Hi everyone, Joe for JaspiesCaseGrakes.com coming after you with our last but the only filler we got to do to unlock that Gilded Triple Threads mixer. But first let's do the pack break itself, number 12, and then we'll give away those teams at the end with a different dice roll. Big thanks to this group for making it happen. Appreciate you. All teams are in. Let's roll it. Let's randomize names and teams six out of five, eleven times. Eleven and final time. Six out of five, eleven times. Four of the teams, two. Alright, here's the first half of the list right here. Second half of the list right over there. And let's just quickly do the break. It's like my Dodgers are cruising against the Orioles tonight. They're up 10-1. Eighth inning. Alright, thanks everybody for getting in. Appreciate you. A lot of breaks lined up, so keep an eye on the schedule. Nights like this is why the schedule is important. I thought I'd just drop the schedule a few minutes ago. Just click that link. It'll take you to a Google spreadsheet. The times are approximate, but pretty close. Flaming green, the Sprite, the Bonus Pack. Nothing too crazy there, but let's see who's going to get into the next break. Let's gather everybody's names. One through 30, new dice, new list. And it's going to be the top 14 after 12. Six into six, 12 times. One, two, three, and 12th and final time. So, from... So, Tony and Tristan, you see they already have teams there. Congrats. Nathan on down through 30, 15 through 30. Thanks for giving it a shot, but not this time. Thanks for trying, though. Top 14. Congrats to you. Tristan, you're in with the team. Tony, you're in with the team. Chris has got a team. So it's got Chris, John, Nathan, Chris, Chris, Eugene, Chris, Chris, Chris, and Nicole. So, after 12, there's the top 14, and here's what you get matched up with. And Nicole, we're going to put prism 12. Next team, so you know you won this prism-sella pack break number 12. Nicole, congrats. You got the Yankees, Chris. Some nice teams here, too. Seattle, Tampa Bay, Kansas City, Eugene with Houston, Chris. You got my Dodgers and the Phillies. Nathan with the Padres. John with the Pittsburgh Pirates. Chris with St. Louis. Scott with Toronto. Chris with Detroit. Tony with Texas. And Tristan with Arizona. There you go, gang. We'll see you in the next video for the break. Go to spreex.com.


Okay, welcome everyone to the second lecture on BC 213, The End Times. We are considering reasons as to why we believe in a pre-tribulation rapture of the church, and so we are looking at Bible reasons for that. We've looked at three, first we said because of 2 Thessalonians 2 or 7, where Paul very clearly says that there is something that's restraining the Antichrist, the man of sin from being revealed. And until that is taken out of the way, he will not be revealed. And so we ask the question, you know, who is that? Is it the Holy Spirit? Is it the church? And our conclusion was that this has to refer to the church and we gave reasons why. Clearly indicating, gave you several reasons that the Bible clearly shows that the Holy Spirit will be working on the earth through the tribulation. The second reason we said was because Paul, in his writing to the Thessalonians, first and second Thessalonians, in both of these episodes, there's a lot of teaching about the coming of the Lord. It seems to be one of the main themes in his episodes to the Thessalonians. And in the context of that, the coming of the Lord, which Paul clearly, he demarcates two experiences. One is the Lord coming for us and they're meeting him in the air. Another of the Lord coming with us, but we are executing church, but the Lord is executing judgment on the earth. So there are two different events in the coming of the Lord in the day of the Lord. And in the context of this, he says, you know, the coming of the Lord is going to result in our salvation from the judgment to come. From the day of wrath, from the wrath to come. So we said, okay, let's put it in context. And therefore we say it's clearly our salvation, our deliverance from the seven years of judgment poured out on the earth. The third reason we gave, which we saw is from Revelation chapter three. But the Lord Jesus says clearly to the church in Philadelphia.  So in the context of the book of Revelation, in which these words are given, the seven years of tribulation is the trial that is to come upon the whole earth. And he says very clearly, I'll keep you from it. Okay, three reasons. Let's move forward. Any questions on those first three reasons? Okay. So let's move forward. Look at another three reasons. Why we believe in a pre-tribulation branch of the church. Number four, because of what Jesus said in Matthew chapter 24. And of course this is repeated, you know, in the other gospels, but we're just looking in Matthew 24. And Jesus, he gives an exhortation to believers. And then he uses the typology of the days of Nova and the Ark. Right. So in Matthew 24, when we went through this chapter a little earlier in this course, we broke it down. We said there are signs that lead up to the tribulation. Then there is the tribulation period at the 24, 15 to 19. Then there is the second coming, the gathering of the tribulation saints and the battle of Armageddon. Then the rest of the chapter is an exhortation to the church to believers to always be ready. So this rapture must take place somewhere here. Between Matthew 24, 14 and Matthew 24, 15, the rapture must take place somewhere here. Because in Matthew 24, 15 is the beginning of the end. Now, while the Lord is exhorting, giving us the teaching of the end times, He then points back to the days of Nova. And he says, in Matthew 24, 36 to 42, Of that day and hour, no one knows, not even the angels of heaven, but my Father only. But as the days of Nova were so also the coming of the Son of Man being. For in the days of Nova, before the flood, they were eating and drinking and marrying and giving in marriage until the day that Nova entered the Ark and did not know until the flood came and took them all away. So also will the coming of the Son of Man be? So he's saying, look, there's a parallel here. There's a comparison here, a typology. So, Noah was there. He was a preacher of righteousness. So while he was getting the Ark ready, he was preaching, telling the people, hey, there's a flood coming. It's judgment coming, but nobody paid attention. They were just continuing on with life, eating and drinking, marrying and giving in marriage until Nova and his family went into the Ark. They were taken out of the place where judgment was going to be poured. And of course, there were the livestock, the animals that also went into the Ark. So they went into the Ark. Then judgment was poured out on the people who refused to hear the preaching of righteousness. Then when that judgment was over, Nova and his family came back on the earth. Now, Jesus is saying, as in the days of Noah, they didn't know until the flood came, took them all away. That's how it's going to be at the end of times. That's leading up to the coming of the Son of Man, Son of God. So if you look at that typology, Noah and his family were taken out of the way in a sense. Of course, I know the Ark was floating on the water, so let's not argue about that. But the picture is, Noah and his family were taken out of the way to a place of safety. While judgment was poured out, the flood came, destroyed the lives, and then they were released back on the earth. So going by that typology, it's a beautiful picture of the church being taken out of the way. While the seven years of tribulation, judgment and wrath is being poured out on the earth, then when that is over, the church comes back. It's a beautiful picture. So that's our fourth reason because Jesus pointed that and says, it's going to be like that before the coming of the Son of Man. Number five is because of the chronology of the book of Revelation. We are going to get into the book of Revelation shortly and we're going to look at the whole sequence. But I'll just give you a little introduction now and then you will get into the book chapter by chapter on overview, right? Not verse by verse. In the third year, we will do verse by verse. But now this course, we'll do an overview. But when you do an overview of the book of Revelation, the book of Revelation, Jesus clearly says, you write the things you have seen, the things which are and the things which will take place. So he's telling John in Revelation 119, write the things which you have seen. So he wrote that in chapter one. The things which are chapters two and three, there were seven churches that were there at that time. He recorded that and the things which will take place. Chapter four to 22, out in the future. So the book of Revelation is broken into these three parts, things that you have seen. Chapter one, he saw the vision of the Lord. Things which are chapters two and three, the seven churches, things which will take place. Chapter four to 22. Now, in chapter four, John is caught up into the spirit and then he's giving a vision of the future. So everything from chapter four verse two is vision into the future. Chapter four verse one, come into heaven, I'll give you a vision of the future. It doesn't mean those things were happening, but those were things that were going to happen. He's seeing into the future. And it's very clearly understandable. Chapters four and five is talking about believers who are in heaven. They're worshiping the throne of God. Where do they come from? That's the raptured church. You can see the elders sitting around the throne with their crowns. Crowns represent rewards which we saw earlier.  The believers are standing with their robes of righteousness worshiping Jesus. So Revelation four and five is a picture of the raptured church worshiping Jesus. Revelation six through 19. Most of it is talking about what the tribulation happening here on earth. Sometimes we go back into heaven and see what's happening in heaven. But we come back and say, this is what's happening on earth. That's Revelation six to 19. And that Revelation 19 ends with the Lord coming in vengeance. Coming with the saints and with the angels of God to execute vengeance on those who do not obey the gospel. That's Revelation 19. Then 20, 21, 22. The millennium, the new heavens and the great wide throne judgment and new heavens and new earth all in the future. So when you look at the chronology of the book of Revelation, it's very clear that church is taken out of the way and the tribulation happens without the church being here. But there are believers, people who will refuse the mark of the beast, refuse people who will believe in Jesus Christ during the tribulation. So when you look at Revelation, it's very clear in the sequence of events. The church is not here on the earth during the tribulation. Lastly, in Daniel, Daniel chapter nine, when the angel Gabriel came and spoke to Daniel and explained to him about his vision, he spoke to Daniel about 70 weeks. Now each week represents a period of seven years. Now that is in the Old Testament. One cross-references in Genesis 29, 27. Genesis 29, 27, you'll find that one week represents a period of seven years in the Old Testament. That means they understood a week to represent seven years. When Laban told Jacob, you need to work for a week for you to marry Rebecca. The week represented seven years. You need to work another seven years to marry his second daughter, Rachel, I think. So Rachel, 70 weeks means 70 times seven. Each week represents seven years. So we're talking about 490 years. And these 490 years or 70 weeks are divided into 69 weeks plus one week. We will study Daniel in detail later on. I'm just kind of explaining this very quickly. There will be seven weeks and 62 weeks. That is seven plus 62 is 69. 