Let us start our today's lecture for this NPTEL video course on Geotechnical Earthquake Engineering. We were going through our module number 8 which is Site Response Analysis. Let us have a quick recap what we have learnt in our previous lecture on this module 8 that we have started learning on site response analysis. We have mentioned how the problem of site response is defined that is it is the prediction of the response of a soil deposit due to the earthquake excitation and in that process we have seen we have three major phases or phases. Three major phases are source, path and site, source of earthquake through which it travels that path of earthquake and the site or the surfacial layer close to ground surface when it travels what will be the behavior. So, that site response or ground response we want to learn in detail. So, for that site response ideally speaking these are the three steps of source, path and site what we have mentioned over here is having the complicacy of in reality getting the complete information about the fault rupture that is the complete information about source then complete information about crustal velocity and the damping characteristics which are not properly known this is regarding the path and then nature of energy transmission between that source and the site is uncertain. So, after knowing those real problems what we practice actually for the ground response or site response analysis are like doing seismic hazard analysis either probabilistic or deterministic it can be and also using the bedrock motions then seismic hazard analysis has to rely on the empirical relationship, attenuation relationship and ground response problem becomes one of determining response of soil deposit to the motion of the underlying bedrock and these ground response analysis where these are used these are actually extensively used to predict the ground motion at the ground surface time history, response spectra, scalar parameters, evaluate the dynamic stress strain, liquefaction hazard, foundation loading due to the earthquake then evaluate the ground failure potential, instability of earth structure, response of various geotechnical structures like retaining wall, earth dam, pile, various foundations on all these things when we want to study their seismic behavior we should first go through the ground response analysis that is the very basic fundamental step. So, some of the definitions also we have learnt in our previous lecture like what is called as rock outcropping motion when a rock surface exposed to the ground level or ground surface that place of ground motion where it is known is known as rock outcropping motion then we have seen what is known as bedrock motion when the bedrock is below the thick soil deposit or a soil layer in that case at the top of the rock surface before the soil layer starts where the earthquake motion or seismic motion if it is known we call it as bedrock motion then another terminology we have seen free surface motion which is nothing but the ground motion which is known at the free ground surface of the soil layer that is known as free surface motion. Then we have discussed in the previous lecture that common situation can arise like this first situation can be say free surface motion is unknown whereas rock outcrop motion is known we need to find out this value how to do that we will see in the second common situation we have learnt let us say at free surface motion it is known we do not know at rock outcrop motion or we do not know the free surface motion at another soil site which is having the same common rock. So, how to obtain those things we have seen there are two basic approach to carry out the ground response analysis one is known as linear ground response analysis another is called non-linear ground response analysis depending on what type of behavior of the soil material we are considering for an earthquake load when we are considering the shear stress versus shear strain relationship of the material linear we call it a linear ground response analysis when we are considering it as non-linear we call it as non-linear ground response analysis within non-linear also we said there are two cases one is equivalent linear another is absolutely non-linear. So, we have seen we have discussed in this we can look at this. So, relationship of linear ground response analysis using G max G tan for non-linear ground response analysis and in between them is equivalent linear ground response analysis using G secant modulus and this is how the shear modulus maximum one is obviously the maximum greater than the secant shear modulus greater than the tangent shear modulus which we have also discussed in our so dynamic properties module. Then in the previous lecture we also learned what is the step for doing the linear ground response analysis first step is if we consider any known motion which we call as a input motion let us say bedrock motion is a known input motion we can represent it by Fourier series and using first Fourier series transform then we can use a multiplier which is known as transfer function transfer function is nothing but a multiplier to the input motion to get an output. That output can be let us say at ground surface when your bedrock motion is known again using the inverse of that first Fourier transform. So, the transfer function it determines how the each frequency in the bedrock motion is getting amplified or it is getting deamplified. So, that transfer function or multiplier decides whether the input motion increases that means amplification or decreases that is deamplification and the output value is coming out. How to obtain the transfer function it is mathematical evaluation also we started learning for the simplest condition of uniform soil layer when there is no layering of soil homogeneous soil of thickness h undamped condition no damping of soil property is considered it is though unrealistic but for the first derivation we have considered it. Then we have seen for one dimensional wave propagation what is the basic governing equation of motion for one dimension which we have discussed in the module on wave motion. In wave motion module we have considered this is the basic equation and if we have a harmonic base motion the solution or response of the displacement function can be expressed in this form. If displacement is expressed in this form then shear stress can be obtained in this pattern because shear strain we can get by differentiating this displacement function in terms of z and multiply with respect to the shear modulus we will get the shear stress. The condition boundary condition which is known to us that will help us to get this values of the constant. So, that boundary condition one which is known to us is at ground surface stresses should be 0. So, using that we got a and b should be equal. If a and b are equal we have seen the equation boils down to this form if it is. So, we can write it in this fashion and the transfer function is defined as the ratio of the displacement at ground surface to that at the bedrock level. So, that is how transfer function is represented here as the ratio of modulus of the displacement at ground surface by modulus of the displacement at bedrock level below a thickness of soil layer of h which on simplification we have seen it came out to be 1 by cosine of k h. So, with that we have seen uniform undamped soil on rigid rock they will follow this type of pattern that is if we follow the transfer function versus the k h plot it will follow this pattern putting different values of k h. And as this k h goes to 0 you can see k h this value goes to 0 the denominator goes to 0 and transfer function goes to infinity it should be k h goes to pi by 2 then the transfer function goes to infinity please correct it k h goes to pi by 2 at that case transfer function goes to infinity at k h equals to 0 transfer function is 1 at k h equals to 0 transfer function is 1 as we can see in this equation k h 0 means cos 0 means 1. So, transfer function is 1, but k h is pi by 2 means transfer function goes to infinity. So, natural frequencies we can write in this form omega n is n numbers of natural frequency we can get here v s times pi by 2 plus n pi n is a integer starting from 0 1 2 3 like that by h. So, fundamental period what is fundamental period it is nothing, but that period which corresponds to fundamental frequency fundamental natural frequency and what is fundamental natural frequency it is the least among the all natural frequency and that is omega 0 that is if we put n value equals to 0 we get that fundamental natural frequency omega 0 as pi v s by 2 h. So, by putting omega 0 as pi v s by 2 h the value of fundamental period we get at 4 h by v s that already we have used earlier in one of the module and also in soil dynamics course that this is the way how to obtain the fundamental period of any soil layer which is having a thickness of h and having a shear wave velocity value of v s. So, with that we completed in our previous lecture now let us start our today's lecture. Now, let us come to a more realistic case of damped soil that is instead of considering undamped soil profile let us now take damped soil layer, but still we are considering uniform or homogeneous soil layer of thickness h, but damped. So, how to obtain the transfer function for that type of soil let us see. So, how to handle that damping in that case we will have a complex shear modulus. How it is defined the complex shear modulus G star?  Remember this value of G we will get is G max because we are talking about linear ground response analysis. So, that can be expressed as what is v s? v s we can express as omega by k where k is a wave number. Now, in this case it is k star which is a complex wave number. So, k star by rearranging this equation we will get as rho omega square by G star under root of that fine. So, that is complex wave number.  This eta is nothing but the damping ratio fine. So, that is how we mentioned let us use it in the form of a complex number.  