In this lecture we will mostly look at their processes that how we actually do generatedifferent types of cross-sections in the transverse sections and then we will look at a very specialtopic which is Aspect Ratio of boudins.Then we will see the Foliation Boudinage we learned about it while we were classifyingthis.We will talk out little bit more on this because it demands a special attention.Then we will see that how Strain Ellipsoid, the bulk strain ellipsoid is related withthe boudinage processes.So which direction, what kind of structures or boudinage we can form.Then we will see the relationship with folds with respect to the boudinage and then finallywe will conclude this lecture with boudinage under superposed deformations.So a lot of topics but they are very small and we will cover it one after another.So here, so we have learned about it in a transverse section we figure it out that theboudins they may have varied shapes and this could be rectangular, barrel shaped, lenticular,fish head and rhombic shapes.Now these dissimilar shapes give us some information concerning the competence contrast betweena boudinaged layer and its host rock and `at the same time it tells us the pre-boudinageand post-boudinage plastic deformation in particular.So what I see here a series of a illustrations are here you see this, this is rectangularboudins, then barrel shaped boudins then lenticular boudins and then fish- head boudins and rhombicboudins.Now these are not necessarily the products during the boudinage.So rectangular boudins yes when you just initiate the boudinaged processes then it is possiblethat you form the geometry of structure like this but with continue deformation we actuallyarrive somewhere here.The rhombic boudins are somehow different will not look at it in detail but if you areinterested you may have a look of a paper by Professor Mandal in 2001.So that describe but we mostly restrict ourselves towards the up to the fish- head boudins.Now the presence of rectangular boudins with edges at right angle to the general layeringthis is what we see here it simply indicates the fact that throughout the course of developmentof boudinage the layer, this layer which is undergoing boudinage processes behaved ina brittle manner.Now at the corners of these boudins there is relatively high shear stress which tendsto deform the boudins.Now this is exactly what happens at the post boudinage processes.What we see here that this was initially probably in this illustration this was initially rectangularboudinage but with continued deformation it is possible.This is the way the boudins deformed or shear stress at the extensional faces or exteriorfaces.So the preservation of the sharp right angles corners of rectangular boudins therefore indicatesthat competence contrasts with in boudins and the host rock is very large.So if the competence contrast is extremely large then you would see this kind of rectangularboudinage but if not then you will see features like this which will be discussing soon.So barrels shaped boudins which is this one.This is a very typical process and this evolves with the boudinage processes.So the barrel shaped boudins with straight edges are produced with some amount of makingwhich is followed by extensional fracture at the neck joints mostly at these places.So this shaped that which we see here this barrel shaped boudins these actually can befurther modified by post boudinage plastic deformation.Now this is illustrated here we will see one after another that how these do happen.Now the boudins are more competent than the host rock this is what we have learned sothey deform more slowly than the surroundings.So the matrix outside deform faster than this okay and if that happens then you developa shear strength at the longer edges of the boudins as it is represented here.So you see that you have a shear strength not only that the gradient of the shear strengthsat there as well.So at the middle the shear strength is the magnitude of the shear strength is less andwhile we are travelling towards the edge of the boudinage the corner of the boudins.The magnitude of the shear strength continuously increased and you also see that the senseof shear is opposite if you make this boudin asymmetric line which is this one.So, since the sense of the shear is opposite in the two halfs of the boudins the shearedis associated with an effective lengthening of that part of the boudin with or which isclose to the contact.So these materials actually tried to drag it and you always remember that in this casethe competence contrast is not as hard as you can expect for the rectangular boudinage.So the shear strength and the associated lengthening decreases towards the mid-level as it is hereof the boudinage layer.Now we can see that as a result the lateral walls of the boudins curved inward, this isexactly what is happening here.So they try to curve inward and also this one.So the zone of curving also undergoes a larger layer normal compression so that the barrellike shapes is exaggerated this is exactly what we see here.Now when a very large amount of such post-boudinage plastic deformation leads to the formationof fish- head boudinage this is exactly what we see here.So here we had a barrel shaped and with progressive deformation during the post boudinage plasticdeformation we arrive at fish boudinage process.Now this can actually further continue to develop something which is exactly the shapeof lenticular