Basement Wall Seismic Drift

[WR1]

What are the code requirements for drift of a basement wall in seismic zone?

 

Lateral earth pressure produces elastic deflections whereas seismic generate inelastic sway (after multiplying elastic by Cd/I in ASCE/IBC). Now how to combine both? and by what combination?

[UmarMakhzumi]

Rana,

 

The basement should be moving with the ground. The argument can be justified as code requires us to design structures by calculating time period of structure using the height above grade only. Depending upon what kind structure you are designing with a basement, your basement may act merely more than a basement (Backstay Effect)

 

http://www.sepakistan.com/topic/1448-location-of-base-for-seismic-design/

http://www.sepakistan.com/topic/1480-diaphragm-flexibility/?hl=backstay

 

Thanks.

[WR1]

Moving with the ground? So what is the maximum limit on that?

[UmarMakhzumi]

You cant have a limit, because basement is your base. Even if you want to check the same interstory drift limits for say 20 story under ground basement, it would always satisfy because of extensive walls all around. You can do a thought experiment to confirm this.

Thanks.

[WR1]

i dont have walls all around. I am designing a big building separated by lot of expansions joints. And so the wall is one just one side of the building part. 

[Muhammad Imran Zafar]

I would suggest you to model soil stiffness on sides of your basement wall. You would not find considerable drift in your walls

[UmarMakhzumi]

i dont have walls all around. I am designing a big building separated by lot of expansions joints. And so the wall is one just one side of the building part.

Then its a normal building and same rules to apply and you are very likely to have some kind of irregularity because of un-symmetric framing.

[Badar (BAZ)]

Lateral earth pressure produces elastic deflections whereas seismic generate inelastic sway (after multiplying elastic by Cd/I in ASCE/IBC). Now how to combine both? and by what combination?

 

 Lateral earth pressure will lead to out of plane deflection of wall, which will be acting as plate to this particular loading. So, they can't be combined any way.

 Lateral earth pressure can also also be considered as point load on beam column joint, if you want to consider its affect in the direction of seismic forces. In that    case, you can add elastic drift due to earthpressure (acting as  point load at one end of frame) to the inelastic drift at that level to seismic forces.

 

But if you have satisfied drift requirements in upper stories, then there can't be a drift-related problem at basement level. There should no problem relating to drift at basement level (even if there is only one wall) even if you have not satisfied the requirement at upper levels.

There are no separate reuirements for basement level, same drift limits apply.

 

You should be looking to control torsion at the basement level as you have mentioned that the distribution of wall is unsymmetrical due to presence of seismic-joints.

[WR1]

1) Yes! I am combining inelastic seismic drift with elastic earth pressure deflection at beam column joint. 

 

2) I still did not get why there would not be any problem in basement for drift. I have multi-basements. Do you mean there would not be excessive drift between basement stories? I am getting it and it is more than allowable seismic drifts....guidance needed pls!

[UmarMakhzumi]

Regarding 2), your understanding is correct that there wouldn't be excessive drift b/w basement stories, however real challenge that I see would be to design diaphragm for the seismic force transfer at podium or ground level.

Elastic earth pressure deflection at beam colum joint should be very small to negligible if you have slabs at that level. Those supports are infinitley rigid as your slabs at joint level wont let the joint move(as slabs bending would be in-plane). The use of static coefficient for lateral earth pressure to design basements supports(where slabs are present at joints) supports my scribble. Just a thought.

Thanks.

[UmarMakhzumi]

If you are still getting higher drift b/w basement stories,, you should share your framing with base shear distribution along height. I am positive that would be helpful to discussion.

Thanks.

[Badar (BAZ)]

Elastic earth pressure deflection at beam colum joint should be very small to negligible if you have slabs at that level. Those supports are infinitley rigid as your slabs at joint level wont let the joint move(as slabs bending would be in-plane). The use of static coefficient for lateral earth pressure to design basements supports(where slabs are present at joints) supports my scribble. Just a thought.