So, that is complex wave number compared to the wave number which we have discussed for the undamped case. Now, knowing this what we can do we can repeat the analysis like before what we have done for undamped case and the transfer function which defines as the same ratio at ground surface to at bedrock level. What will be the change u of 0 t remains same 2 a e to the power i omega t is not it because z becomes 0 there, but at depth h that is at bedrock level it becomes k star h instead of k h which on simplification we will get 1 by cos of k star h instead of k h what we got for undamped case. So, the only change is k become k star from undamped to damped case fine. So, with that now if we want to plot the variation of this transfer function what we will get this transfer function now is a function of not only the frequency, but it is a function of damping ratio also which is involved in the case star which is involved through this v s star we can express it like this. So, how we can express this transfer function that we have seen in the fundamentals or basics of vibration theory. If you recall the module on vibration theory or if you go through my other video lecture on soil dynamics where we have already discussed about dynamic magnification factor if you go through those lectures that module 2 of soil dynamics lecture or module 2 of this lecture you will find we can express this transfer function now in this format 1 by root over cosine square of k h plus eta k h whole square which if you want to express in terms of v s can be 1 by root over cosine square omega h by v s plus eta omega h by v s whole square. Now for different values of eta you can see in this picture now we have plotted these are the values of transfer function or amplification factor by the value k h why we mentioned that transfer function can also be called as amplification factor please note it down transfer function can be mentioned as amplification factor also because if we go back to the definition of it it is the ratio of displacement at ground surface to displacement at bedrock level that means how much it gets amplified that is why the transfer function itself gives you the value of amplification ratio that is why the amplification factor at different values of k h k h 0 means again it will become 1 this transfer function but at different values of eta that damping ratio the different peaks you will get at different values of k h that means it never goes to infinity for a positive value of eta it goes to infinity only if eta equals to 0 that is when there is no damping present fine. So, that is why the profile will become now like this and if the damping ratio of the material damping ratio of the soil layer increases from 5 percent to 20 percent through 10 percent there will be decrease in the peak values of this amplification factor at different values of k h can you see that it depends very much on the damping ratio of the soil material that what value of amplification you will get and also at what value of k h you are computing it that is what value of h by v s you are having for your particular site clear. So, for uniform damped soil on rigid block already we get the solution like this we can note that natural frequencies still exist because we know the as per the definition of natural frequency whether it is damped or undamped natural frequency remains same right. So, natural frequency still exist low natural frequencies they get strongly amplified what does it mean if we look at the natural frequencies lower values get strongly amplified than at the higher values higher values of k h obviously will give you higher values of omega n's am I right that means lower natural frequency get strongly amplified whereas, higher values of natural frequencies are weakly amplified. So, if you have a higher and higher natural frequency the amplification will be lesser. So, this is one very important observation one should made here because we have already discussed that earthquake can have different ranges of frequency when earthquake is coming and hitting at a particular site we have seen between 1 hertz to 2.5 hertz various frequencies it can have. So, if you have a lower range of earthquake frequencies then chances of getting that frequency amplified is more than if you have a higher frequency of earthquake. We will see later on few examples that wherever there are high frequency earthquake chances of amplification is lesser in that way it is helpful in a sense that frequency is large for the earthquake motion, but problem related to amplification or soft soil condition is lesser compared to if you have a low frequency earthquake that will have a more chance or more amplification whereas, you can see beyond a certain value of k h there is no amplification there is inverse of it that is de amplification there is instead of increasing it be above 1 it will be below 1 the transfer function will be less than 1 where that condition occurs at very high frequency it gets de amplified that means if you have any earthquake excitation frequency say very high value of the frequency range in that case you can probably expect that the ground surface motion the frequency what you are getting that will get de amplified whatever displacement you will get whatever acceleration you will get that will get de amplified or lesser than what you have at the bedrock level. So, which is good for a site where we want to construct some structure de amplification is always better because it is reducing the effect of earthquake when it comes to the ground surface or close to our structure compared to long depth or deep below the bedrock level. So, amplification strongly frequency dependent which is quite clear from this result amplification is very much dependent on this frequency fine. Now, let us come to a case where uniform undamped soil we are considering on a elastic rock on an elastic rock instead of a rigid rock that is now the soil condition and rock condition is something like this the soil condition is homogeneous soil uniform soil undamped the basic case first we are analyzing with a soil density rho s and soil shear modulus G s one dimensional wave propagation again we are considering and this is the limit of or axis system of U s and Z s whereas, for the rock elastic rock the rock density is rho r rock shear modulus is G r and this is the one dimensional wave propagation in the rock and the axis system or the coordinate system for the rock profile U r and Z r as shown in this picture. So, what will be the solution for soil layer and rock layer for any wave propagation and their displacement function the displacement function for soil profile will be something like this U s equal is a function of Z s and T will be C s e to the power i omega t minus k s star t plus d s e to the power i omega t plus k s star t whereas, for rock it will be in terms of Z r and T. So, corresponding coefficients can be let us say C r and D r which we need to find out from the boundary conditions. Now, in this case what boundary condition we need to use let us see U s at the value of Z s equals to h that is the soil layer displacement at depth h should be equal to the displacement at depth of 0 as far as rock layer is concerned because displacement compatibility has to be maintained clear. So, that means U s at this level and U r at this level should be equal that is what is mentioned over here. Another boundary condition we can write it like this stresses the shear stress at this level from soil and shear stress from this rock layer at this point should also be equal for stress compatibility. So, this is the condition with that uniform undamped soil on elastic rock maintaining the equilibrium and compatibility of displacement at the boundary the amplitude of the transfer function now can be written as this way f of omega now eta equals to 0 because we are considering undamped case. If it is damped then it will become non-zero as we have already discussed it can be expressed in this form 1 by root over cosine square k s h plus alpha z square sin square k s h where this alpha z is nothing but specific impedance ratio. Already we have learnt this parameter in the previous one of the previous module which is nothing but ratio of specific impedance of upper layer to the lower layer where from the wave is coming. So, the specific impedance ratio alpha z will be rho s by times V s that is shear wave velocity in soil star divided by rho r that is density of rock by V s r that is shear wave velocity in rock media star. So, if we plot how the transfer function will look like for different values of k h again for k h equals to 0 it should be 1 as we can see from this equation whatever be the value of this ratio alpha z but for other values of impedance ratio it will have some finite value even though the k h value reaches let us say pi by 2 it will not go to infinity it will go to infinity only if the impedance ratio is 0 otherwise if this term is non-zero still you will get some value. So, obviously you will get a finite value that is why depending on impedance ratio between the two layers that is soil layer and rock layer if impedance ratio increases your amplification decreases can you see that it is impedance ratio 0 means infinity if it is 0.1 peak is here if it is 0.5 peak is here. So, what will be the impedance ratio for a soil to rock? Obviously it will be less than 1 always because rock will have much higher value of specific impedance than soil. So, it is always less than 1 but you can see as the value reduces from 0 to 0.1 to 0.5 there is a significant decrease in the transfer function or the amplification ratio which is another important finding when we want to talk about the behavior of different soil layers over a rock layer. Now, for this once again we can see this uniform undamped soil on rock layer even with no soil damping that is remember we have not considered any soil damping we considered undamped soil media still resonance cannot occur still this resonance is not occurring we are getting some maximum value but still it is not going to infinity that is what it means why it is so? Because energy removed from soil layer by transmission into the rock in the form of radiation damping that is in the first case when we considered uniform undamped soil layer over a rigid rock we did not consider the radiation damping now when you are considering the rock layer elastic properties of the rock here you are considering that effect of radiation damping which helps to reduce this amplification or reduce this transfer function value. That means even if you do not consider the viscous damping or material damping of the soil layer there is some other damping which is radiation damping this we have mentioned earlier also in one of the module that we have two damping criteria one is material damping or viscous damping another is radiation damping. So, here you can see the influence of both in this case only we are showing the influence of radiation damping and when we will consider the damped soil we can see the influence of both radiation damping as well as viscous damping or material damping now for transfer function evaluation in a layered soil that is let us consider the most generalized case of layered soil and damped soil on an elastic rock. So, that type of layer what we can