect to composition and origin, they constitute a mountain range or system. The term system generally applies to a grouping of several ranges which appear to be similar in form, structure, and alignment. The Cascade Range, Sierra Nevada, Rocky Mountains, and Canadian Rockies, among many other ranges, are all members of the American Cordillera system. - "Young" mountains tend to occur around the margins of continental areas. It has been recognized by geologists for over a century that this basic association is important to understanding the formation of mountains and the evolution and development of continents. Mountain ranges are, one way or another, the consequence of the interaction of lithospheric plates. TYPES OF MOUNTAINS -- Although mountains show a great diversity in form and rock-types, there are several basic kinds. My neighbor, Prof. Terry Engelder, is a structural geologist and would classify mountains as follows: - Valley and Ridge ranges (or, Fold and Thrust belts). This type of range is characterized by a series of broad, alternating synclinal and anticlinal folds which involve deformation of (mostly) the "cover" rocks overlying a nearly-rigid basement. This type is characteristic of deformation in the "foreland," where the cover has slid like a rug over a polished floor. The valleys have developed by erosion within the least resistant strata, such as limestones and shale. In contrast, the ridges are formed by very resistant rocks. The Valley and Ridge province of central Pennsylvania is an example of this type of range. Here, the "cover" consists of Paleozoic strata overlying pre-Cambrian crystalline "basement", gneisses, etc. The cover rocks slid over Cambrian shales (the surface of "detachment"). The deformation extends farther westward with diminished effect (smaller fold amplitude) into the bordering Allegheny Plateau province, with a rise in the bedding-plane detachment fault to a younger horizon -- thus forming a detachment sheet with decreasing displacement westward. The Canadian Rockies and the Jura Mountains in Switzerland and France are other examples. (But, is there a friction problem with these movements?? Simple calculations for such cases, with assumed friction coefficients of about 0.6 (consistent with lab tests), suggest that the block ends might snap off before the blocks could slide. This is a "mechanical paradox"(see discussions above, AND below). - Crystalline core ranges. In the "hinterland" of mountain ranges. the crystalline basement is sliced into thrust sheets which have been pushed toward the foreland by plate-tectonic forces. The core of the hinterland is characterized by metamorphic rocks which have been folded plastically into great crystalline sheets, because the rocks were not able to resist the great forces of orogenesis. These thrust sheets were soft and ductile at burial greater than 10 km. The Blue Ridge Mountains of the southern Appalachians are an example of this type, and similar rocks are found in eastern PA. In other areas, the core of the mountain belts are characterized by numerous intrusions of igneous rocks. The White Mountains of New Hampshire and the Green Mountains of Vermont are examples of this type of core. - Crystalline uplifted ranges. In some areas of the world, continental crust is compressed to the point where fragments of crystalline basement pop up in the form of brittle block uplifts. The sedimentary cover rocks are folded as "monoclines" over steep faults in the brittle basement, in the form of a draping sheet. The Wyoming ranges, and some in Colorado, are characteristic of this type of crystalline block uplift, with monoclines forming over the block boundary faults. The boundary faults are steep; some are reverse faults (Wind River Range, Beartooth Range, Colorado Front Range), and some are normal faults (Teton Range fault against Jackson Hole). - Plateau uplifts. The largest pieces of crustal rock to lift relatively high relative to sea level are called plateaus. If one is standing on a plateau, it is not immediately apparent that one is standing on a mountain range. Topography can be relatively subtle. Yet, the edge of the plateau regions appear clearly as mountains. The world's largest plateau is the Tibetan Plateau. In the United States, the Colorado Plateau is the largest of such features. - Extensional fault-block ranges. Where the crust is being extended or pulled apart, horsts and grabens can form with the uplifted horsts becoming the mountain ranges. These mountains are separated from the intervening valley floors by normal faults of great displacement. The Basin and Range province of Nevada (and some adjacent areas) consists of a system of ranges which formed during the Tertiary, as a consequence of the stretching of the continental crust. Similar mountains are found along the mid-ocean rifts, where oceanic crust is just forming. The Sierra Nevada mountains are a gigantic tilted normal fault-block structure at the edge of the Basin and Range. - Volcanic ranges. Inland of subduction zones, chains of volcanoes pile up as a consequence of eruptions of lava and explosive eruption products, and water-worked volcanic debris. Magma chambers underlie the volcanoes, but may be exposed by deep erosion. The Cascade Range of California and Oregon form a Volcanic mountain range. The currently-active volcanoes are only the latest features sitting on top of the Cascades like candlesticks on a cake, and the range is made up of a complex of volcanic and plutonic features that developed over a long time. 3. More on the Mechanical Paradox of Detachment Sheets So, what is the resolution? At least two explanations can be provided. First, as one of your classmates suggested, perhaps the assumed friction value is wrong, and a weaker material might be present under the pressure and temperature conditions a few miles down. The material might be "plastic", rather than "frictional". In particular, rocksalt and gypsum is very weak and ductile at modest temperature rise, and it has been proposed by some geologists that these materials might be associated with bedding-plane fault detachments under the Appalachian Plateau, extending into New York State (in relation to the Silurian-age salt beds), and also under the Jura. Second, as suggested in our beer can experiments, pore fluid pressure can reduce the resistance to sliding. If the pore fluid pressure nearly reaches the full weight of overburden, the slide resistance almost vanishes. This was demonstrated by sliding of cold beer cans on the polished flat plate. When the can warmed up, the air inside warmed up and expanded, providing an uplift force U that counterbalanced the weight of the beer can. The friction force vanished because U = N, reducting the "effective" normal force across the slide plane. The friction coefficient itself did not change -- it was the about the same for wet and dry cases. In relation to the force balance presented before for the tilted plate, at the critical angle A*, T* = W sinA* = (W cosA* - U) tanP W sinA* = W cosA* (1 - r) tanP, where r = U/W cosA* tanA* = (1 - r) tanP So, as U increases, r approaches 1.0, and the slide angle A* can be much smaller than friction angle P. When U = W cosA*, r = 1, and friction resistance is zero -- despite the fact that the value of P, or f = tanP, did not change at all. So, if the pore pressure of water in the rock in the detachment layer was high enough, the rock layers above could slide over it with little resistance. The above considerations suggest that the Coulomb strength equation needs to be modified to take pore fluid pressure into account. Accordingly, the expression might be written, strength = k + (Sn -u) tanP, where k is cohesion, P is friction angle, Sn is total normal stress on the failure plane, and u is pore fluid pressure. This is often called the Coulomb-Terzaghi equation, because Karl Terzaghi is the guy who recognised the significance of the term (Sn - u), which he called "effective stress." The equation is a standard one, used frequently in geotechnical engineering. For the student looking for more info on the above concepts, and the history of development, look in the book "Mechanics of Thrust Faults and Decollement," edited by me, in the EMS Library. ("Decollement" is just the French word for "detachment").