Makhzomi! you are not keeping the load path in mind. Here is how it works (as a reminder): Slab , which is acting as diaphragm for seismic loads, distributes inertial forces to vertical members, these forces are usually taken as point loads on beam-column joint, and then they are transferred to foundation through vertical element of force-resisting system. I am relating both horizontal forces (inertial and earth pressure) because both have similar load paths, except for diaphragm. Foundation of vertical elements will support horizontal loads due to both effects, slab cannot provide resistant in translational direction. It can only resist rotation of basement wall, which is what you are referring to. The reaction due to basement wall on slab will be transferred as point load to beam column joint, which will cause a drift in the frame (which is usually neglected in usual design calculations.)

 

Joint of the frame is not restricted by the slab to drift. Slab cannot restrict it. Where will it support the reactions? Slab can only resist translational movement in its plane, but relative to its supports, which is beam column joint. And beam column joint is free to drift.

[Badar (BAZ)]

 I am getting it and it is more than allowable seismic drifts....guidance needed pls!

 

That usually does not happen. How many basements you have? Are your keeping the torsion in your basements in check ? Are you modeling your alone basement wall. What type of support conditions are you using? Is it RCC structure?

[Syed Umair Haider]

 

Quote

 

"What are the code requirements for drift of a basement wall in seismic zone?

Lateral earth pressure produces elastic deflections whereas seismic generate inelastic sway (after multiplying elastic by Cd/I in ASCE/IBC). Now how to combine both? and by what combination?"

 

It seems to be an interesting topics accompanied with nice views.

 

 

 

Below grade seismic drift consideration.

 

Considering building structure having several below grade levels and basement walls on a single (or two) sides, I like to share my views as follows,

 

First of all drift limit states are intended to limit the damages in non structural elements in case of lateral movement and from structural point of view to limit the second order effects to a tolerable extent.

 

Therefore, drift indexes defined in code are subjected to diaphragms rather than individual structural elements (like basement walls).It is advised to check serviceability considerations in accordance with diaphragm's drift limitation of code.

 

 

As long as underground structural drift analysis with single side confined is concerned,two separate cases that seems to be required for consideration are as follows,

 

1, When structure moves towards the fill (passive condition).

 

In this cases due to infinite stiffness of soil (assumption to be verified as defined later) adjacent to basement wall,displacement of soil will be negligible and correspondingly differential displacement of basement wall from bottom to top will also be negligible,that creates almost zero drift in below grade floors (diaphragms) if they are rigidly connected to basement wall (i.e the case of monolithic slab-wall joint with adequate reinforcement anchorage for tension directed in plane of slab).

 

Modelling Strategy:

 

This case can be simulated in model by assigning relevant basement wall throughout its height with compression only spring where spring represents lateral soil support.(Usually lateral soil support is modeled using P-Y curve).Then an application of seismic force in the direction towards soil will yield a realistic value of lateral deflection of soil (could violate infinite stiffness assumption) incorporating the effect of lateral soil support.

 

In this case considerations must be given to the design of basement wall as it will be experiencing different earth pressure profile due to seismic excitation.Therefore it must be designed for this (seismic) pressure condition as well.

 

2, When structure moves away from the fill (active condition).

 

In this case as there is no wall to confine structure on the other end,therefore the net drift will be Seismic drift + lateral earth pressure's displacement.Both of these forces will be unidirectional in this case and will be effective in diaphragm drift.

 

Combined drift can be evaluated using loads combination from UBC97 section 1612.3.7 with exception 1612.3.3 (note that there "H" indicates lateral earth pressure).

 

As seismic drifts are required to be amplified to represent inelastic effects then there amplified values must be used in above mentioned serviceability load combinations (could be done through scale factors) whereas drift due to lateral earth pressure doesn't need to be amplified.

 

"2) I still did not get why there would not be any problem in basement for drift. I have multi-basements. Do you mean there would not be excessive drift between basement stories? I am getting it and it is more than allowable seismic drifts....guidance needed pls!"