boudinage which we have learned in the last lecture and this is also evidentfrom experimental deformation and these experiments generally show that with soft models the decreasingcompetence contrast between a layer and its embedding medium extensional fracture is produced.As you have learned by a greater layer parallel homogeneous elongation as well as a greaterlocalised deformation by making.Now if the competence contrast is small the making continuous as we see here.Till the pinched zone stepper of lenticular boudins are separated without the formationof a clearly defined layer normal extension feature.o this has been noted by Hans Ramberg and this is the classic paper of 1995.As we can see the first one this one is a classic lenticular boudin.So there it was like this, this is the shape of this boudin.Okay, this is some sort of a pinched swell structural but the pinch are got teared ofbut here if you look clearly that the shape of the boudin is something like that.So it was initially a barrel shaped boudinage then it turned into fish mouth boudinage andnow its morphology is very similar to that of a lenticular boudinage.So it is a continued process where you actually can figure out that initially you form a barrelthen slowly it tappers inwards and then it forms fish mouth with further progressivedeformation you can arrive at a shape of lenticular boudinage or lenticular boudins.Now let’s talk about the aspect ratio of the boudins which is the next topic we willcover.So here I have given two drawings for you.What I see here is that if you imagine that this layer, this layer, this layer, this layerthey have very similar properties and also this to orange layers.Now what I also see here in this illustration that this layer is thicker than this layer.So this is the competent layer, this is as well compared to the surrounding grey layers.Now if there is layer normal compression of very similar magnitudes, similar deformationrate and so on.Then you can ask yourself a question or I would like to ask you the question what isthe expectation after a finite time of the deformation and the boudinaging is going on?Then where I would form maximum number of boudins in this case or in this case?We can think of this and you can likely back your answers but this is a very interestingproblem and we will see with time that how we can go ahead with that and we can figureout that what would be the aspect ratio of the boudins.But before we jumping to this topic let us have a very common understanding of this.So general observation as we can see here from this illustration it is from Marqueset.al, 2012 that large boudins are generally form thicker layers and small boudins theydo originate from relatively thinner layers.So this is the plot boudin thickness versus boudin width they more or less follow a linearrelationship as we can see here from lot of data that find and collected and he also conductedanalogue experiments we have seen this image in the last lecture.But what I see here that this is thicker layer and this is much thinner layer and with thisthicker layer we have large boudins and with the thinner layer slowly we are increasingthe number of boudins.Now you can also see one more very important thing we will see this also in the illustrationthat the gap between these two is smaller than these gap this indicates that we hadthe first fracture here then this one and so on and this is how it proceeds.So generally what we can figure out that the aspect ratios of boudins are generally measuredin sections perpendicular to a boudin axis.For unidirectional boudinage the aspect ratio is the ratio of width versus the thicknessof the boudins.And you can consider the two-dimensional boudinage then we have also to measure the length tothickness ratio.The width to thickness ratio of boudins interestingly may vary within a wide range.However in most areas there is a general tendency of thicker beds to form boudins of largerwidths.Now what do we see here that the general range of width of thicknesses which are being reportedfrom different field studies that field studies reported that it is generally from 2 to 4if you made it really large 2 to 20 and then some made it really narrow 1.4 to 3.3 andso on and these are from different studies.So the theory of boudinage if we can consider predicts that in any one of the competentbed boudins with a restricted range of aspect ratios should be more frequent than others.Now you can consider a simple situation, assume that a brittle layer is sandwiched betweentwo ductile layers and is subjected to a layer normal compression.This is the case we can consider let us see in this illustration before okay.Now we have understood this before that when stress exceeds the strength of this piecerock it flows and then it forms a fracture in the middle and then the boudinaging processstarts so in a way we can say that when the stress exceeds the strength and extensionfracture develops perpendicular to the layering and the layer is thus broken into two segmentswhich is this case, so this is one segment and this is the second half of that segment.Now if you continue the deformation that means if you continue the layer normal compressionand it continues flowing laterally in the separation between two cases increases sothis is exactly what is increasing and very interestingly that the you have the freshmidpoint fractures from each of this pieces.So you are having these new fractures whether this is