GATE Civil Engineering: Geotechnical PYQs with Detailed Explanation | Part 1 (Year 2021- Afternoon)

Added: 2026-05-25

[00:00:00]Hello everyone, welcome to civil engineering with Sujay channel. I am Dr. Sujay Ti. I completed my PhD from IIT Gandhiagar in civil engineering with geotechnical engineering as my specialization.

[00:00:17]Currently I am working as an assistant professor in the department of civil engineering at SR University Wangal.

[00:00:26]So in this video we are going to solve some of the problems which were asked in GATE 2021 exam of civil engineering particularly focusing on geotechnical engineering. So in this video we are going to solve the afternoon session question paper of GATE 2021 civil engineering. In the previous video we solved the forune session of same year.

[00:00:54]Now as I already discussed in the previous video, first I will complete the series of easy questions from ranging from year 2020 to 2026. After that you go through the easier questions first through the playlist I will create on YouTube my YouTube channel. After that I will create another playlist with difficult level of questions which were asked in the previous years from 2020 to 2026 which you can go through once you gain the confidence through first easy problems. So now starting with this afternoon session of 2021 exam.

[00:01:32]First question is related to types of triacial test. So if you see So if you see what is the question the most appropriate triacial test to assess the long-term stability of an excavated clay slope is what? So answer is consolidated drain test as you can already show on already see on the slide. Why it is consolidated drain test? So first what it is asked try what is the most appropriate triacial test to assess what to assess the long-term stability. What is the meaning of long-term stability of what? Excavated clay slope. So when a clay slope is excavated long-term means after so many years. So after so many years what will happen to clay slope?

[00:02:28]First after if you are taking about long term. Long-term means after so many years first clay will get consolidated.

[00:02:36]Once the clay will get consolidated and for example if you are applying the loading now even if you apply the loading after the excavation or the when you excavate itself there will be loading on the because of excavation also there will be some loading on the clay slope. Now that loading will allow the water to drain because we are taking up we are talking about long term. So in long term the water will drain out from the clay. Right? So what will happen in the long term? First the clay will get consolidated. After consolidation as we are talking about time of so many years the water will also pass through or water will also drain out of the soil.

[00:03:21]So your consolidation is also happening after and after applying the loading the water is also drained out. So your most appropriate tribe will be consolidated drain because in consolidated drain triacial test when we make the when we make the sample and place it in the triacial test first we apply the hydrostatic pressure means in all direction of the if this is your specimen in all direction we will apply first same pressure.

[00:03:53]So this is your consolidation stage. So during this stage the water will be allowed to pass means the soil will be allowed to consolidate. After the consolidation stage is over when we apply the devoteric stress sigma during the application of devoteric stress or during the searing stage also the po water will be allowed to drain out means there will not be any poor water pressure generated. And as the water is continuously draining out during the searing, it represents your long-term condition on the field. Right? So your water is also coming out during the searing stage and you also allowed the consolidation of the sample. So consolidated drain test is the best test to assess the long-term stability of excavated clay slope. Now what are the other option given to you?

[00:04:45]Unconsolidated unrained. So here your two conditions should be there in long term consolidation as well as drainage.

[00:04:53]So here there is no consolidation stage in unconsolidated and test as well as the water is also not allowed to pass during the searing stage. What is the another option? Consolidated undrin test. So consolidation is there but when during the searing the water is not allowed to pass. So it is unrained test.

[00:05:12]Now next is unconfined compression test.

[00:05:14]What is the meaning of unconfined compression test? Unconfined compression test means you are not even allow you are not even having the this confining stress to the specimen and without that confining stress you are just loading the specimen in unconfined compression test the deformation rate of the sample itself is very high that it that test itself become the unrin test. Now whenever you see this kind of test consolidated drained unconsolidated untrained consolidated unrained. So in this the first term represent the behavior in consolidation stage and second term represents the behavior of the sample in the searing stage. So consolidated drain means during consolidation stage consolidation is allowed. Drained test drained means during searing stage drainage is allowed. Unconsolidated means during the consolidation stage consolidation is not allowed and unrained means during the searing the drainage is not allowed. Consolidated unrained means consolidation stage consolidation is allowed but during the searing stage drainage is not allowed.