69 weeks from the time King Cyrus gave command to rebuild Jerusalem until the Messiah, the Prince came until Jesus came. So Daniel foretold 483 years, 69 weeks, 69 times seven, 483 years. That's exactly what happened. For the time King Cyrus said, the king of Persia, he said, go back, rebuild Jerusalem until Jesus came 483 years. But then there's one week left. That means one period of seven years. That is often referred to as Daniel's 70th week. Now, this entire 490 years is speaking very specifically about the Jewish people and Jerusalem. So Angel Gabriel told Daniel, I'm here to talk to you about 490 years. That is about your people, about your holy city. That's about Israel and Jerusalem. So the seven years that's left really is very specific. It's very specific about Israel and Jerusalem, not about the church. So when we go through the book of Revelation, read these, you know, what happens during that seven years of tribulation. You'll find a lot of it has to, of course, it's a global thing that the judgment is being poured out on the whole earth. But there's also something very specific. It's about things happening in Israel and Jerusalem, the temple being desecrated, the two witnesses standing up in Jerusalem. About the Antichrist heading himself as God and the temple of God, as the Antichrist going after Israel to destroy Israel. As all the nations gathering together against Israel. So the seven years, the Daniel 70th week has to do with reference to Israel, not the church. So the seven years of tribulation, the church is out of the way. Because Angel Gabriel clearly said that these 70 years, 70 times 7, 490 years, this last, you know, that also refers to the last seven years, Daniel 70th week. It's about the people of Israel and about the city of Jerusalem. And then he tells us, you know, what will happen here, that this man of sin, this Antichrist for one week, that is for seven years. He's going to, you know, set up a covenant. And then in the middle of the week, in the middle of the seven years, he will stop the sacrifice and offering and all of that. We will come back and I'll explain these verses in detail. But what I'm just pointing out is that the seven years of tribulation is not about the church, but it's about Israel and Jerusalem. Because that's Daniel 70th week. Right. So the church is out of the way. It's not the focus of the things happening in the tribulation is all about Israel and Jerusalem, not focus on the church. So we have seen six reasons why we say the church is not here during the tribulation. The church has been raptured. It's taken out of the way and is not going through the tribulation. But the tribulation has to do with the judgment being poured out on the earth. And it also has to do with the Antichrist going after Israel very specifically. Any questions about these six reasons? Is it clear? Everybody's very quiet. You should be able to give these six reasons if somebody asks you why to believe in a pre-tribulation rapture of the church. You should be able to explain, hey, these are reasons why I believe the church will not go through the tribulation. And of course, you know, show it biblically. Any questions? I'm going forward. So in relation to the rapture and, you know, what is going to happen in heaven, so on, there are some common questions. And we're just addressing these common questions here. So one question that's often asked is who will be raised up from the dead at the time of the rapture? Will we meet the Old Testament saints raised up in Ephesians 4? Now, remember that when Christ ascended, when the Lord Jesus after his resurrection, when he ascended and went into heaven, the Old Testament saints whose spirits were held in Abraham's bosom, they went up with him into heaven. Paradise was shifted, was relocated from being part of what we call as the place for the departed in the Old Testament. Paradise was taken from there as a compartment from Abraham's bosom. It was taken up into heaven. So in the New Testament, paradise is always seen in heaven, not down below the earth. So the Old Testament saints were taken there. Now, there is no indication that they were given glorified bodies, right? That they were taken up in heaven, they were raised up and they were there. And the Bible says also in Hebrews 11, you know, that we are going to be glorified together with them. Are we going to experience this, Hebrews 1140, that we are going to be made perfect together, not apart from us, but together with us. So that completion, the great grand completion is going to happen together with us. Hebrews 1140. So the Old Testament saints were taken up into heaven after the resurrection of Christ. So where are the Old Testament saints? They are up in heaven. What will happen at the time of the rapture?  And they will, when the dead are raised, that means those who have died in Christ are raised at the time of the rapture. We will receive our glorified bodies, right? And the Old Testament saints, we know, they believed in the resurrection that they would be raised up. They believed in all of this, right? And they were held in this sheol, which was the Old Testament. They were held here in Abraham's bosom when Christ was raised up from the dead. He led them into heaven. He transported them into the third heaven. And that's why paradise, you see in the New Testament, is in heaven. So the spirits of the Old Testament saints are now with Christ. And they are with Christ in heaven. Now, even the Old Testament saints, they are referred to as saints, right? Because they've been taken up with Christ. So the big question is, when will they, the Old Testament saints, receive their bodies, glorified bodies? When will they get it?  God will bring with him those who are asleep. So that means they die in Christ, he'll bring with them. So when they die in Christ, they are there. And the Bible tells us, as a reference to Hebrews 11, that they, the Old Testament saints, should not be made perfect apart from us. Or, if you put it another way, they will be made perfect together with us. The second thing you see is that the spirits of just men, this is in Hebrews 12, that these are people who are with the Lord. They are with the Lord, right? That means these Old Testament saints, they are with the Lord.  The spirits of all the Old Testament saints, they're already with Christ because he took them up into heaven. So we say, and a third reason Paul also mentions, he talks about the whole family in heaven and earth. So who's that whole family? It includes the Old Testament saints, right? So there is a family of God, which is in heaven, including Old Testament saints and New Testament saints who die in Christ. They're all in heaven. And then there is a family of God in earth, that is, we believers who are here in earth. So we can say that when Christ is coming and when Paul says, God will bring with him those who are asleep in Christ.  The spirits of just men, the spirits of the Old Testament saints, the spirit of the New Testament saints, they're all there with him. So they will all come with him and receive their bodies at this time. So who will all receive glorified bodies? Everybody who's with the Lord in heaven, it's the spirits of all the people who are in heaven. And everybody, those of us who are alive and remain at the coming of the Lord in a moment in the twinkly of an eye, our mortal will put on immortality. So we will be caught up together to meet the Lord in the air. So every person, the spirit of every person who's with God in heaven and every believer here on earth, we will all be made perfect together. Receiving our glorified bodies at that instant. We will all be made perfect together and we caught up to be with the Lord in heaven. So to answer the question, who will receive glorified bodies at that time, at the rapture? Every saint, those who are in heaven, those who are on earth, receive their glorified bodies. Will we see the Old Testament saints at the time? They're already in heaven. The spirits of just men made perfect. They're already there in heaven. They've been made perfect. And so they're there, they're righteous in God. And we will meet them in heaven. So we'll meet everybody there in heaven. Another question is, who will be taken up at rapture? And I think we discussed this, John asked this in the previous lecture. Will there be people left behind and so on? And so we talked, there is the parable of the ten virgins and the ten talons and so on. So here again, I kind of emphasize what I've shared already, that is salvation is a gift. These exhortations are given to us for us to live ready in the state of readiness. But salvation is a gift. So we have to hold both truths together. We can't take one and discard the other. So if salvation is a gift, it is always a gift. But we have to live in readiness. You have to live in readiness. So take both together. And we should not say that, you know, if you are saved as a believer, you're just going to be left behind arbitrarily. No, everybody who's saved by grace is going to be raptured. And yes, we know that we will all be in different levels of maturity. Some may have been saved, you know, five minutes before the rapture. Some may have been saved 50 years before the rapture.  And being part of the rapture is included in salvation. Another question is, will we recognize each other in heaven? And the answer is yes. You know, how do we know it? Well, we see some examples on the Mount of Transfiguration. Moses and Elijah appeared along with Jesus. Now Peter, James and John, who were there on the Mount of Transfiguration, they had never seen Moses and Elijah. And they didn't have, you know, pictures by which they could identify, oh, that's Moses, that's Elijah. No, they didn't have all that. But somehow they knew that's Moses. That's Elijah talking to Jesus. They just knew. How did they know? Paul says that in heaven, we will know even as we are known. That means there is this knowledge that's given to every person to know about the things of God. So we will recognize each other in heaven. And it is some, it's a knowledge that's given to us. We've never, we've never seen any of these Old Testament sayings or Bible characters, but we will know who each one is. You will recognize each other. Okay. So let me pause here. Any questions so far? Any other questions you would like to ask about the rapture and anything connected to it? Let's go forward. So remember, we mentioned about Daniel's 70th week, right? So I want to just explain that a little bit because that puts the book of Revelation in context. And then after that we will get into Revelation chronologically. So let's go now to Daniel chapter nine, please. We're going to spend a little bit of time there. Daniel chapter nine, and we're going to read verses 24 to 27. Daniel nine, Daniel chapter nine, 24 to 27.  