do when we are for doing the ground response analysis for that type of layered soil we will have different layer thickness of soil like h 1 h 2 like that up to say h n and h j is any j th layer h j plus 1 is any j plus 1 th layer and for individual layer the material properties which are necessary for our ground response analysis are like shear modulus variation damping and density then z we are measuring for each layer from the starting of that layer that means for layer 1 we are starting measuring z from the ground surface for layer 2 we are starting measuring z from the interface of layer 1 and layer 2 like that all the z have been shown over here. So, now how to estimate the transfer function for any layer say any j th layer we will look at the next slide. So, for any layer j the displacement function that is u j as a function of z j and t should be expressed like this because that solution for the displacement we have already seen in terms of coordinate and time. Now, for equilibrium what we can say that whatever be the displacement function equation for j th layer and j plus 1 th layer they must be compatible that means if I go back to this slide that is from the j th layer whatever displacement we are getting at this point and whatever displacement we are getting from this j plus 1 th layer at this point must be equal that means displacement compatibility has to be maintained and also equilibrium has to be maintained that is the stress condition also calculated for this j th layer at this depth of h j and the stress condition at j plus 1 th layer at this level of 0 at the starting point of this j plus 1 th layer should be equal. So, the equilibrium and the compatibility will give us these two relationships by using which we can get this constants. Now, let us look at further if we know the response at layer j then what will be known to us like a j and b j will be known to us how this response at layer j will be known because let us look at this slide once again. Suppose, what are the possibilities in which way we will know the response of j th layer one is if you consider the free boundary the stress condition should be known am I right. Another criteria is when the bedrock motion you are considering if you know the bedrock motion property from that bedrock motion acceleration time history you will get the displacement time history also. So, that will give another boundary value known. So, using those boundary values which are known what one can get one can get the other two unknowns for any other layer and it is a successive process like for one layer to another layer you can transfer this equation like you can write down suppose if you have n number of layers or n plus 1 number of layers for each layer you will have one equation that will lead you to n plus 1 equations and then starting from any of the two boundaries either the ground surface or at the bedrock motion which is known to you you can get the other intermediate layers this constant values is it clear. So, how we can do this exercise obviously for a multi-layer system this exercise need to be done using a computer program and the commonly used computer program to do this ground response analysis are SHEK SHAKE that is a very well known computer program which can do this ground response analysis for a layered soil like this. Another computer program is known as DIPSOIL we will come to the application of those software very soon when we will talk about the case studies. So, now solving for this unknowns what we can get we can express this a j plus 1 and b j plus 1 in terms of a j and b j which we said you should be known from one of the boundary conditions. Now or relating the coefficients to those at the ground surface as I have mentioned at ground surface this coefficient should be known expressed in this format. So, finally a transfer function relating the motion in layer i to the motion in layer j can be written in this form like earlier transfer function we were expressing f of omega and we said for damped layer it will be f of omega and eta that is a function of natural frequency and function of damping ratio of the material. Now if we want to generalize this transfer function from any layer i to any other layer j that is earlier transfer function definition we have used for subsequent to layer right layer 1 to 2 like that. But here we are referring to transfer function from layer i to j. So, in that case the equation can be written in this form a i omega plus b i omega by a j omega plus b j omega where these are individual displacement functions of that particular layer that is the definition of transfer function still remains same it is nothing but the ratio of the displacement between the two layers. So, it is a multiplier or the factor by which we need to multiply the known displacement to obtain the unknown displacement of another layer. So, if we know the motion at any layer we can use this transfer function to compute the corresponding motion at any other layer that is what it means. So, now let us see how this equivalent linear approach of this ground response analysis is carried out. So, the actual non-linear hysteretic stress strain behavior of a cyclically loaded soil can be approximated by its equivalent linear properties like as we have already discussed earlier that for defining the equivalent linear analysis the cyclically loaded soil we consider the stress strain behavior of this, this is the G max, this one is G sec and this one is G tan that we have already seen. So, now we are using this slope G secant modulus which gives us the equivalent linear approach. So, what it means that for a G value which is changing with respect to your chosen value of cyclic strain as you can see if this point is here G sec is this much. If I change this point to say gamma value of this one say this is gamma 1 and this is gamma 2 that is at two different cyclic strain level we are considering. What we can see here the G sec value will be this much. So, obviously the G sec 1 is higher than G sec 2 right is it clear. So, what way we can express this in the previous one of the earlier module on dynamic soil properties what we have discussed let us recap it that when we plot this cyclic shear strain and this ratio of G by G max in this case we actually talk about G sec by G max what we have seen it will be following some trend like this that we have mentioned as modulus reduction curve right where it will start this will obviously start at the value of 1 why 1 because at low cyclic shear strain obviously G sec will be nothing but G max if I look at here this is our G max. So, at very low strain this G sec and G max is nothing but same. So, that is why the ratio will be 1 at low cyclic shear strain and as the shear strain increases there will be a decrease in this ratio below 1 as you can see from this G max is always maximum G max is greater than this one G sec 1 greater than G sec 2. So, as we are increasing our gamma from this initial value to gamma 1 then gamma 2 obviously this ratio of G sec by G max is keep on decreasing and that curve will look like this this is modulus reduction curve. Similarly, the same behavior if I want to plot on this side the damping ratio this or sometimes we use this expression also eta if I want to plot the damping ratio it is having a reverse strain that means at low cyclic shear strain it will have low damping ratio and as the damping ratio increases or I should say as the cyclic shear strain increases damping ratio also increases clear. So, this we have also discussed earlier in our dynamic soil properties that module. So, now let us look at this slide over here which shows this equivalent linear property. So, when we are talking about this axis G it is basically not G it is the ratio of G by G max versus gamma. We will have different values of gamma starting from gamma 1 initial to different value gamma 2 gamma 3 gamma 4 wherever you want to do this analysis of ground response. Similarly, the damping ratio as I said it increases as in there is an increase in the cyclic shear strain. So, how to start this analysis now that is the question like we do not know at which value of cyclic shear strain this material property is actually existing. So, we have to find out that value of gamma 1 where all the results converge. What does it mean? It is a trial and error procedure in that computer program which it can do by starting with some initial strain. So, we always start with some initial value of strain very small value of strain you can select as a first step or sometimes we call it as a reference strain by considering that one can estimate the corresponding value of G sec and eta that is corresponding value of G and corresponding value of damping ratio for that particular strain level low strain level. So, now using that one need to find out determine the peak strain and effective strain also peak strain means what is the maximum value of cyclic strain the material or the soil can reach under a particular earthquake motion. So, that gamma max and this is an operator R gamma which will give you the effective strain gamma effective I will show that how we are applying it in the practical example or actual example. So, now when we are selecting this gamma 1 corresponding G value we are getting next trial what we need to do by using this initial values we got some result. Now by using those results of G and eta you will finally get another shear strain now that shear strain obviously will not match with your initial chosen shear strain. So, one is assumed shear strain another is obtained shear strain. So, what you need to do you need to go for trial and error procedure now in the next level you increase your shear strain gamma 2 and take that corresponding value of G and eta at gamma 2 level and do the repeat analysis until this value converges. So, that is what it says select properties based on the updated strain level gamma 2 in next level compute the response with the new properties and determine the resulting effective shear strain and finally wherever the results will converge that will give you the final effective strain and the final values of G and eta. So, it is an iterative procedure or trial and error procedure. So, this where it converges see repeat until the computed effective strains are consistent with the assumed effective stress. So, that final value where the results converge that is nothing but your gamma effective and that value of G and eta is our final value which is responsible for that particular ground response analysis subjected to a particular input motion. Remember it depends on your input motion also we will see that very soon in an example that is