[00:06:24]So that is the meaning of all these four t. So your answer will be your consolidated drain test which will be which will be better test to assess the long-term stability of excavated clay slope. Through CU test also you can measure the long-term accessibility uh through long-term stability but it will not be as accurate as the consolidated drain test. So your option answer is consolidated drain test.

[00:06:52]Now coming to second problem. So what is the second problem saying as per the unified soil classification system USCs.

[00:07:01]So here they are asking about unified soil classification system. There are different soil classification system like Astro unified soil classification system is code soil classification system. The type of soil represented by MH is what? So what is MH type of soil that you have to tell? So what the what are the option? Inorganic seals with high plasticity with liquid limit more than 50. Inorganic seal with low plasticity with liquid limit less than 50. Inorganic clay with high plasticity with liquid limit 50%. Inorganic clay with low plasticity with liquid limit more than 50%. So what are all these options having? All these option have first type of soil and what is the liquid limit range? All options are having this thing. Now what is the meaning of MH? So MH whenever a soil type is given to you.

[00:07:54]So remember these things.

[00:07:59]M means silt.

[00:08:04]C means clay.

[00:08:09]S means sand.

[00:08:13]G means gravel, right? Then L means low plasticity.

[00:08:34]I means intermediate plasticity.

[00:08:50]H means high plasticity, right? Another symbols will be there like P. P means poorly graded.

[00:09:11]W will be there that means well-graded another symbol will be there O. O means organic soil.

[00:09:24]So here your symbol has M and H. What is the meaning of M? M as I already told silt. H. What is the meaning of H? H means high plasticity, right? So what is it? There is no O in the symbol. So your soil is inorganic. So inorganic M is sealed and H means high plasticity. So inorganic seal with high plasticity. Now for high plasticity soil what is the what is the liquid limit range. So for that you have to see the plasticity chart per plasticity chart. Now plasticity chart there are USCs has different plasticity chart is code has different plasticity chart there is these lines A line U line A line they have same same values same same meaning in both the chart the only difference in USCs classification and is classification is that in USCS classification based on the value of liquid limit so first of all let's see what is the plasticity charge So plasticity chart is on x-axis you will have liquid limit on y-axis you will have plasticity index right. So if your liquid limit is as per USCS classification if your liquid limit is less than 50 then whether it is a clay or whether it if if your liquid limit is less than 50 then your soil will be low plasticity soil L symbol. If your liquid limit is greater than 50%age then your soil will have high plasticity H symbol. If your soil falls above this A line this A line means 0.73 L minus 20. If your soil fall above this A line then it is a clay soil. If your soil fall below this A line then your soil is silty type of soil. Right? So now here as per our symbol it is M. So the soil is this MH.

[00:11:26]Now why MH means high plasticity means what is the range of liquid limit?

[00:11:31]Greater than 50. Right? Now if we see is called plasticity charge it is same X-axis liquid limit. Yaxis plastic plasticity index above A line clay soil below clay below A line seal soil. Same thing till now. Only difference is this liquid limit range. If your liquid limit is less than 35 then it is low plasticity soil. If your liquid limit is between 35 to 50 this range 35 to 50 then it is intermediate plasticity soil. And if your liquid limit is more than 50 then it is high plasticity soil. That is the only difference between USCS plasticity chart and is code plasticity chart. So as per both chart our liquid limit is greater than 50 only for MH kind of soil. So your answer will be inorganic seals with high plasticity with liquid limit more than 50%. MH symbol represent that as per USCS even as per is code also this it will represent the same thing. So that is problem two. Now coming to problem three which is related to area ratio of soil sample. So here we have given a soil sampler. So what is a soil sampler? Soil sampler is a a tool which we insert in the soil and sample is collected into that tool. Now what are the things given to you? Internal diameter of the sampler and external diameter of the sampler are given. What is the sampler type given? Sellb sampler. Right? Right. So, Selby sampler is a type of the sampler. There are different type of sampler like Selby tubes. Uh then split spoon samplers.