Daniel was a man who, of course we know as a Jewish young man, he was taken captive by the Babylonians into Babylon. So he was taken as a captive. And let's put my book back here. So he served under King Nebuchadnezzar, and he served as part of the Babylonian kingdom. Then King Nebuchadnezzar's grandson, Belshazzar, was the last Babylonian king. Belshazzar was killed and the Medes took over. That's another empire, the Medes. King Darius was the first leader there of the Medes. But the Medes were overthrown and then the Persians took over. King Cyrus was the first of the Persian kings. Then came after the Persians the Greeks and so on, and after the Greeks the Romans. So that's the history. Daniel served during the Babylonians, during the Medes, and during the Persians. So during the Babylonian time, God gave him many visions. God gave many visions and he had a call to that for us. He interpreted the dream of Nebuchadnezzar in chapter 2. He had a vision during the time of Belshazzar. That's Nebuchadnezzar's grandson. He shares that with us in chapter 7 and also in chapter 8. Daniel, chapter 9, where we are right now, is Daniel's experience during the time of Darius. Darius was the first Mede king. The Medes took over from the Babylonians. So Darius was king at that time and during his reign, Daniel had this experience of chapter 9. So in chapter 9, Daniel is praying for his people. He realizes that Jeremiah said the people of Israel would be in captivity 70 years and then they would come back. So Daniel is praying about that prophecy saying, God, 70 years is almost over. We need to go back. And during that time, Gabriel appears to Daniel and he gives him this understanding about the end times. So let's read Daniel, chapter 9. Somebody could read verses 24 to 27, please. 70 weeks are determined for your people and for your holy city to finish the transgression, to make an end of sins, to make reconciliation for iniquity, to bring in everlasting righteousness, to seal a vision and prophecy and to anoint the most holy. Know therefore and understand that from the going forth of the command to restore and build Jerusalem until Messiah the prince, there shall be seven weeks and 62 weeks. The street shall be built again and the wall, even in troublesome times. And after the 62 weeks, Messiah shall be cut off, but not for himself and the people of the prince who is to come shall destroy the city and the sanctuary. The end of it shall be with the flood and till the end of the war, desolations are determined. Then he shall confirm a covenant with many for one week. But in the middle of the week, he shall bring an end to the sacrifice and offering. And on the wing of abominations shall be one who may desolate, even until consummation, which is determined, is poured out on the desolate. Okay, thank you. So, Daniel Gabriel is speaking to Daniel and he explains to Daniel what is going to happen. So, let's look at it first by verse. Daniel 9 verse 24. He says, Gabriel tells Daniel, 70 weeks are determined for your people and for your holy city. Now, he's saying, Daniel, I've come to talk to you about 70 weeks. And these 70 weeks are specific to your people, that is, Israel, Jewish people, and your city, your holy city, Jerusalem. Now, I mentioned earlier that we know 70 weeks, one week represents seven years. We know it from in any cross-reference. You can see Genesis 29, 27 and 28, where in the ancient Hebrew, a week represents seven years. That's how they used it. So, what Gabriel is saying is, Daniel, I've come to talk to you about 490 years, 70 weeks, 70 times 7, 490 years. I've come to talk to you about 490 years and these 490 years speak specifically about your people and your holy city. And then Gabriel says, this is what is going to happen during these 490 years. He gives two sets of things. First, he says, to finish transgression, to make an end of sins, to make reconciliation for inequity. The first part, sin, transgression, inequity is going to be dealt with. That means this matter is going to be dealt with, transgression, sins, inequity. Secondly, he says, to bring in everlasting righteousness, to seal up vision and prophecy, to anoint the most holy. The second set of things that are going to happen is, everlasting righteousness will be introduced, will be ushered in. Vision and prophecy will be fulfilled and the most holy one will be anointed, so appointed as king. So that we understand as the millennium because the millennium is the time when righteousness will be ushered in, prophecy is fulfilled and Jesus Christ is anointed to rule and reign. The first part, to make an end of transgression, inequity and sin, that's Jesus Christ dying for us on the cross. So 490 years, two big things are going to take place. First, inequity, transgression, sin is going to be dealt with.  Second, righteousness will be ushered in prophecy will be fulfilled and the most holy Jesus will be anointed, set as king. So in this 490 years, okay. But how is this going to happen? Verse 25, know and understand that from the going forth of the command to restore and build Jerusalem until Messiah the Prince there shall be 7 weeks and 62 weeks. 7 plus 62 is 69. So 69 weeks, 7 plus 62. The street will be built again and the wall even in trouble sometimes. So he's saying, Daniel, from the time the command is given to go and rebuild Jerusalem. Now that was going to happen. Remember, Daniel, this was the time of King Darius, the Mede. After him, the Medes will be overthrown, the Persians will come. King Cyrus, the first Persian king, he is the one who gave the order, go back and rebuild Jerusalem. So what did Gabriel say? From the time King Cyrus gives this order till the Messiah comes, Jesus comes will be 69 weeks, that is 69 times 7, 483 years. And that's exactly what happened, right? 483 years from Cyrus giving a decree to go and rebuild Jerusalem till Jesus came. Now, of course, when they rebuild Jerusalem, like he says here in the end of verse 25, the street will be built again and the wall. So the city was rebuilt, but in difficult times. So the streets were rebuilt, the wall was rebuilt. Nehemiah came and rebuilt the wall. The temple was rebuilt, but it was rebuilt in difficult times. Then verse 26, after 62 weeks, that means at the end of the 483 years, 7 plus 62, at the end of the 62, that means totally 69 weeks, Messiah will be cut off. Jesus will be crucified, but not for himself. So he didn't die for himself, he died for everybody else. And the people of the prince who is to come shall destroy the city and the sanctuary. So after Jesus died, the city was destroyed, Jerusalem was destroyed and the temple was destroyed by whom the people of the prince was to come. That means the Romans. So the general Titus, a Roman general, he destroyed the city and the sanctuary. Jerusalem was destroyed, the temple was destroyed.  The end of it will be with a flood, and till the end of war, desolations are determined. That means from the time of the destruction of the city and the sanctuary, on till the end of war, there is going to be desolations. That means this city is going to experience a lot of trouble. Jerusalem is going to experience a lot of trouble till war can cease, which is the beginning of the millennium. So which is true. From the time of the Romans on till now, Jerusalem is experiencing desolation, is experiencing war and trouble. That's going on. Then verse 27. Now, we are picking up verse 27 without context, but in chapter 7 and chapter 8, Daniel has had visions about the Antichrist. He has had visions about the little horn. This man who will speak blasphemous things against God. So he's already seen all that. So now verse 27 is in connection with that. He says, then he, that is this little horn, this man of sin, this Antichrist, will confirm a covenant with many for one week. So he's saying, Daniel, see 69 weeks, 483 years from the time Cyrus gives the issue to go back to Jerusalem till Jesus comes for 83 years. Then there is a long gap for almost 2000 years. Long gap. The war and desolation will continue. Then this man will come for the final week. That's Daniel's 70th week. This man will come. The Antichrist will come for this final week. So 69 weeks plus one week. Daniel's 70th week. And what will happen to this Daniel's 70th week? This man will come and he will sign a peace treaty and confirm a covenant. I'm looking at verse 27 for one week. So the 70th week is when the Antichrist is operating. And what will he do in the middle of the week? That means after three and a half years, he will stop the sacrifice. He will, that means the temple will be rebuilt and there will be sacrifices happening. And on the wings of abomination, wings of abomination means he's moving very fast to do evil, abomination before God. He will be the one who makes desolate. He's going to bring utter destruction. And until the consummation, until that 70th week is going to lead up to the consummation, the final judgment, God, Christ is going to come. And there's going to be the consummation of everything. So what does Daniel's 70th week? It's just one week that is still pending. And it's that one week the Antichrist is going to operate. And that's what Paul the Apostle and Second Thessalonians chapter 2 was referring to, the man of sin, the perdition, who's going to set himself up in the temple of God. All that is revealed in the book of Daniel, we're only looking at Daniel chapter 9. But what I want to understand is what is spoken of in Daniel 9.27, this one week, that is the tribulation week. That is Daniel 70th week. That is what much of the book of Revelation is talking about, the details. Okay, so next week, we're going to start going through Revelation chronologically and see all of these things unfold. So did everybody understand Daniel chapter 9? Okay, I see John's question. The flood mentioned in 26. Yeah, so it is literally there was not a flood and when Jerusalem was destroyed at that time, they say that okay, there was a fire and so obviously to put out the fire and all of that, there was the flood. So there was not flood in the sense of like an overflow of a river and submerging a city or something like that. But when Jerusalem was destroyed, it was at that time, the Emperor Titus, the destruction happened in that manner. So it could refer to that or it could just refer to something that overwhelms the city in a symbolic way. But historically, there was no big flood that submerged Jerusalem in that sense. But it's talking about how the city was overwhelmed, overthrown and until the end of war, there will be desolations on that city. It will be really disrupted and troubled until the end of war, which will happen in Revelation 19. Good, any other questions? Okay, so I hope you're following me. I hope it's not too difficult to understand these things. It is quite amazing actually when you look at scripture and look at Bible prophecy, how beautiful it is. Let's take a moment to pray and we will close. Could somebody pray, close and dismiss the glass, please. We thank you for this time of learning. We thank you for your promises, the words that you have spoken, long back which is being fulfilled even today, God, we want to thank you for the assurance that you have given us and the beautiful privilege that you have given us to be known by you Lord. We pray that we would continue to learn about your coming and the end of times and we would prepare ourselves to meet with you and also to spread this word to people around us, God. We thank you for this time. In Jesus' name we pray. Amen. Thank you so much, Rohan. We'll continue this next week. God bless. Bye now.