 

If this is the case i.e you have considerable inter-storey drift then an important consideration here must be the thickness of basement wall.In this case the support condition hinge (i.e zero horizontal displacement) cannot be assumed for basement walls at slab levels as diaphragms are undergoing considerable lateral displacement.Therefore, in order to evaluate flexure in basement walls it is advised to model a line element along the height of wall (meshed at wall area edges) to compute flexure in basement walls rather than using theoretical model of prop canti-lever assumption that seems to be invalid due to diaphragm's horizontal movement .

It is recommended to design basement walls first (before analysis for drift) based on above methodology and model its accurate thickness, as the in this case basement wall is serving as a tie member between underground diaphragms and its thickness will effect differential diaphragm movement between different levels.

 

"Sir but the point is that slab will distribute the lateral load to all supports. Like seismic or wind. Lateral load is a lateral load and that would keep the earth pressure drift to minimal." 

 

I think that lateral earth pressure for several below grade levels could be significant enough to be considered.

 

For eg if we consider 6 below grade levels 6@10' with length of basement wall=200' and Ca=0.33 + soil density=120 pcf then net horizontal diaphragm force due to lateral earth pressure in bottom most (5th diaphragm) above foundation will be as,

 

p_{(intensity@mid height b/w 5th& 6th level)}=Ca.We.h=(0.33)(120)(55)=2178 lbs/ft²

 

p_{(intensity@mid height b/w 4th& 5th level)}=Ca.We.h=(0.33)(120)(45)=1782 lbs/ft²

 

_{Force (tributary to 5th diaphragm per unit length of basement wall)=(1782x10)+0.5x(2178-1782)(10)=19,800 lbs/ft}

 

_{Net force tributary to diaphragm=200x19,800=3960 Kipps It seems to be a significant figure but needs to be checked as in contrast with magnitude of seismic force at same level.}

 

_Thanks 

[Badar (BAZ)]

It is good to see detailed discussion on a topic, and a very good way a modelling passive resistance of soil has been presented. However, I have reservations on some comments.

 

In this case the support condition hinge (i.e zero horizontal displacement) cannot be assumed for basement walls at slab levels as diaphragms are undergoing considerable lateral displacement.Therefore, in order to evaluate flexure in basement walls it is advised to model a line element along the height of wall (meshed at wall area edges) to compute flexure in basement walls rather than using theoretical model of prop canti-lever assumption that seems to be invalid due to diaphragm's horizontal movement .

 

Assuming the diaphragm as rigid, there will be negligible in plane displacement of diaphragm with respect to its supports,which are vertical elements of lateral load resisting system, at particular story-level. Lateral displacement of diaphragms is with respect to story-levels. Hence, the support provided by slab to basement wall, at a particular story-level, can be considered as hinge as it will resist translational movement due to in-plane stiffness of rigid diaphragm.

 

Why would someone be worried about out of plane displacement of basement wall, when it will be proportioned for out of plane forces( earth pressure). As it has been correctly been pointed out that drift limits in building codes are intended to control NON/STRUCTURAL damage, and to limit secondary forces due to P-delta effect. The point is: one should be worried about drift of frame  (in/plane relative displacement), rather than the out of plane displacement of basement wall.

[UmarMakhzumi]

Okay, here is something important that I wanted to write but didn't had the time as I was travelling. 

 

Modelling Strategy:

 

This case can be simulated in model by assigning relevant basement wall throughout its height with compression only spring where spring represents lateral soil support.(Usually lateral soil support is modeled using P-Y curve).Then an application of seismic force in the direction towards soil will yield a realistic value of lateral deflection of soil (could violate infinite stiffness assumption) incorporating the effect of lateral soil support.

 

In this case considerations must be given to the design of basement wall as it will be experiencing different earth pressure profile due to seismic excitation.Therefore it must be designed for this (seismic) pressure condition as well.

 

 

I doubt if you can do that. The reason is that basement wall backfill would least likely to be compacted. Imagine doing that would increase load >> significantly which is not desired. Normally the lateral spring coefficients provided by geotech report are for undisturbed soil or soil well compacted. Dumped backfills would provide much softer springs that I would suggest be considered as void regions (Same thing as designing a pile for lateral).