what about equivalent linear approach. Now, let us come to non-linear approach in non-linear approach what is the difference in this case you are no longer going to use that G secant you remember now you need to use the G tangent modulus. So, to do that first thing we should start with solve the wave equation incrementally that is in the relationship of this what we have already learnt here tau versus gamma relationship we have to study now incrementally this small small segments we have to study. So, that incrementally you have to solve the wave equation as shown over here like d tau by d z is equals to rho times d del 2 u by del t square equals to rho times del u del t based on the displacement function approximate partial derivatives you can express in this form that is incremental form that is we are going to now start doing this differential process of wave equation in numerical way by representing them in different numbers of segments that is i plus 1 h segment and i h segment over a small interval of delta z and delta t. So, then you can get the velocity function also expressed like this fine. Now, what are the steps let us see solve the wave equation incrementally to do that we have to start with the initial stiffness G max because remember this G max is nothing but it is also a tangent modulus it is called initial tangent modulus as we already learnt in our dynamic soil properties this G max is nothing but it is also a tangent but it is initial tangent. So, that is why our analysis will start from this initial point. So, from here where we have to take this G max clear. So, that is what we are doing over here start with initial stiffness G max then compute the response for small time step delta t that incremental time step compute the shear strain amplitude at end of each time step use that stress strain model to find G tan for next time step remember at next time step when we are getting another strain level now instead of taking G max it should follow the exact this variation of tau versus gamma incrementally right. So, we are now getting individual G tan for each individual increment. So, that is what use the stress strain model to find that G tan for next time step compute the shear strain amplitude at end of next time step and continue this step through time for entire input motion that is the entire input motion of earthquake whatever you are using for that entire time you divide it into number of small time step and repeat in the process for each time step. So, solve this wave equation incrementally what you will get finally the tau versus gamma relationship that is stress versus strain shear stress versus shear strain relationship you will get something like this that is from the incremental one that will give you non-linear responses simulated in incremental linear fashion that is piecewise small small small linear, but when you join them you are getting non-linear fashion. So, material damping is taken care of by the hysteretic response that hysteretic response if you take this obviously your material damping is well taken care of and approach requires good model for description of the soil stress strain behavior that is when you are doing this you need to use a proper soil model. Now, to do that there are two major soil models non-linear stress strain soil models which are in use for this ground response analysis one is known as cyclic non-linear model and another is called advanced constitutive model. Now, what is cyclic non-linear model? In cyclic non-linear model this is the reloading part this is the loading part you can see what are the things you require you require this backbone curve this is nothing, but the backbone curve. Now, unloading reloading rule must be followed here and pore pressure model can be modeled in this cyclic non-linear model that is known as from your suppose if you are carrying out in the laboratory cyclic triaxial test you will get for your soil this kind of behavior based on your number of loading and unloading right. So, that curve will give you nothing, but the backbone curve and loading unloading data also you will get that will also come along with the pore pressure model that model can be used as one of the stress strain model when you are starting your ground response analysis. So, that is cyclic non-linear model that is a simpler one. Now, a higher model is called the advanced constitutive model when you are using advanced constitutive model suppose if we have these three orthogonal axis direction sigma 1, sigma 2, sigma 3 plane individual principle strain plane we require the yield surface how the yield surface is getting formed in this constitutive model. Now, strain hardening rule should be known failure surface should be known and the flow rule should be known. So, these are the characteristics of any constitutive model and when you are doing the non-linear stress strain cyclic shear stress versus cyclic shear strain model you have to use this advanced constitutive model there are various advanced constitutive model which are available in this standard deep soil or shake software. Now, a comparative study between this cyclic non-linear model and advanced constitutive model as I said the advantage of cyclic non-linear model is it is relatively a simpler model because you can easily get that how the behavior of stress strain non-linearly based on your cyclic triaxial test or cyclic other lab test result and it is small number of parameters are involved in that model whereas, the disadvantages of this models are simplistic representation of the soil behavior. Why simplistic because here you are not aware about what flow rule is taken care of while stress hardening rule is taken care of all these issues and cannot capture the dilatancy effect that is another drawback of this cyclic non-linear model. Whereas, in advanced constitutive model advantages it can better represent the mechanics of the yield and the failure altogether, but the disadvantages obviously several parameters are involved in this advanced constitutive model and it is very difficult to calibrate to a particular soil profile using this advanced constitutive model. So, once you are going for advanced constitutive model in your ground response analysis obviously, it is expected to give a better result, but it will lead to a complex analysis of your ground response study. So, with this we have come to the end of today's lecture we will continue further in our next lecture.


girl To another video if you're new here, my name is Kara do not forget to like it coming in a subscribe So girl we are on our way to a Pilates class if y'all seen Lori Harvey at the Met They were like, how do you get your abs? And then she's like Pilates Pilates So y'all I've been really trying to be consistent with Pilates Because I really want some abs girl Yes, and I want to show y'all my workout outfit that I have on I may do another workout with my trainer But I don't know I'll say it's from a gym plus coffee I love these leggings y'all especially the pocket love these leggings cuz they suck you in where it needs to be you already see You see it. Yes, you see it and also the sports bra that I have on is from gym plus coffee as well I love the quality. I love that it's having the girls sit in nice and right because I don't want to be you know Jumping around y'all the quality is amazing Gym plus coffee is an Irish athleisure brand powered by the community to make life richer from workouts to weekends And everything in between gym plus coffee has you covered and y'all the best thing about this These leggings that I love is the pocket holder for my phone. It's been so perfect And I love that about these leggings like I know these items are gonna last me forever and ever and I'm a person I love quality over quantity and then also from gym plus coffee. I have this hoodie y'all The best hoodie quality ever. Oh my god. It's so soft I'll throw this on right now to go to Pilates But yeah, it's just this nice lavender color So you'll be able to get your own gym plus coffee as well All you need to do is click the link down below and you'll be able to use my code Kyra for 20% off on your first order of Gym plus coffee and I definitely recommend the swift leggings and the swift bra Because the coverage is amazing and also it just holds everything right in tight while you're working out in the gym So like I said, gym plus coffee has you covered I'm about to be making my way out the door because I don't want to be late and I want to get a machine so I'll see y'all at Pilates Hey girls, so I just got out of Salakor and Girl, the house was so intense, but I really liked that instructor though. She was really helping Yeah, y'all I'm in a minivan But um, no, she was really so good She was helping us and Salakor you were like slack because you don't know what you're doing But she would like come around and correct you and make sure you're doing it the correct way And I really like that and appreciate that So I'm definitely going to start doing classes with her and Aliyah came as well I'm going to my second workout right now with my trainer. He was out of town.  He's like, can we just like do abs or something? So yeah, I'm gonna act on that.  I was like No, they really be working out at that gym y'all after they have but today we had a different of them, so I'm about to get it in. Hopefully hopefully He'll take it easy on me cuz Anyways Let's get a crookie my way to Go to Seb laser. I have a laser hair removal appointment If you aren't new to my channel, you already know I get under arm laser Hair removal, I've been getting laser for like a good year now and it is a game changer I love it so much. It helps with hyperpigmentation Because it's men and women girls, you know, we have a little we tend to have a darker armpit other than others You know and I don't really like that I like my skin tone to just blend, you know what I'm saying So I really like that it helped with that a lot and also obviously the benefit of not having a lot of hair During like weeks, so I really love it It's really good and I was going to ideal image first But I've seen they had a set about here, which is really popular in like the LA area So I'm gonna try or also I was looking at laser away as well, but But I just booked like an individual session they didn't I haven't gone just my first time going there So they'll probably ask me do I want to like, you know, get a little package, which I don't mind Getting if they're good, you know, cuz sometimes these lasers y'all it can burn like laser hair removal The it's hurts.  