Let's try to see if we can compromise and do a deal that doesn't lead to first our exit, second to the breakup of the United Kingdom because the Scots are going to leave and then all the islands are going to leave and then if we have a breakup then it's not going to be just a breakup of the United Kingdom but it's going to be the beginning of this integration of the European Union and it might not be such a good idea.


It is going to be epic. Yeah, everything we had thought everything we had hoped now There was no coffee bong or coffee funnel depending upon where you are from with MC DC in his office But to be honest we haven't seen his office yet So that could still be on the way MC DC is electrifying he gave numerous speeches one of them in the leading Team meeting of training camp the one where you're gonna set the tone for the team Here's the rules man. All right. Here's the rules. Don't be late. Nope.  We'll fight you here. We'll fight you there. We'll fight you to landfill man And feel man. He said I like the other tone. That's a freight train, man At the end hard knocks brought it all together with that song playing while they're training There were some moments that made me go. Oh, this is a movie


Statistics and Excel. Bell curve batting average comparison. Get ready, taking a deep breath, holding it in for 10 seconds, looking forward to a smooth soothing Excel. Here we are in Excel. If you don't have access to this workbook, that's okay because we'll basically build this from a blank worksheet. But if you do have access, currently five tabs down below. The two example tabs in essence answer keys. The two practice tabs having pre-formatted cells. So you can get to the heart of the practice problem. The blank tab, blank worksheet so we can practice formatting cells within Excel as we work through the practice problem. Let's go to the example tabs to get an idea of what we will be doing starting with the data tab where we will be pulling baseball statistics information in from an online resource, building them into a table so that we can sort and filter the table, pulling what we want from the table and


Why are Kim K and Leonardo DiCaprio being questioned by the FBI about their relationship and connection to this round Asian man? Wow, we are talking about the story of Jeho Lo right now. This is going viral in the Western world. It's been going viral in Asia for several years now. Andrew, long story short, this fat guy, Jeho Lo, got in charge of the 1MDB fund in Malaysia. It was worth $5 billion USD. And instead of deploying that money to help alleviate poverty and stimulate the economy in Malaysia, Andrew, he took it and spent it to become cool in Hollywood, just gifting people $10 million, giving them paintings. He's made the whole movie, Wolf of Wall Street. And basically, Andrew, now he's on run from Interpol International Police. And he probably will be on the run for the rest of his life if he doesn't go to jail for Malaysia for a very long time. But it's going viral right now because the Malaysian government is trying to get some of its money back. And the FBI is helping them do it. Yeah, so the FBI right now in America is shaking down some celebrities who were gifted stuff from Jeho, obviously because that money originally comes from Malaysia and belongs to Malaysia. So they're taking those assets back. Even people like Kim K, Leo, they're being asked to put money back. The producers of Wolf of Wall Street, who made money off of that movie, who was funded by Jeho, has to give money back. So it's good. I think what the FBI is doing is right. Right. And it's because he funneled the money from Malaysia through the American banking system. Andrew, some of the American authorities, they do feel somewhat responsible for this whole thing. So make sure you like, subscribe, turn on your notifications, guys. We're about to break it down from what we know. Andrew, this guy one time paid Emily Radijowski $25,000 just to go to the Super Bowl with him. Andrew, he paid for Paris Hilton's $7 million birthday party. He paid. Well, he helped. She's washed. One time, partying with his friends over eight months, he spent $85 million. And they used to call him the panda. Dude, I can just imagine right now. He's like, hey, it's Jeho, yeah, at your service. Like, when you want a party, Paris Hilton, you want $7 million. You want the castle. I got you. I got you. Yeah, like, no problem. You know, and like, that's a kind of like, aside from obviously the crime that he did, which he should get punished to the maximum, in my opinion, because obviously Malaysia really needed that money. And now that not only ruined and took away that those billions of dollars from the Malaysian government that was going to be used to help the country out. It also just showed the rest of the world and scared a lot of other potential investors from investing in Malaysia in the future. Right, it ruined the confidence. Bro, it's bad. It's bad. It's not good. So you got to get into some of the comments real quick and then we'll get into some larger takeaways. Andrew, somebody said, dude, of course, they were only just hanging out with him for the money. Look at this guy.  And why would the world celebrities or American celebrities want to hang out with him if he wasn't like paying for everything, paying for all the jets, paying for all the parties, buying $100,000 bottles at the club on a whim? OK, so two parts to this. I feel two different ways. First of all, I agree with the comments.  But really, otherwise, he's not producing movies. He's not really directing movies. He's not adding any creative input, right? So he's not really part of the world. However, but I will also say, you're putting celebrities on a pedestal. If you're saying, why would this and that person want to hang out with this guy? Because I do think these comments are racially motivated. Looking at him being like a round Asian dude and seeing automatically, oh, a round Asian guy has no other value than the money. Now, it's probably true, by the way, but I'm just saying. Right, it is true by the ranking of Western society, but I also hate that ranking, but it is what it is.  Why would you ever want an Asian guy around? I'm like, whoa, whoa, whoa, OK. Hey, maybe he's nice and fun to party with, but also a criminal. Somebody said, yeah, that Victoria's secret model, Miranda Kerr that was dating for a little bit, clearly just after the money. Because what is she there for, the looks? Probably was true, probably was true. Somebody said, man, he was the real Wolf of Wall Street, stealing all the money to fund that movie, Wolf of Wall Street. My goodness. Yeah, man, I mean, in that movie, they're kind of right. The whole movie's about pumping up stocks. Yeah, pumping up stocks and taking money from the middle class people and rich people. And then, yeah, they took money from the Malaysia government. The one MDB fund was supposed to boost Malaysia's economy. Well, it's supposed to alleviate poverty. So think about it. That's like, if you just imagine the stimulus checks that we got during COVID, except someone stole those checks and then used them to pay for celebrity parties. Somebody said, man, this is such Hollywood hypocrisy. All these people are always talking about saving the world. And here they are taking all these gifts, bought with fraudulent money from Jeho, flying around the world, creating all this carbon emissions on Jeho's private jets.  You just know that they're fun, rich people, right? That's what it is. They think of the money's coming from Dubai. They think of the money's coming from Malaysia. They don't even know where Malaysia is. And also another layer is that the director of the FBI is a Republican, right? And a lot of Hollywood celebrities are Democrats. So you're saying there's a possible angle here. It's nearby election time. Somebody said, if I would have steal an entire government fund, I shouldn't sure wouldn't spend it on people who didn't care about me. But somebody else said, I don't know, dude, if I had all the money that he'd stole, I probably would have did the exact same thing. It looked like he had a lit, fun time. Dude, when you talk about going out in a blaze of glory, man, this is exactly what he's doing.  But most likely he'll get caught. That's my prediction. But man, he lived life. And no, maybe not everybody respected him. Maybe not everybody knew what he did. Maybe not everybody cared about him. Not every woman was attracted to him. But yeah, he spent that money. He spent that money, man. Somebody said, man, it's only easy to have this much fun when you're playing with stolen money. There's no way anybody who worked hard or families worked hard for that money would ever spend it this way. I kind of agree. I kind of agree. Somebody said, man, there are so many poor Malaysians living below the poverty line. Do you know how many lives he could have changed with just $100,000 bottle that he bought for Lindsay Lohan on her 23rd birthday? Like I said, man, it didn't just impact Malaysia by taking that $5 billion away. It actually ruined Malaysia's chances in the future of getting potential investment from other people who are now looking at it being like, well, you guys got a corrupt government over there. So I don't know where my money's going to go if I give it to you guys. I don't trust it, you know? So that's what's really bad. So we got to get into the takeaways real quick to just to touch on that politician angle. It's so important who you elect in your government, right? Because the government takes not only foreign investment but also taxpayer money and whatever money that's developed from the people and they're supposed to deploy it. But if you get corrupt people to deploy it, they can just steal it, right? And that's why corruption begets more corruption. So that's why a lot of countries when they do find out someone is being corrupt, they come down very hard on them. Yeah. Aren't more of a personal angle, Andrew? This kind of made me sad a little bit or not sad, but it kind of reminded me of a story from high school. There's this guy I know and I'll hide his identity by changing his name. His name is Michael Finn, okay? And his parents own a bunch of fur shops, but he really wasn't in the AZN street world or anything close to that. He wasn't about that. He was more like always trying to appeal to the section of like preppy white kids. So he used to pay junior and senior year of high school. He used to come out of his own pocket and sign all the liability forms to rent out these houses on the lake to throw like these parties to be cool. And sometimes he didn't even get the girl he wanted, but he was just trying to rise up the ladder as like also a big faced round Asian guy with low leverage, trying to be cool at like Hollywood high school or in my case like hometown high school. And did it even feel like that that group truly respected him? Maybe they liked having him around. They enjoyed his time, but did they respect him? I would say they liked having him around because he's super helpful. You always have somebody to pick you up from the airport, run errands for you. I would say it's 50, 50 or like 30% out of 10 people probably ended up appreciating him and seeing through his like low visual value. And then seven out of 10 were more like on the using side. Well, it's not just visual value, right? It's maybe like personality wise, he wasn't like the coolest person. They're like, oh, this is like a great person. But listen, a lot of people don't understand. If you're just only great to other people, Andrew, here's this picture of J. Ho Low pushing Buster Rhymes around in a rickshaw. If you just do that for people, who's gonna like hate you? Because you're playing like the Alfred to Batman role. If you only serve people, why would they be mean to you? Right. Why would they like- They would have no reason to be mean to you.  I mean, the truth is in this elite world, man, there's a lot of J. Ho's of friend groups.  From a sovereign point of view. Take that aside, I'm just saying his position of being like, hey, invite me over, man. I'll bring over all the gifts. Or I give you- Kiss her. Yeah, I give you the best birthday gifts. Or, oh, I just pick up the extra meals for you so it's easier for you to hang out with me and you like me more. You know, and that's the thing, man. And it just reminds a lot of Asian guys like, damn, is this the only way that a big, chubby Asian guy is gonna hang out with these types of people? And oftentimes, man, I feel like a lot of Asian guys when they want to enter the Western world elite circles, they oftentimes have to finance their way in. I would say maybe if you're a pretty Asian girl, there would be other ways in, maybe you could just hang out with your way in or date your way in. But for Asian dudes, especially if you look like J. Ho, you gotta buy your way in. Yeah, yeah, no. And that's why the FBI, I support them. Take them pains back, man.  Yeah, no, by all means, guys, this is not a win for Asian guys, not. I mean, this guy is a bad guy. He did bad stuff.  I mean, this is one of the biggest financial frauds of all time. You know, I noticed Chinese Malaysians in the media a lot lately. Oh, yeah, that's a good point. J. Ho, low. Michelle, yo, Nigerian, even Ronnie. Shout to Ronnie. These are all much better people than J. Ho, by the way. Right, but I'm saying they active. They're Chinese Malaysians. There's something about Chinese people from Malaysia, man. They are, they are getting out there. So, hey guys, I want you guys to let us know in the comments section below, have you heard about this story? What do you think about what he did? Was it just human? Maybe he was just acting like a 15 year old or 13 year old who wanted to be cool in high school because he remembered his growing up in Britain high school or whatever. Or was this just like, it just is what it is, man. All right, everybody, let us know in the comments down below. You are watching the hot pop boys, everything from serious to frivolous. We're talking about it all. Thank you so much and until next time, we out. Peace.