[00:13:18]Right. What are the SLB samplers dimension given to you? 48 mm diame 48 mm internal diameter 52 mm external diameter. So, it is like samplers are like holo cylinder with a cutting edge at the bottom. So, when you insert it through the cutting edge, the soil will fill inside the holo cylinder. What you have to find the area ratio of the sampler rounded off to in percentage rounded off to two decimal place you have to find the area ratio value. Now as I already told the sampler will look like this. So there will be this inside part in which the soil will go right. So here this d1 is your internal diameter d2 is your external diameter. Right? So here it is given two diameters are given to you. Internal diameter and external diameter D1 and D2 are given to you. Now you have D1 D2 both diameters are there with you.

[00:14:16]So area ratio is D2 square minus D1 square divided by D1 square. So D2 square is outside diameter. So outside diameter square minus inner diameter square divided by inner diameter square into 100 is your area ratio. Now why area ratio is important? So area ratio value will decide whether your sample is undisturbed sample or disturbed sample.

[00:14:40]Now what is the meaning of disturbed sample and undisturbed sample? So undisturbed sample means when you collect the sample the soil layers will not mix. Then the soils whatever the condition on the field like density, moisture content, whatever the mineral composition that will be completely as it is or almost near to as it is condition on the field that is undisturbed sample. Disturb sample means you may preserve the moisture but density may change the layers may mix right. So this kind of thing are disturbed sample. So based on area ratio value it will be decide whether your sampler will collect a disturbed sample or undisturbed sample. Now if your area ratio value is less than 10 then for soft or sensitive clay and loose sandy soil you will collect undisturbed sample. If the area ratio value is less than 20 then for hard or stiff clay and dense sandy soil it will be still undisturbed sample. But if your area ratio crosses the value 10 then for soft clay or loose sandy soil the sample will not be undisturbed. And if area ratio co value cross 20 then for any soil it will not be undisturbed sample. Right? So that's why area ratio is important. It is not asked in the question but just giving you the information so that if in future in any GA get exam it comes then you can write the answer correctly.

[00:16:06]So now to us internal diameter and external diameters both are given to us right. So external diameter D0 do equal to D2 is given to us 52 mm. Internal diameter DI equal to D1 is given to us 48 mm. We can substitute these values here in the formula and we have to multiply by 100. So you will get area ratio value equal to 17.36%age.

[00:16:34]Right? So your final answer is 17.36% which is rounded off to two decimal places. So we have already rounded it off to two decimal places. So your value final answer is 17.36 percentage. Now 17.36% means if you use this sampler if you use this sampler for soft sensitive clay or loose sandy soil then whatever sample you will collect that sample will be disturbed sample because your area ratio value is greater than 10. But if you use the same sampler in hard stiff clay or dense sandy soil then whatever the sample you will collect that sample will be undisturbed sample because your area ratio value is less than 20%. So this is where the area ratio values are used. So that's all from this problem number three. Now coming to problem number four. Now what is the problem number four saying?

[00:17:32]It is saying that a clay layer of thickness h. So clay layer of thickness h has a preconolidation pressure sigma c dash. Now what is the pre-conolidation pressure that we will discuss while I will discuss the answer of this question and initial void ratio of e node. The initial effective overburen stress at the mid height of the layer is sigma dash. At the same location the increment and effective stress due to applied external load is delta sigma Z.

[00:18:04]The compression and swelling indexes are given that means compression index is CC. Swelling index is CS.

[00:18:12]Now what is the condition given? If sigma dash is less than sigma C dash is less than sigma dash plus delta sigma Z then the correct expression to estimate the consolidation settlement of the clay layer is what? So the condition given to you is sigma dash less than sigma c dash less than sigma d plus delta sigma z. So based on this condition you have to determine which is the correct expression for the determining consolidation settlement. So as I also discussed in the previous previous videos to determine the consolidation settlement first we need to determine whether our soil is normally consolidated or over consolidated. So how to decide whether our soil is normally consolidated or over consolidated? So that we'll discuss one by one. So if your soil is normally consolidated first what is the meaning of a normally consolidated soil? So normally consolidated soil means the whatever the current effective overburden pressure is there at the midpoint of layer. It will be same as the maximum pressure that soil has experienced. Now what is pre-conolidation pressure or over consolidation pressure? Pre-conolidation pressure or over consolidation pressure sigma C dash is the maximum pressure that soil has experienced in the past.