the first one and then you arise atthe new fractures.Now the stress within a competent fragment increases with increasing widths that meansthat is the length at a right angle to the boudin axis and decreases with increases thickness.This means very interestingly that it becomes increasingly difficult for a bed or for alayer competent layer to fracture when boudin width become shorter right and this is veryeasy because if we have a shorter boudin the length of the boudin is less than insteadof fracturing it will try to produce if the ductility of the layer is pretty high butstill more than these two layers then it can form the barrel shape, fish mouth shape andso on.So this is the reason why it is expected that the boudins of a bed would show a small rangeof width to thickness ratios.Now then the question comes what would be the final aspect ratio?The final aspect ratio which is obtained after this processes this midpoint fracturing isa function on its initial length and this become clear if we consider you can thinkof an example and you can imagine that the critical aspect ratio for example you canthink of that will be the two.Now what is crystal aspect ratio here?That there is always a critical aspect ratio below which further midpoint fracturing isnot possible that means the boudinage processes for that particular layer is finished forthis particular deformation.Now you can think of that if we start from a layer segment of aspect ratio 20 where youcan consider that the critical aspect ratio for that particular layer is 2 then by successivemidpoint fracturing you can arrive at a value of 2.5 this is simple arithmetic.Now since this is larger than your critical aspect ratio or Ar, the segment will sufferfurther extension fracture to yields stable boudins with aspect ratio in that case itwould be 1.25.Now if instead you can consider that instead of 20 if the starting layer segment has anaspect ratio 30 we get the final aspect ratio to 1.875 of a stable boudins.So depending upon the initial length of the layer segments in a transverse section thefinal boudin aspect ratio may range between the original critical aspect ratio which isAr to Ar by 2 as it is written here.Now in the nature because this is some sort of geometric aspects that we are consideringhere but in nature the range is likely to be modified by lot of other factors such asyou can consider the occurrence of flows in the competent bed, variation of strength andmicro structuring in different parts of this bed, some defects or some initial fractureswithin all these layers and so on.So these also control the aspect ratio of the boudins but in general if everything ishomogeneous then you expect the aspect ratio of the boudin between the critical aspectratio and half of it.Let us move to the next topic which is the foliation boudinage (I know) we have learnedabout it this foliation boudinage.If you remember the classification we also consider that the boudinage is possible inmultilayers and also in foliations.Now in somewhat, in the somewhat similar way of single layer boudinage processes, the multilayersor foliations can get densely packed and generate boudinage structures with a thickness thatis considerably greater than that of individual layers or lamina and these are known as foliationboudinage.Now what do you mean by this?So for simple single layer boudinage processes we understood that requires a competence contrastsbetween the boudinage layer and the layers outside.But when we have a foliation like this or multilayers like this there is apparentlyno competence contrasts, it is almost a continuous layer it very high and strong an isotropic.But what is interesting in this kind of situation that you are applying still a flow along thelayers and therefore you can also imagine that there is a layer normal compression.Because an isotropic is very-very high and layers are very thin you can expect the factthat a group of layers can fracture at one point of time or one after another.When that happens then you arrive at a situation where everything flows like this outside andthese layers are fractured and they appear like this.The layers on the other side are like this and so on.Now you see that this actually is representing your like a shape of boudins.But apparently these segments, this segment, this segment or this segment they do not haveany competence contrast with respect to the surrounding layers.So this is very interesting process and we see this in nature people do research on itand here is an example of the foliation boudinage.Now foliation boudinage is common in well- foliated rocks, the foliation simply tearsas I have explained here they just break in little pieces which allows for more extensionand foliation boudinage is therefore a type of structure that develops at a relativelylate stage of deformation because we need this strong an isotropy and it generally formsafter the foliation is extremely strong and is well developed.Now foliation boudinage as we have classified can be symmetric or asymmetric, so symmetricfoliation boudinage is where we do not have any, you have only separation by tensile fracturesthe separated zones or the makes zones as we can see here they do not undergo any sheardeformation, so it is only separation by tensile fractures and if that happens then this isa symmetric foliation boudinage as we can see here so you see that these layers, thispacket of layers here they got boudinage and this is the tensile