Welcome to lecture series on advanced geotechnical engineering being offered by the department of engineering IIT Bombay Professor BVS Vishwanatham. So we are in module 4 and lecture 6 on stress strain relationship and shear strength of soils. So in the previous lecture we introduced about Mohr-Colem criterion and then introduced also the PQ space and in this lecture we will try to discuss more about the Mohr-Colem failure criterion and then interpretation and its correlation with the PQ space and further we will concentrate on definition of failure and interlocking concept and in its interpretations that is definition of failure particularly as far as the friction is concerned with interlocking concept and its interpretation. So as we discussed in the previous lecture we can actually express the principle stress relations shifts at failure as follows, sigma 1 is equal to sigma 3 tan square alpha plus 2 c tan alpha where alpha is equal to 45 plus 5 by 2 and which is also called as the failure plane inclination and in case if you are having sigma 3 is equal to another way as sigma 3 as the major and sigma 1 as the minor where sigma 3 is equal to sigma 1 tan square 45 minus 5 by 2 minus 2 c tan 45 minus 5 by 2. Now the Mohr-Colem idealization of geomaterials if you look into it we have a sample a cylindrical sample subjected to principal stress sigma 1 dash and sigma 2 dash and sigma 3 dash. So here as being sigma 2 dash is equal to sigma 3 dash in Mohr-Colem idealization what has been assumed is that sigma 2 is equal to sigma 3 has been assumed or sigma 2 dash is equal to sigma 3 dash and this is the stress strain variation d-way trick stress versus axial strain where axial strain in the direction of major principal stress. So this is the idealization and the slope of this is the elastic modulus and this is the curve which we may get experimentally and this is idealized in this fashion it is shown. So as we have discussed the Mohr diagram and Colem enolope if you look into this Colem has given during the investigations of retaining walls an equation which is actually called as tau is equal to c plus sigma tan phi and Mohr enolope actually has given as the tau is equal to function of sigma and this nonlinear enolope is actually for Mohr Colem Mohr enolope and this one is for the Colem equation. So this actually has been idealized to a straight line and Colem in his investigations of retaining walls proposed a relationship tau is equal to c plus sigma tan phi where c is the inherent shear strength also known as the cohesion c and phi is the angle of internal friction. So the criterion contains two material constants here c and phi and which are actually called as shear strength parameters and there are different methods to determine these shear strength parameters in the laboratory they are primarily called the direct shear test and triaxial test and the triaxial test actually has got you know the three different four different classes you can say and the first category is that where we do a triaxial test with no cell pressure then you know in that case it is actually called as unconfined compressive strength test is called UCS test and when we do this test with you know a cell pressure that is unconsolidated undrained triaxial test and when we do you know the triaxial test by allowing the consolidation you know during by allowing the drainage during consolidation and no drainage during shear then it is called consolidated undrained triaxial test. When we allow both you know the drainage during consolidation as well as the shear it is called consolidated drained triaxial compression test. So when we do this when we as we have discussed it that when we do a different cell pressures we get the different sets of Mohr circles if you are interpreting in terms of total stresses we will get total stress envelopes if you are actually interpreting in terms of effective stress effective stress parameters then you will get the effective stress envelopes and with that we will able to get the C dash and phi dash. So here in this particular diagram where the Mohr you know envelopes is actually shown along with the Coulomb envelopes and with the slope of inclination is phi and alpha f is that failure plane. So the criterion basically consists of Mohr Coulomb criterion basically consists of two parameters that is C and phi as opposed to one material constant for the Truska criterion as far as the Truska criterion is concerned and there is only one material constant. So yielding and failure takes place in the soil mass when mobilized axial stress at any plane tau m becomes equal to the shear strength tau f which is given by. So yielding and failure takes place in the soil mass when mobilized actual shear stress at any plane tau m becomes equal to when tau m becomes equal to the you know the shear strength tau f which is actually given by tau m is equal to C dash plus sigma dash n tan phi dash is equal to tau f where C dash and phi dash are the strength parameters then we can write this as in terms of function of sigma dash as tau minus sigma n dash tan phi dash minus C dash is equal to zero. So this we have written in terms of function of sigma dash we have written like tau minus sigma n dash sigma dash n tan phi dash minus C dash is equal to zero. So one point we need to note here in case of the Mohr Coulomb idealization we have discussed that because of the you know the non-consultation of sigma 2 dash as can be seen here when we have sigma 1 dash and then sigma 2 dash when with sigma 3 dash with the minor principle stress that this Mohr circle is actually you know is in contact with the failure envelope. So where sigma 1 dash is greater than sigma 2 dash greater than sigma 3 dash and here note that the value of the intermediate principle test does not actually influence the failure. So this particular you know the value of the sigma 2 dash actually does not actually influence the failure. So in the case of Mohr Coulomb idealization the intermediate you know principle stress sigma 2 dash is neglected. So further and to the Mohr Coulomb idealization of geomaterials and in this we consider a tau versus sigma and where you have got a Mohr circle and you have a sample which actually has got you know if the sample is homogeneous we actually have got the conjugate failure planes in both the directions and you can have a failure plane in this direction and you can have a failure plane in this direction and with that you know here this is the failure plane and the parallel to this is the failure plane inclination which is actually shown here. And so we can write from the geometry of the Mohr circle by considering a Mohr circle tangent to the line that is a stress state associated with the failure that is at this point and using the trigonometric relations the alternate form of tau is equal to c plus sigma f tan phi can be obtained. So in terms of principle stresses it can be written as tau f is can be seen as tau f is equal to sigma 1 minus sigma 3 by 2 and sigma f is equal to you know which this point is nothing but sigma 3 plus you know the sigma 1 minus sigma 3 by 2. So if you look into this this will become sigma 1 plus sigma 3 by 2. So this point is sigma 3 0 to it measures an ordinate of sigma 3 dash and this point actually measures you know this distance so that is actually obtained as sigma 1 plus sigma 3 dash by 2. So we can actually write this in terms of principle stresses sigma 1 minus sigma 3 dash by 2 is equal to c dash cos phi dash plus sigma 1 plus sigma 3 dash by 2 sin phi dash. So when we put this in one side and we can actually write f is equal to sigma 1 minus sigma 3 minus sigma 1 plus sigma 3 sin phi dash minus 2 c dash cos phi dash is equal to 0. So that is what actually to be stated here where f is equal to sigma 1 minus sigma 3 dash sigma 1 dash minus sigma 3 dash minus sigma 1 dash plus sigma 1 3 sigma 3 dash sin phi dash minus 2 c dash cos phi dash is equal to 0. So this you know we actually deduced from the trigonometric relation by satisfying the trigonometric relations and from the geometry of the Mohr circle. And this was actually earlier we have actually when we have done with relation between the kf line and Mohr Coulomb failure and all of and this also can be expressed in terms of you know principle stresses and when we plot pq plot with q is equal to sigma 1 minus sigma 3 dash by 2 and p is equal to sigma 1 plus sigma 3 dash by 2 when we plot so when q is equal to sigma 1 minus sigma 3 dash by 2 and p is equal to sigma 1 plus sigma 3 dash by 2 when you plot this is the kf line and which is actually inclined at an angle psi. So when we compare you know typical Mohr circle and this thing when we said that sin phi dash is equal to tan psi and c dash is equal to a by cos phi. So by using this also we can get the other form of tau is equal to c plus sigma tan phi as sigma 1 minus sigma 3 dash by 2 is equal to c cos phi plus sigma 1 plus sigma 3 by 2 sin phi dash. So with this also we will able to get the expression which we are talking here sigma 1 minus sigma 3 dash minus sigma 1 plus sigma 3 sigma 1 dash by sigma 3 dash sin phi dash minus 2 c dash cos phi dash is equal to 0. Now with no order implied by the principle stresses sigma 1 sigma 2 sigma 3 the Mohr Coulomb criterion can be written as in the form of this six equations and this represent to two equations, this represent two equations, this represent two equations wherein this is nothing but plus or minus sigma 1 minus sigma 2 by 2 is equal to a into sigma 1 plus sigma 2 by 2 plus b plus or minus sigma 2 minus sigma 3 by 2 is equal to a into sigma 2 plus sigma 3 by 2 plus b and plus or minus sigma 3 minus sigma 1 by 2 is equal to a into sigma 3 plus sigma 1 by 2 plus b where a is equal to M minus 1 by M plus 1 that is A is equal to M minus 1 by M plus 1 and M is equal to C0 by T0 which is nothing but 1 plus sin phi dash by 1 minus sin phi dash and B is equal to 1 by M plus 1 and C0 is equal to M by M plus 1 where T0 is equal to C0 by 2 into 1 minus sin phi dash where A is actually within 0 to 1 that is 0 less than or equal to A is within 0 less than or equal to A less than 1. So the values of this C0 and T0 are actually defected here, C0 and T0 are defected here and which is shown here the C0 by T0 which is nothing but the ratio of these two C0 by T0 and this is the typical more coulomb failure and all of with a Mohr circle C and Mohr circle D. So we have said that these six equations are there and wherein we actually have got A is equal to M minus 1 by M plus 1, M is equal to C0 by T0 and B is equal to 1 by M plus 1 where C0 is equal to M by M plus 1 and T0 is equal to C0 by 2 into 1 