[00:19:31]Now if current effective pressure is equal to the maximum pressure that soil ever experienced then your soil is normally consolidated soil. That is what primary consolid is what meaning of normally consolidated soil. Now if you understand it with the e log sigma curve. So this e on yaxis and log sigma on x-axis. This curve you will get from the 1D consolidation test. So this straight line is compress this curve is compression curve and this curve is recompression curve. Now the slope of compression curve is CC compression index. So this slope is CC.

[00:20:14]Slope of recompression curve is CS swelling index or recompression index.

[00:20:20]Right? So CC is slope of compression curve. CS is slope of recompression curve or swelling curve. Now normally consolidated soil means if for example this point is your pre-conolidation pressure or over consolidation pressure then both your sigma dash value that is your effective stress which will be either more than sigma cd dash or almost equal or equal to sigma cd. So whatever your effective stress value it will be more than over consolidation pressure as well as if you add the additional stress delta sigma Z that will also on the right side this side. So now both your sigma sigma dash and delta sigma Z both points this yellow point and blue point both points are on compression curve. So to find the settlement you will use only this slope CC slope which is your compression index. So when your both sigma dash and delta sigma z both points are on compression curve your primary concentration settlement you will use the cc slope which is compression index.

[00:21:27]So in in case of normally consolidated soil your primary concentration settlement will be c by 1 + e log sigma dash plus delta sigma z which is this point sigma d plus delta sigma z divided by sigma dash. So basically you are evaluating this slope values right and you are using the slope CC right so in normally concentrated clay it is going to be CC H by 1 plus E not log sigma D plus delta Sigma Z by sigma D so CC is your compression index which is slope of compression curve e not is initial viation is the thickness of the layer correct so this is for normally concentrated clay now coming to overconated clay what is the meaning of overconolidated clay. Over consolidated clay or OC clay means whatever the current effective overburden pressure or effective stress is there sigma d it will be lower than the maximum pressure that soil ever experienced in the past right that is over consolidation pressure. So your current effective stress is so your current effective stress sigma dash is less than sigma c dash. So that is the meaning of overconolidated soil.

[00:22:42]Now your sigma dash plus delta sigma z point can be here also and it can be here also. So there will be two cases in case of overconolidated clay. First case of overconolidated clay is your point is still on the still on the left side of sigma c dash. Right? So what is this case? Your sigma dash is less than sigma dash plus delta sigma z is less than sigma c dash. So this is the first case.

[00:23:11]Now in this case you are both both sigma d this is yellow point and sigma d plus delta sigma z both points are on initial portion of the compression curve. Now this slope of this line is not same as cc value right. This line is more flatter. Now then what slope you will take? Now if you see this recompression curve this line line slope of this line is approximately equal to slope of recompression curve. So if your both point sigma dash and sigma dash plus delta sigma z are on initial portion of the compression curve then you have to use the slope cs.

[00:23:55]So you will use the slope now cs. So in this case where your sigma dash is less than sigma dash plus delta sigma z is less than sigma c dash your cons primary concentration settlement will be csh.

[00:24:08]The difference from normal concentrated cr in this case is cc is replaced by cs because your points are on initial portion of the compression curve. So now your cs now you are using cs instead of cc. So that is for this case.