It hurts just like my tattoo removal hurts anything with like a laser Hurts, okay, it really does. But anyways, I'm on my way there now and then also I'm gonna grab a smoothie after I'm done cuz When I came the last time I think it's my camera I came the last time there was a smoothie place next door and that smoothie was so good So and I haven't ate all day. So I want one Yes, so I'll probably check in with y'all once Get there. I'm excited cuz I'm due for a laser treatment. So, you know Gotta have these warm-paste Roy's a guy a guy Because I'm raising my hand and what love a guy I'm kidding Really? Oh, y'all are different cuz y'all have the zero Yes Y'all When I mother-wait, hold on. Let me see my camera clearly. That was probably the best laser experience I ever had because at my um, this is why it makes my tattoo removal so easy is Because ooh, I think they looking at me but anyway, I don't care but um But um, I think that The laser for my tattoo is so easy because they have this machine and it blows out Cold-ass air like negative degrees and I think it's below zero I think that's what the machine is called and I literally don't feel the laser and y'all when I tell you I was like, oh my god, I don't feel nothing and y'all I would dread going to my laser hair removal appointments because it hurts so fucking bad like literally I was sweat In my appointment, but that was a good experience. I was like, oh, hey And the girls in there were so nice. I was with Sylvia. She was so sweet and then she was like, um I don't know. She was just asking me questions.  I got shoes all I was like, hmm Maybe I might be back. But yeah, y'all said Elena y'all gotta come try them They got the the cold air on their machine and you don't even feel it. No wonder they're so popular because I'm sure like what's the hype about That's what the hype is about but anyway So I ended up getting a smoothie at the place next door. It's called. Um What is it called roots juices it's called roots juices.  I don't know. It was so good But I'm waiting on Jeremiah to get done with his white house session And I just have to go pick up some things from fix that just came in for me. So That's what we're about to go do And yeah, I'll probably take him with y'all after but Yeah, I'm so happy of that experience. That really made my day I gotta come shop with my boy Don't play with him. So we got the what are these quads? Okay, what what Jen I'll be the Rossi. Okay. We're not the age shame So yeah, I'm going to try these on y'all. I might get these So let's see what it's giving. Can you all this or just set it right here? It's giving very much classy and nasty at the same time Damn grumpy. I feel a little bit nasty. Yeah, I didn't 10 out of 10 For sure, you need them in every part I am selling thinking I'm all selling fee picks business is giving selling food here them russ mom These are huge Okay, we get it I know you're gonna have an address, but they what is it some morning?  I might be running my motherfucking tab You need to get these you need to get these y'all Anything y'all see me get is cuz Jeremiah calling me like Four pairs or Louie. He's a bad influence. I keep all four pairs of designer shoes. Wow. Why Louie?  Four pairs of designer shoes That's a lot Anyway, y'all it's real good On Saturday, it's two packs. My anxiety is very very But I must check out and I'm gonna show y'all everything that I got Prize you don't do that was first. Yeah, that's Well, so me and Jeremiah just ate at Dan Thomas Um, it was okay. I had ordered some asparagus asparagus is good and a Caesar salad. That was actually my first time eating there Um But he had got these egg rolls and also, um lobster Snappers, I think that's pretty cool. I don't know that was good though, but I'm stuffed. I really want some fro y'all y'all. It's raining like crazy outside But this is my favorite type of weather.  I was changing my GPS like location Girl that officer seemed on that damn phone I was like, oh officer. I'm just a little dear. I'm so sorry He was like, yeah, this is a um uh Hands-free state So he was just like welcome to Georgia Welcome to joe Uh, I just want to go home Y'all don't understand. I've been up since set six o'clock Are y'all listening to me? I've been up since six a.m on a saturday I'm tired No caffeine nothing No matcha today. No coffee Just straight bugs So anyways, I'm gonna talk to y'all once I am and I'm gonna show you everything that I got to I got some cute pieces. So I'm excited See how she talked to me No They heard you the first time Y'all so and mama wanted to come to our garden, you know, it ain't no really like good foods out here Like really good restaurants So she wants to come out garden So we're here y'all. I forgot how cold it is It was constant Y'all know it's 80 degrees in Atlanta.  Thank you Y'all look at my sister.   Oh, let's just go there. Okay I'm gonna wash my hands. I don't have any so Did you see here about them people dying at sandals and behind them? No Can't go there It's all together and separate It's going great. I can't wait till we redo my closet and find some chairs.  Can we all cooperate, please? I'm cool. I go My okay Okay, y'all What is this about? You and nobody's things that's not gonna be flying around is it because I don't have time to be sitting out. It's a puppy in here. It might be dead I was supposed to do this yesterday I don't like animals My in my house Action go act natural. Okay. Hey y'all. This is the lighting this okay, so This is our mother's day. Um post vlog We have an activity with angel And Kyra she's in town Because you're so fascinating. Yeah, I got time. Hey y'all welcome back to Kyra J's channel We are here doing a little Mother's Day activity. Okay. What do you have this amazon box that you need to show us because Yeah, like what's what's good? What's tea like show us now that's the character. Okay go So today we have in this box right here. Yeah, it's just a little so big That's the camera up here like Yeah, do a different angle. I'll hold it for you. You go Annoying Mom please So today I have in this box is something that I will Want me she's right there Okay, so in this box is something that is going to be dear to both of us Me and Kyra because in december we almost lost our mother, but we did it. They didn't almost lose her She was just fighting for her life I have to say it again because mama.  We'll do that later. Just let's do it. I'm the mama I make the rules. What do you tell her? She don't want to do it all three. She want to do it separate off camera Y'all I would rather do it all three and have one one all three But she needs something for her house Exactly all three of us go together. But we she has her We would get our individual. Yeah But why would y'all want to be individuals when y'all sisters that y'all need to be in each other house that we are a family So that's okay. We'll do that later. Yeah, so three hands need to be and do we have a three hand bucket That's why I said send these back and no You got do you understand what I'm saying? It should have been the three hands. So you have the three hands She has the three hands And I have the three hands because you will get our together forever But then she got her own hand with her mama and I got my own hand with my mama and then Collectively so you're gonna have to reorder three more buckets I know And those aren't have them in the I already wanted to do that I haven't been the my cart. Well, you can order that's a large one for the three hands And that is of the angles. That's okay. I don't know the directions You plus size size. I'm fluffy as hell. Let's play. Okay. What's what's the instructions? Where is the instructions at? Do we have to peel back? Probably let's see They don't get called a youtube video Let's just open one and see how that go Yeah, because we don't we don't want to waste too. Yeah, open it Let mama open it. Yeah, this is my almost there. Yeah Oh, she did you show live room just for you. Thank god Yeah, and they gotta be like 75 degrees because it's just warmer She's the reader three degrees We're in other protective material out and work is Oh Keep safe hands. So basically it's just clay stone And I'm probably gonna keep in my office and my mom's just gonna hold my And you just hold hands in the clay all the time, but she don't listen. I do listen pop that It wasn't feeling the vibe. So I'm consuming and me and my mom will have to catch a flight So we're just gonna have to do it next time when I come back in To town but um to see like Me be a back in here vlogging like this used to be my background when I used to wake up at Or or 2 a.m. 2 a.m. I used to wake up at 2 a.m. To get to work at 4 a.m It's crazy and I used to vlog It just brings back so many many breeze. Sorry. My mama's washing But I'm about to drink a green juice and my camera is dying and me and my mama have a flight So we'll probably see y'all once we get to the A Um, I can't wait to get back home. I don't know. I just love being home Now like I just don't see what's gonna feel like I just don't know any who but mother's day off your time with your mom And you know bonding with them and stuff like that because time was precious and you could not get time back So I'm doing a little stuff here this morning worked out Y'all my mama is already At it with the cleaning.  Y'all it's been A long two days or whatever But ever since we got back me and my mama She's been cleaning my house up to her standards. So because she's like You know, some people just can't work in environments where they're not comfortable or feel First of all, my house is clean, but Working on that area over there Like my dining area she wanted to like make sure it was clean up to her standards before You know, we get started on the projects Because we are well, we yeah, we are Painting canvases to go over the coffee table. My chairs are coming And it's just gonna be a whole transformation in that area, which I'm so excited to see But yesterday y'all I went to target and I um got a few items that I wanted to show you Before I put my items away and I did not know target had like a new line of body washes So I got two of them. They're supposed to be like a necessary do So this is what they are called Nitrium, I think that's how you say it nitrium, so I got the Vitamin C wash obviously vitamin C brightens and even skin tone And it says gently cleanses exfoliate and brightens for radiant looking skin So I got this to see but I really don't care for the smell um That's why honestly normally I use two body washes anyways For skincare benefits and then also one for like smell good Yeah, like This doesn't give me like oh I want to use this for scent wise It's giving me just for the benefits for my skin This one as well. It really doesn't have a scent like I said And then I also got some more mighty patches because I was running out love these if you're having A little breakout put these over them.  