minus sin phi and where A is in between 0 to 1. So this T0 is the theoretical Mohr coulomb uniaxial tensile strength and that is on the negative side of the Mohr circle you can see that in tau sigma plot and that is not observed in experiments rather a much lower strength T is measured and the sigma 1 is equal to 0 and the sigma 2 is equal to that is a sigma 1 is equal to 0 and sigma 2 is equal to minus T that is actually shown here. So with the failure plane being normal to sigma 3 plane, so sigma 1 plane is here and the sigma 3 plane here so the failure plane being normal to the sigma 3 plane. So the C0 is the theoretical Mohr coulomb uniaxial compressive strength. So C0 is the theoretical Mohr coulomb uniaxial compressive strength, C0 is the theoretical Mohr coulomb uniaxial compressive strength. Now the shape of the failure surface in principal stress space is depend upon the form of failure criterion. So the shape of the failure surface in principal stress space is depend upon the form of the failure criterion, linear functions map as plants, planes and non-linear functions as curvilinear surfaces. So the shape of the failure surface in principle stress space is dependent on the form of failure criterion primarily it is linear functions map as planes and non-linear functions as curvilinear surfaces. So the following six equations the equations which we have said you know which we just discuss are represented by six planes that intersect one another along the six edges defining the hexagonal pyramid. So the following six equations which are actually discussed just now are represented by the six planes that intersect one another along the six edges of the defining a hexagonal pyramid. So that is these six edges which are actually defining this hexagonal pyramid these equations actually represent these equations represent the six planes that intersect one another along six edges defining the hexagonal pyramid. So this is the failure surface that means that this is the failure surface and this is the hydrostatic axis, this is the hydrostatic axis where sigma 1 is equal to sigma 2 is equal to sigma 3 and this is the failure surface on the equipressure plane sigma 1 plus sigma 2 plus sigma 3 is equal to constant or pi plane this is also called as the pi plane perpendicular to the hydrostatic axis. So perpendicular to the hydrostatic axis so if you take the projection of this one you will have the this is the pyramid surface which is you know hexagonal pyramid surface and which is also called as the pi plane which is actually perpendicular to the hydrostatic axis and where Mohr Coulomb criterion can be described as irregular hexagon with sides of equal length where Mohr Coulomb criterion can be described as irregular hexagon with sides of equal length. So here the pyramidal surface in principle stress space and cross section equipressure plane is actually given here and these the equations which you know are shown here they actually represent the all the six edges which are forming the hexagonal pyramid surface and the failure surface on the equipressure that is sigma 1 plus sigma 2 plus sigma 3 is equal to constant or a pi plane perpendicular to the hydrostatic axis where the Mohr Coulomb criterion Mohr Coulomb can be described as irregular hexagon with sides of equal length. So this is the irregular hexagon with is actually shown once again here where this is the hydrostatic axis and here is the point where the sigma 2 dash is there. So isotropy requires three fold symmetry because an interchange of sigma 1 sigma 2 sigma 3 should not influence the failure surface for an isotropic material. So if you have a isotropic material the requires three fold symmetry because of an interchange of sigma 1 sigma 2 3 should not influence the failure surface for an isotropic material. Note that the failure surface need only be given in any angle in any of the one of the 60 degrees regions that is one of the 60 degrees region that is what actually shown here. So note that the failure surface need only be given in any of one of the 60 degrees regions and Mohr Coulomb failure surface is a regular hexagon in principle stress space. Now consider the transformation from principle stress space sigma 1 sigma 3 to Mohr diagram sigma tau. So although the radial distance from the hydrostatic axis to the stress point is proportional to the deviatory stress a point in principle stress space does not directly indicate the value of the shear stress on a plane. However each point on the failure surface in principle stress space corresponds to Mohr circle tangent to the failure analog. So though the radial distance from the hydrostatic axis to the stress point is proportional to the deviatory stress a point in the principle stress space does not directly indicate the value of the shear stress on a plane. However each point on the failure surface in principle stress corresponds to Mohr circle tangent to the failure analog. So further extending the discussion for the particular case where sigma 2 is in the intermediate principle stress in the order sigma 1 dash greater than sigma 2 dash greater than sigma 3 dash or sigma 1 dash greater than sigma 1 dash greater than sigma 1 greater than sigma 2 greater than sigma 3. The failure surface is given by the side ACD of the axogonal perimeter. The failure surface is given by the side ACD of the perimeter that is the side ACD of the perimeter here which is actually shown in the surface ACD. D is this point sigma 2 dash. The principle stresses at point D represent the stress state for a traction compression test where sigma 1 and sigma 2 is equal to sigma 3 at point D and at point D is given by circle D in the Mohr circle diagram. The point D that is given by the Mohr circle D which is actually shown here. So this is the Mohr circle which is actually shown here point D. This is Mohr circle D. Similarly for point C with principle stresses sigma 3 and sigma 1 is equal to sigma 2 associated with the triaxial extension test. Mohr circle C depicts the stress state where point D and C can be viewed as the extremes of the intermediate stress variation. So where points D and C can be seen as the extremes of the intermediate stress variation and the normal and shear stresses correspond to failure are given by points Df and Cf. So this indicates the Cf and Df indicates the extremes of the intermediate stress variation. So it can be seen that the Cf and Df will give the failure points and so for this is for the triaxial test and where Mohr circle C depicts the stress state and points D and C can be viewed as the extremes of the intermediate stress variation and the normal and shear stresses correspond to failure are given by points Df and Cf. And points lying on the line CD on the pyramidal failure surface will be represented by circles between C and D. So points lying on the line CD that is this they are represented by the, represented by circles between C and D that is we are actually talking about circles between C and D, between circles between C and D. And as can be seen this hexagonal you know pyramidal surface has the corners that may sometime create problems in computations and however this particular difficulty is quite easily welcome by introducing a local rounding of the corners according to Griffith 1990. So the Mohr Coulomb in space that is Mohr Coulomb in principle stress space which is hexagonal pyramid surface has corners that may be sometimes create problems in computation. So this particular difficulty is quite easily can more come by the introducing local rounding of the corners according to Griffith 1990. So as we have discussed the other way of describing tau is equal to sigma, tau sigma plus tan phi in terms of principle stresses as f is equal to sigma 1 dash minus sigma 3 dash minus sigma 1 dash plus sigma 3 dash sin phi dash minus 2c dash cos phi dash is equal to 0. So this can be obtained further in order to make attempts to derive a consistent conditions of the Mohr Coulomb in space with p dash is equal to you know where specific volume is equal to 1 plus e and p dash is equal to 1 by 3 sigma 1 dash plus sigma 2 dash plus sigma 3 dash and q is equal to square root of sigma 1 dash minus sigma 2 dash whole square plus sigma 2 minus sigma 3 dash whole square plus sigma 1 dash minus sigma 3 dash whole square. So the whole divided by 2 and for triaxial conditions as well we have said trying when we have got a triaxial sample that is a cylindrical sample sigma 2 dash is equal to sigma 3 dash when we have this sigma 2 dash is equal to sigma 3 dash and what we get is that p dash is equal to 1 by 3 sigma 1 dash plus 2 sigma 3 dash and q is equal to sigma 1 dash minus sigma 3 dash. So when we put this into when we put this this we get simplified to q is equal to sigma 1 dash minus sigma 3 dash and p is equal to 1 by 3 sigma 1 dash plus 2 sigma 3. Now by substituting these here we can write sigma 1 dash is equal to sigma 1 dash is equal to 3p dash minus 2 sigma 3 dash. So sigma 1 dash can be written as 3p dash minus 2 sigma 3 dash. So if you put p dash is equal to 1 by 3 into sigma 1 by 3 into sigma 1 dash plus 2 sigma 3 we will get sigma 1 dash and sigma 3 dash is equal to sigma 1 minus q and if you substitute q is equal to sigma 1 dash minus sigma 3 dash we will get sigma 3. So by using these values with sigma 1 dash is equal to 3p dash minus 2 sigma 3 dash and sigma 3 dash is equal to sigma 1 dash minus q and substituting in this particular equation and what we get is that as the sigma 1 dash is equal to 3p dash minus when you substitute for sigma 3 dash here what we get is that sigma 1 dash is equal to 3p dash minus 2 sigma 1 dash plus 2q and where with this we can write sigma 1 dash as 3p dash plus 2q by 3 where p dash is equal to sigma 1 dash plus 2 sigma 3 dash by 3 and q is equal to sigma 1 dash minus sigma 3 dash and similarly sigma 3 dash is equal to sigma 1 minus q and by substituting these values we get 3p dash minus q by 3. So with this what we can write is that you know sigma 1 dash plus sigma 3 dash is equal to when you add these two sigma 1 dash plus sigma 3 dash is equal to 6p dash plus q by 3. So sigma 1 dash plus sigma 3 dash is equal to 6p dash plus q by 3 and which is you know when we add to this what we get is that when you substitute in this equation when you substitute in this equation sigma 1 minus sigma 3 that is nothing but q is equal to sin phi plus 6p dash plus q by 3 plus 2c cos phi. So by simplifying this we get 3q is equal to 6p dash sin phi plus q sin phi plus 6c cos phi. So what we get is that 3q when you do the cross multiplication is equal to 6p dash sin phi plus q sin phi plus 6c cos phi. So the equation