fracture that it hasdeveloped right.So there is no apparent sleep along this or no feasible sleep between this segment andthis segment and this segment and therefore this is a symmetric type of foliation boudinage.However asymmetric foliation boudins are separated by brittle shear fractures or by ductile shearbands showing a relative displacement along the fracture or bands as you can see herethat it had a tensile fracture at one point of time but after that it has a sense of displacementalong the fracture zone and this is an excellent example as we can see here.So we can imagine that this is a packet and then is another packet defining the boudin,this is another packet which is defined in the boudin and this is another packet whichis defined in the boudin.And you can clearly see that it got relative displacement along the make zone or fracturezone of the boudins and therefore this is asymmetric foliation boudinage.Now we will switch to the next topic that how this boudinage are related or budins arerelated with the strain ellipsoid?Now the boudinage is a deformation induced process this is quite obvious we have learnedit, so the structure must corresponds to the stain ellipsoid either regionally or locally.The transverse section, where we generally see the boudins in a row can be approximatedto the XZ plane of the strain ellipsoid.However, the Y direction is also important for kinematic analysis, as it is not necessarilyis always under plain strain and we will see this very soon.Now depending on the relative magnitudes of the 3 principal axis of strains, the 3D dispositionof an entire layer undergoing boudinage may display variety of structures and this isexactly what we are going to see into next slide and I request you to recall the strainlecture or go back to the strain lecture because we will be seeing now plain strain, constrictionalstrain, flattening type of strain and so on and then we will see how we form the boudinageor some other related structures along with this kind of various strain ellipsoid.Let us have a look, so what do we see here in this slide this dispersed image it lookslike a gift box but it is not.So this is you can consider a unit cube and this brown then blue and this green layersare competent layers which are aligned perpendicular to X, Y and Z axis.So for example this blue layer is aligned perpendicular to the x-axis, the brown layeris perpendicular to the z-axis and the green layer is perpendicular to the y-axis.Like one can also ask this question, do you see this kind of features in geology in structureswere you have three layers cross cutting each other?The answer is yes, you can consider one is your primary bedding plane and then othertwo could be two different types that have intruded at different stages of time and thenthe entire packet is undergoing deformation so this is not a problem therefore we willsee this that yes this is a possibility.Now first we will take over this problem of uniform flattening, uniform flattening ifyou remember that your z-axis has to be shortened and y and x-axis should move or should flowequally.So the condition is x equal to y which is greater than 1 and z is less than 1 this isthe condition.Now if that happens then this brown layer because it is flowing in perpendicular tothe z section therefore the brown layer would get boudinage along the X direction also alongthe Y direction and therefore this layer if I consider this brown layer here this oneexactly then it would produce two sets of boudinage and this is known as we have learnedit chocolate tablet boudinage okay.If that does not happen if the strain is like a plain strain that means your y-axis is constantthere is no deformation along the y-axis then this brown layer which is the horizontal layerperpendicular to the Z then the flow is only along the X direction and shortening alongthe Z direction so this brown layer of would actually experience a layer normal compressionand layer parallel extension therefore we would have a boudinage of shape like this.And if we have a uniform constriction which is shown here that means this brown layeris very interestingly would flow in X direction so no problem that it is forming boudinagealong the X direction but because it is uniform constriction so it is getting compressed alongY direction.So along Y direction because it is getting compressed it will produce some compressionalstructures like fold.Also the green layers would produce a compressional structure if you view perpendicular to theX section and the blue layers also produce on both section because this is somethingthat we are looking at the layer is undergoing compression in all directions.So this is how you have the chocolate tablet boudinage, a simple one layer single boudinageor single boudinage as we see here and then boudinage with folding you can form this ina single deformation we will see soon that boudinage in superposed deformation.But the message I would like to give you with this slide is that if you see a chocolatetablet boudinage or if you see a boudinage in one section in another section the samelayer is folded that not necessarily indicate that it is a result of superposed deformationso when you conclude your observations it is very important you look at some other sectionsor you observe things in a better way to arrive at a conclusion that whether these are theproducts of superposed deformation or from a single phase deformation.And speaking of which we will come to