 

 

"Sir but the point is that slab will distribute the lateral load to all supports. Like seismic or wind. Lateral load is a lateral load and that would keep the earth pressure drift to minimal." 

 

I think that lateral earth pressure for several below grade levels could be significant enough to be considered.

 

For eg if we consider 6 below grade levels 6@10' with length of basement wall=200' and Ca=0.33 + soil density=120 pcf then net horizontal diaphragm force due to lateral earth pressure in bottom most (5th diaphragm) above foundation will be as,

 

p_{(intensity@mid height b/w 5th& 6th level)}=Ca.We.h=(0.33)(120)(55)=2178 lbs/ft²

 

p_{(intensity@mid height b/w 4th& 5th level)}=Ca.We.h=(0.33)(120)(45)=1782 lbs/ft²

 

_{Force (tributary to 5th diaphragm per unit length of basement wall)=(1782x10)+0.5x(2178-1782)(10)=19,800 lbs/ft}

 

_{Net force tributary to diaphragm=200x19,800=3960 Kipps It seems to be a significant figure but needs to be checked as in contrast with magnitude of seismic force at same level.}

 

 

 

That is correct. However, If you have basement walls all around, then you get equal lateral pressure, thus net force on diaphragm due to lateral earth pressure is zero. However, I appreciate your comment as for the building being discussed basement walls are unsymmetrical. But, if you consider the lengths of basement wall and all the lateral force resisting system, the stiffness would be huge and I don't expect a significant response in unsymmetrical case, but, it depends on a lot of variables and number crushing in every situation is required before judging the situation. Good Catch though!

 

 

 

Assuming the diaphragm as rigid, there will be negligible in plane displacement of diaphragm with respect to its supports,which are vertical elements of lateral load resisting system, at particular story-level. Lateral displacement of diaphragms is with respect to story-levels. Hence, the support provided by slab to basement wall, at a particular story-level, can be considered as hinge as it will resist translational movement due to in-plane stiffness of rigid diaphragm.

Exactly!

 

 

For Rana,

I would suggest to keep modelling approach simple unless deemed necessary. 

For buildings with a number of basements, if you really want to complicate things, you should probably check your stiffness for basement below stories and basement above stories and use 2 different R values for both systems and apply recommendation in code for 2 different R systems. 

 

Thanks.

[Syed Umair Haider]

 "Assuming the diaphragm as rigid, there will be negligible in plane displacement of diaphragm with respect to its supports,which are vertical elements of lateral load resisting system, at particular story-level. Lateral displacement of diaphragms is with respect to story-levels. Hence, the support provided by slab to basement wall, at a particular story-level, can be considered as hinge as it will resist translational movement due to in-plane stiffness of rigid diaphragm."

 

All written above regarding rigid diaphragm is correct,but in fact I am indicating the net displacement of diaphragm along with connecting LFRM rather than its in plane deformation relative to LFRM which is assumed as zero in case of rigid diaphragm.

 

For eg if we suppose six basements of 12' each and assume that inter storey drift in each basement is 1" then net displacement of diaphragms w.r.t origin at 5th,4th,3rd,2nd & 1st level  will be 1",2",3",4" & 5" respectively and as these basement slabs are acting as a horizontal support to basement walls therefore the support deflection @ wall's 1st,2nd,3rd,4th & 5th support will also be 1",2",3",4" & 5" i.e these slabs will not be acting as a rigid horizontal support to basement wall at storey levels but instead they will be undergoing lateral deflection along with wall.In this case the deflected shape and correspondingly flexural behaviour of wall will be quite different from the case of propped canti lever model that enforces assumption of basement slabs as rigid support with zero horizontal displacement.While propp canti lever assumption works adequately for the case of entirely confined basements from all sides but will not simulate the condition defined here due to absence of lateral confinement from other side.

 

I have modeled both cases separately and have attached herewith deflected shape diagram extracted from both cases that indicates the difference in their behaviour and correspondingly in flexural forces.