actually has got pi dash and here also pi dash and here also pi dash and here also pi dash and pi dash. So q is equal to 6 sin phi dash divided by 3 minus sin phi dash into p dash plus 6c cos phi dash divided by 3 minus sin phi dash. So this is actually indicated as q is equal to n the new p dash plus c star where new is equal to 6 sin phi by 3 minus sin phi dash and c star is equal to 6c cos phi by 3 minus sin phi dash where this is actually called as formulation for the Mohr-Coulomb model in pq space. This is actually called as a formulation for the Mohr-Coulomb model in pq space and assuming that the flow rule and ideal plasticity condition and we can write f is equal to f function of p dash q is equal to q minus a new p dash minus c star is equal to 0. So by taking the differentiation with respect to p dash and dou f by dou p dash dp dash plus dou f by dou q into dq is equal to 0. So this is actually consistency condition which is called as far as the Mohr-Coulomb model in pq space is concerned. So what we have done is that from the alternative way of expressing tau is equal to c plus sigma tan phi which we have taken and from these considerations of by using these invariants p dash is equal to one third of sigma 1 dash plus sigma 2 dash plus sigma 3 dash by 3 and q is equal to root over sigma 1 minus sigma 1 dash minus sigma 2 dash whole square plus sigma 2 dash minus sigma 3 dash whole square plus sigma 1 dash minus sigma 3 dash whole square by 2 and then for traction conditions when you put sigma 2 dash is equal to sigma 3 dash we get p dash is equal to one third of sigma 1 plus 2 sigma 3 dash and q is equal to sigma 1 minus sigma 3 dash. So what we have written is that we have written this sigma 1 dash is equal to 3 p dash minus 2 sigma 3 dash. So this is actually expressed in terms of sigma 1 dash is equal to 3 p dash minus 2 sigma 3 dash and this is actually expressed as q is equal to that is sigma 1 dash minus sigma 3 dash. So sigma 3 dash is equal to sigma 1 minus q. So that is what actually we have written. Then what we have done is that sigma 1 dash is equal to 3 p dash minus 2 sigma 1 dash plus 2 q. So we actually substituted for sigma 3 dash sigma 1 minus q and then expressed in terms of p and q that is sigma 1 dash is equal to 3 p dash plus 2 q by 3 and similarly when we have taken sigma 3 dash is equal to 3 p dash minus 2 sigma 3 dash minus q and with that we have got 3 p dash minus q by 3 and then added sigma 1 dash plus sigma 3 dash then we have got sigma 1 plus sigma 3 is equal to 3 p 6 p dash plus q by 3. When you add sigma 1 dash plus sigma 3 dash we have got in terms of p dash and q where p dash is equal to sigma 1 dash plus 2 sigma 3 dash by 3 and q is equal to sigma 1 minus sigma 3 dash we get 6 p dash plus q by 3. Now this particular expression which is for sigma 1 minus sigma 3 this is actually replaced by q and then sigma 1 plus sigma 3 was actually replaced by 6 p dash plus q by 3 and then simplification yielded a consistency and more column model in the p q space which is q is equal to n that new p dash plus c star where mu is equal to this particular coefficient that is 6 sin phi dash divided by 3 minus sin phi dash and c star is equal to 6 c cos phi dash by 3 minus sin phi. So f is equal to the formulation for more column model in p q space can be expressed as q minus new p dash minus c star is equal to 0 and assuming the associated flow rule in and ideal flow ideal plasticity which we have started with by idealizing the geomaterial in case of more column criterion where a function of p dash q is equal to q minus new p dash minus c star is equal to 0 which is dou f by dou p dash dp dash plus dou f by dou q dq is equal to 0 which is actually called as the consistency condition. Now some limitations of more Coulomb theory this we have discussed but we are again elaborating. So one of the prime limitations we actually said is that the more envelope is a curl and the Coulomb equation is a straight line. So within the usual range of the experimental range in the laboratory what has been done is that it is actually assumed as a circular that is within the usual experimental range in the laboratory. So possible over estimation of the safety factor for the slope stability calculations can be interpreted and difficulties in calibration because of the linearization. So we actually have taken linearization so there are some difficulties in the calibration and then second is that the effect of the intermediate principle stress sigma 2 dash on the condition failure though we actually discussed that it is not influencing the failure but it is obvious that sigma 2 can have no influence on the conditions at failure for more failure criterion and no matter what magnitude it has. So though in the Coulomb criterion it is actually stated as a limitation but it is obvious that sigma 2 can have no influence on the conditions at failure and no matter what is the magnitude of the sigma 2 and the intermediate principle stress sigma 2 probably does have an influence on in real soil but the more Coulomb failure theory does not consider it. In real soil it may have influence but the more Coulomb failure theory does not consider it and the more Coulomb failure criterion is well proven for most of the geometricals but that of a place is still contradictory that is one of the limitation and the soils on shearing exhibit variable volume change characteristics depending upon the pre consolidation pressure and which cannot be accounted with more Coulomb theory and in soft soils volumetric plastic strains on shearing are compressive that is negative dilation takes place while the more Coulomb model will predict continuous dilation. So in soft soils or loose sands the volumetric plastic strains on shearing are compressive in nature that is the undergone negative dilation and whilst the more Coulomb model will predict the continuous dilation more Coulomb more Coulomb model predict the continuous dilation. So this is also stated as one of the limitations of the more Coulomb theory. Now the definition of failure when we further you know correct ourselves to friction and interlocking concept in order to correct that let us look into what is the definition of failure and failure along a plane in a material occurs by critical combination of normal and shear stress that is when we have tau is equal to function of sigma and tau is equal to C plus sigma tan phi the shear stress is the function of material cohesion or a soil inherent strength and an angle of internal friction. So this internal friction can be due to the sliding friction but the sliding which actually can happens between two particles or also due to interlocking that is one particle get locked into other particle and then there is or part depends upon the shape of the particle like an angularity and then angularity and size of the particles. So the failure along a plane in the material occurs by critical combination of normal and shear stress where tau is equal to C plus sigma tan phi where shear stress is the function of material cohesion C and angle of internal friction phi. So if you look into the definition of failure when we have got tau sigma annulope and when you have a point A stress point A and this is actually said that it is stable no failure occurs and but when actually no shear failure occurs for A and but when it is an actually on the failure annulope and when it actually on the failure annulope then it is you know the shear failure occurs and this is the tau is equal to function of sigma is actually represented here and when it is here that means that you know the stress state cannot exist above the failure annulope that means that the failure would have already taken place. The failure would have already taken place similarly when you draw the Mohr circle above the failure annulope that implies that the failure would have already taken place. So the point C is cannot exist and at point B which is you know at failure and point A is actually is stable the safe against the failure. Now we can also look into the flow rule for Mohr Coulomb for dilatancy angle and for Mohr Coulomb flow rule is defined through the dilatancy angle of the soil where G of sigma dash is equal to tau minus sigma dash n tan psi dash minus constant is equal to 0. So this is the plastic potential function so this is the you know for the dilatancy angle so G sigma dash is equal to tau minus sigma dash n tan psi dash minus constant is 0 where psi dash is the dilatancy angle and which is actually less than which is less than the angle of internal friction and which is less than the angle of internal friction. Now the interlocking concept and its interpretations when we look into it the frictional soil behavior is mainly influenced by the two factors one is you know frictional resistance or sliding resistance between the you know two particles upon shearing and to expand the soil against the confining pressure. So then the soil which actually can get undergo increase in volume upon the shear under confining pressure so and angular friction can be defined as pi is equal to pi u plus beta where angle of sliding friction between the mineral surfaces and beta is the effect of interlocking where that is also a combination which is can be said as because of the angularity of the particles and all. So where pi is equal to pi u plus beta where pi is the angle of sliding friction between the mineral surfaces and beta is the effect of internal interlocking. So the pi varies with the nature of the packing of the soil so denser the packing higher is the value of pi the denser the packing that is the in a given volume if there are more number of particles are there then it is called as denser packing higher is the value of pi if pi u for a given soil is constant and b must change with the denseness of the soil particle. So if pi u for a given soil is constant let us say for a particular angularity particular shape and if it is constant b must change with the denseness of the soil particle. So b increases with increasing denseness of the soil and because more work to be done to overcome the effect of interlocking. So because the particles are get locked in a dense configuration the soil actually has to work a lot in order to undergo this movement and so beta increases with increasing the denseness of the soil due to shear and because more work to be done to overcome the effect of interlocking which actually arises due to shear. So the effect of the angularity of the soil particles if you look into it soil possessing angular soil particles will show high friction angle effect of angularity of the soil particles if you look into