the boudinage which are related to the folds becausein folds it is very interesting because a layer at one point of time undergoes compressionand then it can go extension at one point of time.So at one stage then it can again come to compressional field and so on because it isvery complex with respect to the local orientations of the strain ellipsoid we have understoodit in the fold lectures.So generally in the most cases the majority observations that people have seen that boudinaxis are roughly parallel or perpendicular to the fold axis but that is not the thumbrule.The boudin axis or the length of boudins need not to be either parallel or perpendicularto the fold axis, the boudin axis maybe parallel, perpendicular or oblique to the fold axis.Now how to conceive this idea?Let us have a look on this with some simple drawings.Will see this in the form of illustration but let us imagine the fact that we have alayer then we are applying layer parallel compression, so when we do that then thisis undergoing the interlayer is undergoing at least in this section compression, so thelayer would produce a gentle fold.Isn’t it?What is the orientation of the principal axis of the strength in this case?Now this must be your Z direction isn’t it?Because this is the shortening direction, so this is your Z okay if that happens thenit is extending in this direction okay because this could be a long axis so we can considerfor the time being this is X that the principle extension direction and we can assume thatalong the side there is no strain or plain strain condition so this can be your Y.Now with further deformation if we assume it to the next stage then the fold would getwould produce a tighter fold and then we will see very nicely if the orientationsare same this is your Z, this is your Y and this is your X.That these limbs of this folds are slowly orienting themselves along the principle extensiondirection.
So therefore this layer if I consider this particular segment here or this segment hereis actually suffering or slowly undergoing a deformation which is extension along thelayers.However the bulk strain ellipsoid is still the same direction the way we started.If that happens then essentially these layers with further rotation they would form boudinagelike this and so on.So you see that under compression the global strain ellipsoid is under compression butin this particular case as we see here with the continue deformation we are forming boudinagestructure which is associated with the fold in a single deformation.So if we try to get it that we have just learned that not necessarily it has to be in thiscase actually, in this case we have seen that this is the fold axis, this is parallel tothe fold axis however if the compression is oblique to the layers then you can actuallyform.Let me wipe this one out because I do not have any more space.You can actually form boudinage which can be oriented oblique to the fold axis, I amjust giving you the rough idea.Now we will learn about this processes soon in a different way but the boudin axis orthe length of the boudins need not to be either parallel or perpendicular to the fold axis,so this is what is important and the lengths of the boudins can be also oblique to theaxis of the folds and such oblique boudins as we see here that these are oblique, boudinaxis are oblique to the fold and these oblique boudins may develop if the bed is orientedoblique to the principle axis of stresses.Now the geometrical relation of boudinage structures with folds should never be takenfor granted, especially in rocks which are known to have undergone repeated deformations.This is something as I told also (with) when you look at the boudinage and try to correlatewith the strain ellipsoid the same warning or same measures must be considered when youtry to correlate the boudinage processes with the fold.So this is because of occurrence of the boudinage structure in a transverse section of a folddoes not necessarily imply that the boudin axis is parallel to the fold axis.The reason for emphasising this obvious point that I am trying to convey you repeatedlythat the parallelism of the boudin axis and the fold axis has so often being emphasizedthat you or the student tend to make this assumption when they observed boudinage structureson a fold profile and they consider that this is either parallel or perpendicular to thefold axis and this may not be always true.However, it is true that boudin axis and fold axis are often approximately parallel butin making this assumption without actual observation or measurement there is a possibility thatwe are losing a vital piece of information in the reconstruction of the history of thesuperposed deformation.So in areas of superposed deformation the earlier boudin axis may be oblique to thelater fold axis.So the boudin orientation may got completely modified and since the plan view of the boudinageis very rare to see in the field.So such evidences unless a careful search is made is likely to be overlooked.Now you can also think of the pinch and swell structures and extension fractures boudinagein which boudin axis parallel to the fold axis they cannot form at the initial stageof the folding processes.
And in the next week we mostly we would focus on a new topic and which will be mostly concernedthe brittle deformation of rocks and this would be fractures, joints and faults.So thank you very much and I wish you all the best, see you in the next lecture.