I don't ever pick my face. So I just like to use these to you know Get rid of that bump right away and then also I got this white tea and aloe bath bomb Just to see what it's giving and then I got some more if you're an og follower and you know Like my skincare routine from like a while back when I showed y'all like the steps I used um To transform my skin. I was using the pixie glow tonic glycolic acid exfoliating toner And I seen this girl on tiktok say that she used glycolic acid, but she doesn't use it with a pad She just presses it in in her pores and I was like, oh my god. Let me try that But I wanted to go back to my og um product, which was the pixie so I got this Again, because I really want my skin to be at its best this summer And I really want to perfect my nighttime skincare routine because I do want to give you all that video Because I feel like my skin is thriving.  I'm just like wow my skin looks So good. So but yeah, I wanted to add this back into The mix and then also I got this oil control on the go I'm definitely going to keep this in my purse because I do not want to be looking like a grease monkey um this summer so Yeah, got this and then also I got a new charger piece Because I do have a one charger that I want just to keep in my purse And I was like, let me just get a new charger for my house. So So But I do want to get a A charger and I got the long one. I do want to get like a charger like a station for on top of my um night stand to Just put my phone in like my AirPods and stuff like that right on top. So I know where it's at And then I got two feet mask y'all. I've been really into like feet mask and like perfect to my feet I didn't know so many people were into um Like fee content because I uploaded my uh my shoes with my toes on instagram and everyone was like, oh my god Your toes are like so cute. What color is that that are I so I want to start posting like fee content Like when I go get my feet done and stuff like that So I haven't got my feet done yet So but I want to do these feet mask first and then I want to do feel like me going to get my feet done Because I get so many people asking what color do I get and stuff like that? So I'm going to show that on camera. And then I did get the mighty patch. Um, the longer ones just in case if I have like a breakout Um, like an area with multiple breakouts. I can just throw it on there and you know And then lastly, I just got some nail polish remover because my mama asked me to get this so Oh, and then I got some more of the scrub daddy sponges Yeah, and then I just got like water and like cleaning supplies and stuff like that So y'all don't need to see that But anyways, a lot of y'all I have to ask me um from my taxes video. How do I upload receipts? um On my card So I'm about to show y'all right now because I'm about to do a few of them And then I'm going to get this room a little picked up because I'm about to Um transform this room this week this week coming up because my chair My new chair is coming on monday, which I'm super excited about and girl It's just going to be a whole new vibe up in here and I just can't wait. So Yeah, so anyways, so I used my business card with um To make those target purchases so um So basically the app is on my phone hold on and Y'all this so easy because y'all know receipts tend to fade And I still keep them and I'm gonna organize them a little bit Because my mom brought back a portfolio thing Or whatever. Um, so I'll just go to the account that I use the card that I use So it's gonna say on their digital receipts I don't really want to show y'all without showing the numbers But anyways, well, y'all can see this. I guess it doesn't matter I'm gonna say add receipt right there add receipt. So I'm just gonna click it So I'm just gonna click it in the camera. Oh god But anyways, the bad camera is on so it's looking for a receipt. So What I do is Basically take the picture of the receipt Looking for a receipt. It can't automatically do it or you can just press the button on there Okay, take a picture Capturing hold still Yeah, so It has the receipt on there So and then it'll have all the items on there As well, which is pretty neat like that red blonde thing I just showed you in the price and like other items on there Which is nice. I don't y'all technology these days is crazy Like I'm not gonna show y'all this part, but I'm gonna go to the card in my transactions and then I'm gonna link receipt to The but it's pending so when my um Transactions are pending I can't attach the receipt because it won't even let me click on the transaction But as long as this in there It's good. So Yeah, but anyways, I have a few receipts I need to upload so I'm about to do that right now And then this one is already done So this needs to go over there And then yeah, so that's what I'm just about to do is just pick up this room And then me mama have like this appointment to go get our body scanned to see where our fat is stored Girl who wants to know that but I mean, I guess that's important to know so you can know what to Work out in the gym, you know But this is English trash and I'm about to pick up our room It I'll probably talk to y'all once we head out and do stuff And then we're going to stop and get the canvases today as well too because we took measurements Yesterday, and then I got to show y'all um a little some more home updates Um Once I get out the shower Yeah, so my mama wanted to come Get her fat red like I told y'all earlier, but anyway, I'm gonna keep y'all updated on what happens with Of these guards and stuff like Anyway Okay, so once you feet this direction on your back center it along this line as best you can okay All right Yeah, so I'm not gonna get mine stone because we were running late But um, I'm gonna probably make it on Monday or some other day to schedule an appointment But basically it's just an x-ray to see where your fat is coming from So Okay Press your arms over your chest for me. Will you now I'm gonna reach underneath you arch back to me Thank you so much. All right back down comes in just like we have This I know it's too hard. I do it too. I use a strap all the time. Go ahead and relax them all the way down If not, I'll have to pull my fingers off your hips if you can do it. Okay. Yeah I'm so wide Just a little bit. Yes, just a little wide Now that's right No, no, no, it's your it's your hips. It's my hip. Yeah your hips. So what happens is They said how they didn't say why? I know. Well, you can't start to measure yourself when you lay down. You know what I'm saying? All right What it does is it measures it mirrors one arm to the other, okay We'll get we'll get the other arm in some way. So do me a favor Just go ahead and put this arm here and speak to you towards me just about that much Yep, hold on Now I am going to pull this arm in though So This is this is what the fit 3d is Kira It makes a three dimension. Oh, don't take a picture of me. Oh, I'm not I have that here. Okay. Okay. I've got hair You take pictures of those little guys. So this is so basically it's skinnier fat, correct What's that? It's basically an x-ray of trying to find out where your fat is. This is the x-ray of your fat That one is external body measurements.  Even for a bra or something. No moving I'm moving miss angela But it takes about 500 different measurements of you. So it's super accurate And Ultimately based on those measurements It creates a three-dimensional avatar that will go to your email. Okay, but it also I had these printed But it creates a super cool avatar view So what I say it's the best selfie you'll ever get Oh, so it's the oh, it's the avatar of your body. Yes. It's really neat. Okay, but this This is different What the way I explain the difference is this is the inside. That's the outside. So what this is going to get Miss angela is your total body composition. So everybody wants to know their body fat percentage, right? Right. What is that?  So we're going to get your fat and pounds lean tissue Bone bone density and visceral fat. So let me back up and explain Your fat's pretty self-explanatory, right? We can usually pinch that so right beneath the surface, right? under our skin Lean tissue is anything that's not fat or bone.  It's not a true bone density scan Okay, so it's a little elevated from a normal bone density scan If you need to have a sample, how old are you by the way? I think D F is where you are And the last thing we get and probably one of the most important metrics we get out of this Is visceral fat. Okay.  I know I've got a lot. You do? Some of that could be sub-PT. So can you pinch it? Yeah. Yeah, if you can pinch it, it's not visceral So visceral fat's behind your abdominal wall. You can't pinch it But you can see it. You've seen guys with the big old beer bellies. Yeah, okay. That's visceral. That's very hard It's there is deep in there and it's correlated with cardiovascular metabolic disease. We do not want that Okay, so it's metabolically active and it's not good Not good fat, but if you can pinch it If you pinch that fat, that's not pretty, but it's not going to kill you. Okay, so Let's look we'll see how it breaks down. I'm going to get up on this We don't have to have our feet exactly on these just wherever it'll get your weight and your weight distribution It's getting posture analysis.  Shoulders back, right? You got it Once you're here Straight and relax, you're going to push these white buttons in. That's after you pull them up Now it'll start to turn table moving This locks the arms and it starts to turn table. Once it starts moving It needs you to be a statue. Okay. Don't move. Am I still holding these? Yes, you have to hold them and hold the button while you're doing it. Yep. Yep And it takes literally 30 seconds. Okay. Now you can be in here with her because I'm going to give you privacy because So do you want to tell the girls about your dexaphate experience? Yeah, she's hangry right now. We're on our way to go get some food Um, but even though the lady just said The lady She told my mama she can have absolutely no sugar. So what are you doing? Um, so she can't have sugar anymore. Um, what else? She said she needed to start lifting weights. No cardio because it's not helping you boo. Um, what else did she say? She doesn't want to talk to y'all because I'm letting it I'm letting it marinate It's hungry It's she's letting it marinate that she has to really change her lifestyle So she can live forever It's just that even if right now they said I'm living to 80. That's still long.  