it soil possessing angular soil particles will show high friction angles then that of rounded soil particles because angular soil particles will show a greater degree of interlocking and higher value of beta. So the so called this beta will be high for you know angular soil particles because of the greater degree of interlocking and higher value of beta. Now further the interlocking concept with interpretations with dilation so if you look into that here beta is the function of the you know the dilation of the function of the dilatancy of the soil. So if you take a loose arrangement of the grains if you take a spherical grain and you can see that these are the void spaces. So when they are subjected to a vertical you know in the vertical stress and a shear in the horizontal direction and this is the case the soil actually undergoes you know negative dilation in the sense that the soil undergoes a compression and which actually takes place like this. So this is you know called as a negative dilation so the volume decreases here but here when you have the soil particles which are actually you know dense then you can see that there is you know they increase in the volume there is an increase in the volume takes place. So you know this interlocking concept and interpretations can be interpreted by taking CISA concept or analogy wherein when we take this into consideration then we can see that you know the so called the dilatancy angle and other concepts can be discussed. So the interlocking concept and interpretation with dilation for loose sand the volume decreases with shearing for loose sand the volume decreases with the shearing that is called what we calling a negative dilation. And for dense sand the volume initially you know very marginally decreases and then thereafter it shows actually an increase in the you know the dilation so this is increase in the volume increase in the volume upon shearing. So this shows that this shows in this actually the tendency of this dilatancy decreases with increase in the confining pressure which increase in the confining pressure. So let us consider the interlocking concept and interpretations where dilation and direct shear response as we said that one of the tests if you do by using for determining the shear strength of the soil is the direct shear that is that you will be placing a soil mass in a box and then two boxes and even we allow the box to undergo movement then you can see that you know the shear is actually applied along the pre-determined failure plane which is horizontal. So here this is for the dense sand a typical variation for dense sand where Q by P versus X that deflection so Q is the shear force and P is the normal force and so this is for dense sand and this is for the loose sand. So loose sand actually has undergone you know there is a compression and then a dense sand so here where it can be seen that where it can be seen that the shear which actually undergoes a movement with this we can actually calculate what is the you know the friction angle with reference to you know application of this so called the dilation. So here the total work done is equal to DW which is nothing but P into delta Y that is in the vertical direction P into delta Y in the vertical direction and Q delta X that is in the horizontal direction so delta X is the horizontal movement in the X direction and delta Y is the vertical movement in the vertical direction so work done is net work done is equal to P into delta Y and Q into delta X. So we can write P delta Y plus Q delta X is equal to is counted by mu P delta X that is the friction which actually mobilized along this one. So by dividing delta Y by delta X is equal to mu minus Q by P when you simplify this what we get is that delta Y by delta X is equal to mu Q by P and which is nothing but which is nothing but tan psi and where tan psi is equal to tan phi m is minus tan phi c where phi c is equal to tan inverse mu. So this alternatively we can say that phi m is equal to phi c plus psi. So what we have done is that in the with reference to interlocking concept in interpretation the total work done is equal to DW is equal to P delta Y plus Q delta X and then we divided right through by delta X and with that we have got delta Y by delta X plus Q is equal to mu P and then when you simplify further and what we have got is that delta Y by delta X is equal to mu that is due to sliding friction by minus Q by P and is equal to tan inverse psi. Tan inverse psi is nothing but the so called inclination of this one that is called delta Y by delta X and which is nothing but tan psi is equal to tan psi is equal to tan phi m that is the due to friction minus tan phi c that is because of the interlocking and so with that phi c is equal to tan inverse mu and which we have written here and alternately we can write phi m is equal to phi c plus psi. So phi m is equal to phi c psi that is what actually we have say from the deliberation discussed just now. So how to understand this so called dilatancy so why do we get volume changes when apply the shear stresses and this can be explained with a simple analogy which is saw blade analogy can see that the orientation of these planes they are upward and this is the shear direction and this is the normal stress and similarly what will happen is that when the particles are under dense configuration when it is subjected to shear the particles will raid and another particle and be subjected to a similar analogical movement. So the analogy was actually we have been brought between the interlocking saw blades and dense packing of the grains so the simple analogy we can actually relate correlate is that interlocking saw blades with the dense packing of the grains when they are actually subjected to shear you know the inclination of that interlocking plane blades is the dilation angle and this angle and that angle is actually represented here this is psi and this is psi. So it is phi is equal to psi plus phi m that is the due to friction the apparent externally mobilized angle of friction on horizontal planes phi is larger than the angle of friction resisted resisting the sliding on the inclined planes so the strength is equal to friction plus dilatancy so it is actually nothing but the actual strength of the soil is nothing but the friction plus dilatancy the friction plus so the angle of internal friction is not only that you know it actually has got only friction but also the component of the dilatancy. Now this further you know can be the saw blade analogy can be extended to initially dense and a critical and initially loose conditions so you can see that in case of you know in case of initially dense the particles actually have no way to move except they have to raid on one another so the raiding of the particles takes place on the one particle raid on another particle and this particle raid on another particle so the orientation of the sea blade can be seen on the upward direction in case of critical condition where you know you can see that is horizontal but in case of say initially loose soil you can see that this is you know horizontal this is inclined down that means that it actually undergoes the compression. So when the soil is initially denser than the critical state soil is initially denser than the critical state it must achieve then as particles slide past each other going to the imposed shear strain they will average separate so when a soil is initially denser than the critical state it must achieve you know a denser configuration then as the particles slide each other going to the imposed shear strain then they actually have got a tendency to separate the particle movements will spread about an angle and that is actually called as dilation so see the orientation of the sub blade here so this is analogy and this is actually what happens in the soil in the real soil and when you have you know the orientation which is actually you know the initially loose soil when the soil is initially looser than the final critical state then the particles will tend to get closer together as the soil is disturbed and the average angle of dilation will be negative indicating a contraction. So that is why the sub blade you know inclination or plane of inclination is actually shown below so this is initially loose soil tend to become you know denser here and when we have you know have a place where it is constant you know in the sense that critical state if the density of the soil does not in the critical state is the where no volume change occurs so if the density of the soil does not have to change in order to reach a critical state then there is a zero dilatancy as the soil shear at constant volume. So the soil shear takes place at a constant volume so it is important to realize that the critical state is only reached when the particles they have the full opportunity to juggle around the and then come into the new configuration so if the confining stress is increased where the particles are being moved around then they will tend to finish up in a more compact state. So we have seen for initially dense state initially loose state and also in a critical state and in the critical state what we are saying is that if the density of the soil does not have to change in order to reach a critical state then there is a zero dilatancy of the soil shear at constant volume and it is important to realize that a critical state is only reached when the particles have had full opportunity to juggle around and coming to new configurations so if the confining stress is increased when the particles are being moved around then they will tend to finish up in a more compacted state. So in this particular lecture we try to understand about the Mohr Coulomb in the pyramidal hexagonal surface and also we discussed the consistency condition as far as the Mohr Coulomb condition is concerned and thereafter we actually introduced also to interlocking concept and then we also said that introduced to that when the soils particularly in the dense soil or in over consolid soil and when it undergoes shearing and we said that it is going to experience a phenomenon and which is called dilation and that angle is called dilation angle and that is actually the phenomenon is called dilatancy and the angle which is called the psi the dilatancy angle and this dilatancy angle decreases the suppressment of the dilatancy or dilation phenomenon can be observed once there is an increase in the normal stress so we will further discuss in the forthcoming lecture after having introduced about the different methods for determining the shear strength and further we will connect with these two spots.