[00:24:24]Now coming to another case. What is the another case? Another case is your in it is overconented soil means your sigma dash will be always less than sigma c dash. But your sigma dash plus delta sigma z can be on the right side of sigma c dash. So in this case from sigma dash to delta s sigma dash to sigma c dash you will use cs slope. from sigma c dash to sigma dash plus delta sigma z you will use cc slope understood so from sigma dash to delta sigma dash to sigma c d slope will be cs from sigma d sigma c dash to sigma d plus delta sigma z your slope will be cc so for this kind of case what is this case sigma dash less than sigma c d less than sigma d plus delta sigma z this is the case given to you in the question sigma dash less than sigma c is less than sigma d plus delta sigma z. So in this kind of case as I already told from sigma dash to delta uh from sigma dash to sigma - c you will use cs slope and from sigma c dash to sigma d plus delta sigma z you will use cc slope right so this is what your final equation will be for this case. So you have to see that sigma c dash is in the den numerator sigma dash is in the denominator because you are going from this point to this point. Similarly you're going from this point to this point. So sigma c dash is in numerator and sigma dash plus delta sigma sorry sigma cd dash is in denominator and sigma dash plus delta sigma z is in numerator. So now you have to find the correct answer from the option. So what is the correct answer here? Sigma C dash is in numerator.

[00:26:16]Sigma D Sigma D plus delta Sigma Z is in nuh numerator and sigma dash is there.

[00:26:23]Sigma C dash there is in the denominator. So this is your correct answer. Why this is wrong? Because here it is CC. It should be CS here and it should be CC here. So this is wrong.

[00:26:35]Similarly here also it is CC. It should be CS here. Here it is CS but the terms are inverted. Here the terms are inverted here. Right? So correct answer is option B.

[00:26:49]Right? Now coming to problem number five. So what is the problem number five? So problem number five is related to waterbox limit. So from laboratory investigation the liquid limit what are the things given? Liquid limit, plastic limit and natural moisture content and flow index of a soil specimens are obtained. So liquid limit is 60%.

[00:27:13]Plastic limit is 27%.

[00:27:16]Natural moisture content is 32%. And flow index is 27. Now liquid limit maybe you know plastic limit also you know natural moisture content you know flow index what is flow index? flow index.

[00:27:30]When you do laboratory test, you make a curve between you make a curve between moisture content and you make a curve between moisture content and number of number of blows required to close the groove in liquid limit test. So that curve when the moisture content increase the number of blows will decrease. So on x-axis there will be number of blows y-axis there will be percentage moisture content. So when your number of blows increases decreases number of when sorry when your moisture content when your moisture content will increase number of blow will increase or decrease what will happen if your moisture content increases number of blow will increase or decrease.

[00:28:20]If your moisture content is increasing, number of blows should increase or decrease, it should decrease. Right? So whenever you make the curve between percentage W and N, whatever the slope of that curve, that is the flow index, right? So you flow index is also given to you. What you have to find? You have to find the corresponding toughness index and liquidity index of the soil specimen. First you have to find toughness index. Then you have to find liquidity index. So what you have to find toughness index it liquidity index L data given to you liquid limit WL plastic limit WP natural moisture content percent W and flow index if is given to you. So liquidity index can be found using W minus WP that means natural moisture content minus plastic limit divided by liquid limit minus plastic limit. So liquid limit minus plastic limit is equal to plasticity index. So your liquidity index is W minus WP divided by plasticity index.

[00:29:22]What is toughness index? Toughness index is plasticity index divided by flow index. Plasticity index is liquid limit minus plastic limit. So liquid limit minus plastic limit divided by flow index is your toughness index. So you have everything to determine these values. No need to find anything right extra everything is there. So first we will find toughness index. So first we will find this is toughness index.

[00:29:56]So if first we will find toughness index it.

[00:30:00]So liquid limit is given 60% plastic limit is given 27% flow index is given 27. So plasticity index divided by flow index. Plasticity index WL minus WP divided by if. So WL is 60, WP is 27, if is 27. So your toughness index will be 1.22.

[00:30:23]Now coming to liquidity index. For liquidity index you require liquid limit, plastic limit and natural moisture content. So you have to substitute these values. So 32 is natural moisture 27 plastic limit 60 liquid limit 27 plastic limit. So your liquidity index will be 0.15 toughness index 1.22 liquidity index 0.152.

[00:30:47]So first is toughness index. Toughness index 1.22 liquidity index 0.15. So your answer is 1.22 and 0.15.

[00:30:57]So that's all from this video. Thank you for watching the video. If you have any doubt, you can contact me through my email id which is given in the which is given in the description of the