We was late because of you sweetie. No, it was late. My mama do not know how to drive y'all She is terrible Anyways, we're on our way to this is like my second time coming here There's this uh salad bar. It's like a salad bar. It's called chop. It's so good Y'all gonna see our salad bar after you go to this dex of it. Yeah, she was trying to she's like I don't know if I want to sell it girl. Just cancel that payment. I told you you can't eat Okay, so Um, but yeah, this is salad bar out here and then what are y'all it's so good And then when I went in there the girls were so helpful in there.  You can only have water um We're on our way there and oh, yeah I'll check them back. We try once we get there Michael's for the win so we need to But let's do it y'all. So it's a don't be vlogging in my car.   Girl?  Oh, that's my alarm. Yeah Vlogs know your birth control.  I'm not turning back You don't have to I can just take you when I get back on As long as I take you But anyways, we are on our way to the garden room. That's what Jeremiah wanted to go eat at So that's what we're going y'all. I put this amazon ponytail in real quick. I haven't done a little faux ponytail Disrespectful I haven't done a faux ponytail. Do we do but I'll check them trial once I get there Y'all, I missed the pilates class this morning. There was no way I was making it At 6 a.m. But this morning me and my mom are getting away. It's my camera. That's better Me and my mom are gonna be on our way to get finished yet getting everything for the canvases We have them already. They're in the car and then um, Yeah, we just got to go get like the paint and then like the The protector or whatever so we'll be able to do our arts and crafts and don't make a mess and then also, um We're going to be stopping at this furniture store this morning, but I'm about to pour me up some green juice I'm about to pour me some of the suja Organic grains Anyways, y'all, I'm just going to finish drinking this and then I'll check in with y'all once we start wintering our earrings How are you all today? Good This cute What's the outside? That is cute. It's cute. I'm trying to go These chairs is cute But they're not comfortable Oh, look at those chairs The ones I've seen somebody with those Somebody got them in a house somebody um Some these are for outside so they don't move. I know but somebody got these in the house. That's cute You don't like that What why I don't It's like an off-white Don't even go with nothing That's kind of cute But it's like cream All these chairs is cute The outside look All the Toyota What's that called? That's so though. I know I think it's a dresser though, but I guess you can make it in here You know I wouldn't put nothing in here. I mean I don't know You like this No videos Just to see No I'd rather have something textured than But it's like wire I don't know If this is more bronzy than gold Yeah, that's too gold Yeah, there's too cheesy gold I don't like Like cheap though I mean, this is the same thing It's just right here Oh, that's connected see And this is a Oh You know what I'm saying? Yeah I'm gonna go with you You this is kind of cute so I don't know No Let's not go on with the bottle Oh I like this but I don't like the The glass because it makes it too glammy. Yeah, so we're not I think I For sure. I think you like the texture of it. Yeah, I like the texture But I for sure like that the uh the cream one, but you said you can get it in black Y'all so now we're at Lowe's I'm picking out trim for the canvas because it's going to be like the actual Like if you bought like a canvas from the store, you know, how they have like the trim wrapping around The outside so we are Lowe's putting that out now Other side I saw you boys I feel so refreshed. Where is she at? Yeah, I'm picking out now and then also these are the colors. We're gonna paint the The canvas These colors with a hint of black and y'all won't probably see like the whole Um painting um in this vlog. It'll probably be Oh, there she go Where's the trim? Another one another time to But y'all so we just got home and we stopped at Home Depot and got the trim So basically this was gonna look like because y'all know my Um dining table is like dark wood So we decided to go with the lighter wood. So it's not too like What's it called?  She don't want me to do one and she do one. I'm like, do you want to see who's is better? She's like no No, we don't have time for that But um, we're gonna lose no competition. We're gonna Yeah, it's not a competition like it's not a competition when it comes to my house. Okay. I need everything perfect No, it's not a competition because there is none. I will win Anyway, no, it's not a competition because I'm not competing That's not a competition. We're not competing. It needs to be right the first time period So we are going to be We're going to be stifling this and also gluing the wood to the canvas What I'm just excited Because this was so plain And now We're gonna have some artwork Done by me. Okay. I get it So anyway, that's gonna charge and we're gonna do this. So Yeah, hey girl. So it is the next day and yesterday y'all I was gonna follow with y'all so yesterday was um, kind of a fail because We went to go get the trim For the canvas is right over there um As y'all seen before But the trim is too short And it's off and it's not given the look that we want to go for So this will probably continue. Um Until the next vlog because um, I'm ending this vlog off here um So yeah, y'all gonna have to stay tuned for more home updates in that area In that the next vlog, but I'm super excited and also be looking out for my closets Uh redo because my chair Comes tomorrow. So I want to do that in all in one day really because it's really just Me re-ranging things adding things a new rug a new chair um No lights and it's just gonna be a whole different look to it. So Yeah, I want to do that all in one day though Well, I'm gonna try Like I said, we always run into difficult things or whatever, but I'm so proud of my skin like My skin always heals so fast because of the products I use but Soon I'm gonna do like a nighttime routine skincare routine soon until I perfect it. I don't know if I told y'all that but Oh, yeah, I want to do a daytime skincare routine soon So y'all can look Glowy and healthy for the summertime But anyways, that is it for this vlog. I'm just ending it off I just wanted to update y'all. My hair is a mess. Everything's a mess. I need to Do a whole Sunday reset Like lit this week the week that just passed y'all was Up a week for me Like I talk about being depressed and down all the time, but this was probably the lowest I ever been like It's just oh my god y'all like But this week coming up. I just can't I can't Stay there. You know, I gotta take the next the steps that I need to to get out of it because I can't let it get in the way of My life and stuff like that. I just need to Get it together. So today I really want to take the time to really focus on Getting back on track for the new week. So I just want to end this video off because Yeah, I want to just start the week off fresh. So Yeah, girl, stay tuned for the home updates.


I'm kind of stressed out right now because I just made a break. Oh, the tea is nice. Hey guys, so it is currently 5, 10 p.m. I'm currently on the way to the gym. I haven't gone in like a week just because I feel like I've just been so behind and busy that I just haven't found time to go. I'm gonna go with Julia and we're gonna get back at it. We gotta get back on a routine just because it's so easy to get out of a freaking routine. I feel like it takes so much effort to make a routine and get a routine established takes so much effort but it's just so easy to step out of that routine. Like you just have to keep consistent and not get out of the routine even though it's so easy to. Anyway, so I'm just on the way. I can't wait to get back into it. Gotta get my motivation back for the gym because I go honestly sometimes in waves where like I'm super motivated. I'll go all the time and then like that motivation will just leave then I gotta find it back and sometimes I just have to force myself to go and then I get motivated that way. Yeah, so we're on the way and it's beautiful weather right now and we're going to Juliana's house tonight to just chill and yeah I'm just gonna be vlogging the weekend so. Hey guys, so I finished up at the gym, went home, ate dinner, showered and now we're back here. I'm on the way to Juliana's house right now and I'm just picking up Julia. The gym is so nice now because you don't need a book of appointments. You don't need to wear a mask. You can see as long as you want. So we're just taking our time because we haven't gotten to take our time during a workout in so long. Well, the sun is so pretty. We just had an hour window before so it was so nice that you just had like unlimited time and it's so nice just being able to go whenever because sometimes I just don't know what my day is gonna look like or what time I'm gonna feel like necessarily going to the gym. So it's nice that you can just literally go whenever. But yeah, so we're just on the way to Juliana's. We're gonna hang out there for a bit. I'm not gonna drink because first of all I'm driving and second of all I just need a break because I feel like I've just been partying every weekend and it kind of gets exhausting. But yeah, I think I'm passing for this weekend. Yeah, we'll see. I'm gonna be vlogging this weekend like I said. Hey guys, so it is Saturday and we just went to the beach. My hair is literally disgusting. I'm just about to take a shower. I'm not gonna wash my hair though because I think I might wash it tomorrow just because I want my hair to be fresh for the week because I have like the background movie gig. So I want like fresh hair for that. I want my hair to look somewhat decent. So I'm just waiting extra time to wash my hair and it just feels so gross but it's fine. But yeah, I'm just gonna shower and wash this disgusting sand off of me and my hair is so gross. Hey guys, what is up? So it is currently 1112 and my eyelash appointment is in three minutes. I just got here. I'm kind of stressed out today because I got up in the morning. I was editing and I have this video that's going up today but it's so freaking long. Like it's over 30 minutes, the raw footage. So it's taking me forever to edit.   