 

 

Why would someone be worried about out of plane displacement of basement wall, when it will be proportioned for out of plane forces( earth pressure). As it has been correctly been pointed out that drift limits in building codes are intended to control NON/STRUCTURAL damage, and to limit secondary forces due to P-delta effect. The point is: one should be worried about drift of frame  (in/plane relative displacement), rather than the out of plane displacement of basement wall.

 

It is correct that basement wall's out of plane bending is not a sensitive issue when it is proportioned for out of plane forces as you have indicated.Similarly all indicated above is about its correct proportioning w.r.t condition defined by Rana (significant lateral drift in below grade levels).

 

I doubt if you can do that. The reason is that basement wall backfill would least likely to be compacted. Imagine doing that would increase load >> significantly which is not desired. Normally the lateral spring coefficients provided by geotech report are for undisturbed soil or soil well compacted.

 

Your doubt is meaningful for shallow depth basements but I think in case of several below grade levels, soil bed could be reasonably compacted by overburden pressure from above lying soil itself as an example overburden pressure @ depth of 40' could be 4800 psf for a soil density of 120 pcf. This high overburden generally enables soil to create a massive passive resistance.

 

For an eg passive resistance of soil for a basement wall of 200' length at same depth (in cohesion less soil) will be as follows, (Brinch Hansen's eqn),

 

P=3.H.B.Kp.Density=3.(40)(200)(3)(120)=8640 Kipps that seems to be a considerable value.

 

Dumped backfills would provide much softer springs that I would suggest be considered as void regions (Same thing as designing a pile for lateral).

 

Above mentioned cases demand sound engineering judgement for consideration\unconsideration of lateral soil support but if loose characteristics of adjacent soil is certain,then all below grade levels (regardless of single\all side's confinement) should be included in seismic analysis and base location for seismic shear must be at foundation level that automatically includes all below grade levels in drift analysis without any side support.

 

Thanks & Regards.

 

 

 

 

 

   

[Badar (BAZ)]

The deformed shape, on the left, is the one that will be required to maintain compatibility with deformations of VLRM. Wall can be proportioned for second order effects as a result of this deformed shape. But, these second order effects has to be negligible because there are much-much stiffer frames running in the direction of lateral forces, which will carry almost all of the forces due to second order effects, and you haven't included them in your model.The figure on the left is possible when second order effects are more than the effects that will arise due to retaining of soil, and in that case you are right. But if the effects of active earth-pressure are more, than the wall should be treated as continuous beam, and its behavior would be similar to the deformed shape shown on right.

 

I would proportion the wall  by assuming that the slab is able to provide adequate reaction.

Another point is that the critical scenario for out of plane forces for wall is passive soil resistance. One has to proportion the wall by considering it as a continuous beam, supported by diaphragms.

 

Having said that, accurate modeling, in this case, should involve spring-supports, not the hinge-support.

 

 

 

 

 

[UmarMakhzumi]

 

Dumped backfills would provide much softer springs that I would suggest be considered as void regions (Same thing as designing a pile for lateral).

 

Above mentioned cases demand sound engineering judgement for consideration\unconsideration of lateral soil support but if loose characteristics of adjacent soil is certain,then all below grade levels (regardless of single\all side's confinement) should be included in seismic analysis and base location for seismic shear must be at foundation level that automatically includes all below grade levels in drift analysis without any side support.

 

You are correct, however, my comment was more in terms of considering soil as springs.

 

Good Discussion everyone!

Rana, is your problem solved? Where are you with it?

[WR1]

Thats very lengthy and detailed discussion. I appreciate and thanks you for this.

 

Anyway, What I got, I put it in simple words...

 

1. Inter-storey drift is okay now as you all said (we have reduced the system R and Cd values, anyway).

 

2. I was not talking about basement wall out-of-plane bending or displacement. I was talking about frame drift (but not only on EQ, rather on H too). So this was my question, how do I combine H & E. Sir baz and Umair mentioned how to combine it in their replies.