I need to make the thumbnail, finish the video and I just like don't have any pictures for the thumbnail. Like when I was making this video, I didn't have like the thumbnail in mind. Like I wasn't even thinking of it and I wasn't even taking pictures. Like I don't know what I was thinking. So I need to take pictures as well for the thumbnail which if the thumbnail was done or pictures were taken, I wouldn't be as stressed out. But it's just because like I need to literally make the thumbnail from scratch. I have nothing for it yet. I need to finish editing the video, upload it and get it done by three o'clock and I'm probably not going to be home until past one. So kind of stressed out right now but you know what? We're just going to go relax and get my lashes done and we're going to figure it out when I get back. My lashes are probably going to be done in like it's only like a fill. So it's probably going to be just until like 12 30. So just like over an hour maybe even less than that. I'm not sure. I hope so. But yeah, you know what? I'm just not going to stress too much. I'm just going to I'm just grounding myself right now because I know everything happens for a reason. Everything that's going to work out the way it's supposed to. And you know when you're in a stressful situation, that's what you got to have your mentality. Like you just got to know that things are going to work out and however they work out. That's how they were supposed to be working out for you if that makes sense. So getting stressed over something, it's just going to do your body harm and it's not going to do your body any good. So if you can help that and help your body not be stressed, then that's a lot healthier for you and good for the long term. Okay, I'm going to text her that I'm here and walk out. So I'll see you guys after I'm done. Got to put my mask on. We're good to go. Let's go. Okay guys, I just got my fail and I don't have time to do the errands because it's already 12 30. So I'm going to zip home so I can get my video edited and everything up by three o'clock and I still need to eat. So I'm thinking of maybe just like, yeah, I was going to say I'm maybe picking up food but then that's just going to be me eating really shitty. So maybe I'll just go home. I just like make toast quickly, just to put something in my stomach and then go from there. But maybe I'll just pick up a coffee or something because I need the energy. So let's go home. I'll see you guys at home. It's going to be a hectic couple hours. So it's getting sweet. Okay, so I'm currently at Tim Hortons and I want to get an iced coffee just because we don't have any cold brew left at home and I don't think we have any of the milk that I like. So I'm just going to pick a coffee up from Tim's. I need to get to work right away when I get home. So I need to be speedy. I usually do like to drink water before I have any sort of substance. So I think when I get home I'll just like chug water. I mean, it doesn't really matter. Anyways. Hi, can I please get a medium caramel iced coffee with almond milk? Okay, thank you. Joel wanted to decaf but I never knew that they didn't do decaf iced coffees. That's very interesting. I guess you learn something new every day. Thank you so much. Thanks you too. Got the good. Sometimes like they don't put enough caramel in it. Like last time that I got it from here, they literally like it didn't even taste like they put caramel in it. And so I feel like sometimes they just don't put caramel in it. And but the thing is, is like one time I asked her extra caramel, it was way too sweet. Like it just depends. I guess who's making it and how they're making it that day. But the thing is, is that when you go to Starbucks, you know, like it's always consistent when you order a drink every time it's going to taste the same. But with Tim Hortons, it's like a hit or miss. Honestly, it really is a hit or miss. Hey guys, so it's currently 4.18. I was a little stressed out. Not going to lie because when I got home, my laptop or it wasn't my laptop, it was the hard drive that I added off of was being so slow. And so I didn't get the video up until 3.45. So I literally just posted it like half an hour ago. And it's the first time that I haven't posted at 3 o'clock in six, seven months now. And that's what made me feel so like uneasy. But I just have to realize that like it's fine. Like that's fine.  And at least I got the video up. I'm so happy that I did. And things were just being a little extra slow, kind of frustrating, but it's fine. I'm good. I've recentered myself, got the video up, and there's just no need to worry. Nothing bad happened and no one got hurt. My video was just 45 minutes late, which is literally not a big deal whatsoever. Anyways, cheers to that. Literally have like drinking no water today. Night's bachelor at night. I'm going to go watch, potentially watch the sunset. I don't know if we're doing that anymore. And I don't know. I just feel like I was literally all over the place today because I was just like hardcore working on the video. And I was just so under pressure, but it's fine. So later today though, the only thing I have to do is so I have a background casting call for Wednesday and Thursday and it's Monday today. I just got like the outfit info. So I need to make six outfits to bring. I just want to be prepared for Wednesday and just like get prepared for that. And yeah. Okay guys. So it is currently five o'clock and we're just on the way to meet up with Juliana because we're going to go to the mall. I wanted to go to the mall like while I was already in that direction when I was getting my eyelashes done. But I did not have time, which you guys know. So making the trip out again now because I need to return something. I don't know if I mentioned that, but I need to return something. And yeah, I kind of want to go to this little like sunset, cute little spot afterwards. And then both like before we watch the bachelorette. Also, I need to eat more today. I literally probably only put like 500 calories in my body and it's five o'clock because I only had like a lunch because I was literally just stressing out a little bit and I just wasn't eating. So I need to get some food consumption in me and I think I'll feel better. Today has just felt like a chaotic day in my mind. And usually that never happens. Usually I'm very like nonchalant.  But today I was feeling the stressed out vibes and they're still lingering. So I need to get them out of my head. Okay, we're perfume testing. Oh, we'll spray that back. Okay, okay. It's between the teas and seduction right now. No, it's between teas and original bombs. Okay, give me a minute to stimulate the senses. Stimulating. Let me smell something.  Yeah, I know. I know, but anything. Oh, yeah, I know. Oh, the bombshell is stronger. But it's like, it's really nice. But the teas are really nice every day. Like it would never overpower you. Ever. Oh, this one's $90. Wait, let me smell the teas. Yeah, but look how big it is. You're never going to run out of tea. Oh, Joe has it on a cart. Which one's the teas? That one. This one's the teas. Oh, the teas is nice. Smell the bombshell. Oh, this one smells really good too. This one smells better, but this one's more smelly. It's just more of an every day. Maybe I need to... Oh, it smells really good on the tea. It's the last verdict. I love the tea. Oh, it's a huge one. It's probably the most popular one. Right, the ice cream place. We're just online. And then I'm so cool. I cannot wait to have dessert. I'm so craving dessert. It's not that grand, because I already know you're going to say. Okay, so fun fact of the day, when me and Joel first started dating, we carved our name in one of this, like this wood thing, because everyone carved their initials, and we carved our initials, but it was like so long ago. I think we did it like four years ago. So we can't find it, and it's definitely been like carved over. It's carved. It's been too long. We tried to find the last time, and we couldn't, so. So we're currently going to re-carve our initials, since we don't know where the last ones went. There's like nothing over there. M plus J, not J plus one. You know, just carving in our initials with the nice sea breeze going on, the waves crashing to shore. It's a romantic, helpful honeymoon.  We got to go. Yeah, and we're going to watch The Bachelorette. Today's hometowns, right? No, today's Mentel. There's like a little bit before, and then Mentel. Oh, I wanted this. No, this is where all the drama comes in. I love it. It's good, but it's slightly, but at the same time, it's a good thing. Yeah, it's like, yeah. You just get to see all the guys back again, which is like. Yeah, which is me. But at least they're, I think they're giving us a little something before they start the Mentel. But yeah, I'm sort of with Mike. Yeah. That was good timing. Hi guys, we're in Julia's closet. We've never been in here before. Whoa. Can you see, are you? And so for my casting call tomorrow and Thursday, they told me to bring three business outfits and three casual outfits. Oh, gosh.  Or ignore the tag.  I wear it with a tag on.  It gets past the return date by now. Four years. I just haven't ripped it off. It's cute. Yeah, it's nice. It's really cute. Oh, it's cute. Oh my God. It's really cute. I know, right? You feel like... Like I feel like I'm a business woman. Like a lawyer. It's great. Lawyer who? This is actually really cute, which is like not that businessy, but for you. Oh, those can be good. Yeah. Those businessy. I can't remember. Like what makes a pants business? I have also these other pants. There's just like no occasion that I ever needed business stuff for, but I feel like dressing up businessy is fun. Like you feel like a lawyer. I want to get like more like different blazers though, because I couldn't even dress up like that. With a jean shorts and a tobbling throw. Like a pastel. Yeah, or a like fun color blazer on top. It just looks cute. I saw this one at Forever 21 and it was like a pastel green. And it was so cute. That would be so... Oh my God, just after... Oh, like giving this? Yes. Oh my God. With like kitten heels. Oh, so cool. Oh my God. Oh, I forgot that you had these. She bought those. I had them at the beginning of quarantine. Yeah, at the beginning of quarantine. And I haven't worn them yet. Those are so freaking cute. And I need an event to wear them too. Those are so cute. I honestly, I really want to get kitten heels. They're really cute. And they're just in style now. And I feel like they're just good to wear with whatever and I don't even have one there.  Yes. They're like so cute. And they're so like jeans. Yeah, oh my God. I just like dress this thing up a bit. You have to go shoes, shoes, shopping. I need shoes. Like sandals shoes. Like I have a kind of like high heels. I need like wearable shoes. Just like cash-sandals. Yeah. Yeah, because you do have a lot of shoes.