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# Retaining Wall - Active pressure with rock face within failure plane

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 danyul (Geotechnical) 4 Dec 08 20:13
 I have a solid basalt rock face and want to build a retaining wall in front of it... there will be soil placed between the wall and rock slope.assuming the rock slope starts at the bottom-back of the wall and is steeper then the active wedge how do you calculate the active pressure?  I assume it will be less than the full active wedge. I know there are the charts for negative backfill but that is not the same thing correct?Thanks
 fattdad (Geotechnical) 4 Dec 08 23:02
 A drawing would help us more fully understand this question.  Ultimatly, you'll have active earth pressure from the rock and also some active earth pressure from the soil backfill.  It seems unlikely that you'd have sufficient width to develop full Rankine active earth pressure from the soil backfill.  Just some component of the overall earth pressure.  What do you know about secondary charactistics in the basalt (i.e., orientation of fracture planes and the like)?f-d ¡papá gordo ain't no madre flaca!
 danyul (Geotechnical) 5 Dec 08 14:00
 well i was assuming there wouldnt be any active pressure from the rock face... and i dont know the exact geometry yet.  I was hoping there was a way to get the active force from the angle of the soil wedge between the rock and wall.
 dgillette (Geotechnical) 5 Dec 08 14:31
 This isn't a simple question, even if the basalt is all bulletproof and would not contribute any active force (assuming that the cut is stable and wouldn't slide even without the wall).  Depending on width of the space, and the type and compaction of backfill, I can see several different possibilities:Arching could cause very large lateral forces. ORCompaction pressures on a stiff wall could cause very high lateral stresses, above Ko near the top of the wall.  See, for example, Duncan, Williams, Sehn, and Seed in the ASCE JGE, December 1991, with errata in March 1992 (important), and discussion and closure in July 1993 (also important).  This is based on placement and compaction of the fill in lifts, which imposes pressure higher than Ko at the top of the fill.  If the horizontal dimension of the wedge of fill is small, it may not take very much deflection of the wall to allow enough horizontal strain that the pressure is much lower than with a rigid wall.ORIf the fill is not compacted much and/or the wall is flexible, you might be able to modify the Coulomb active pressure (based on sliding block) to account for the hypothetical sliding surface being steeper than 45+phi/2.  Fattdad is, I believe, correct when he says you could not get the Rankine active condition (backfill material all at yield, with sigma1 vertical and sigma3 horizontal).If it were me doing the design, I would start with the 2nd one, and see whether a reasonable reduction in the pressure makes a big difference in the design.  Depending on height, length, and results of analysis, the cost difference to the client could be pretty minor, trading off hours you don't bill him for the additional study to nail down the loads better, versus the additional rebar.  Or, the cost savings could be huge compared to the cost of your time to refine the analysis.Could you compact the majority of the backfill well enough to control settlement, but leave a thin zone at the wall and abutment contacts that is not compacted as well, so the pressure is not so high after each lift is placed?  EXCEPTION: If this wall forms the spillway chute for a dam, you need tight compaction against both sides, requiring wheel rolling, jumping jacks, pogo sticks, etc.How's that for some vague and speculative advice?Regards,DRG
 PEinc (Geotechnical) 5 Dec 08 16:09
 What kind of wall and how high?  What kind of backfill?
 hokie66 (Structural) 5 Dec 08 16:41
 Just a suggestion, but you may want to consider backfilling the space between the rock face and the wall with stabilised sand or liquifill placed in lifts over a few days.  I think this would largely remove the uncertainty of the pressures imposed by compaction.
 danyul (Geotechnical) 5 Dec 08 18:05
 say if we just poured gravel into the gap between the rock face and rock wall? is there a way to calc the active force based on the rock face and a known friction angle of the gravel?we dont know the height of the wall or material but say 15 feet high made of stones and backfilled with some select gravel fill or clean gravel.
 aeoliantexan (Geotechnical) 5 Dec 08 22:51
 Richard Handy treated this case analytically in the ASCE Geotechnical Journal a few years ago.Don't forget, that if water should saturate the backfill, the water pressure alone will probably be greater than the soil pressure you designed for.  Water doesn't care how wide the space is.
 fattdad (Geotechnical) 5 Dec 08 23:33
 To the question, "is there a way to calculate the earth pressure?"  Sure.  Let's say the wall backfill extends 2 ft behind the wall.  Take a protractor and mark a line with a 45-(phi/2) measured from vertical.  At some depth (likely around 3 ft or so), you will begin to intersect the vertical rock face.  Calculate the active earth pressure at that depth and use that value for all depths below that depth - the earth pressure will remain unchanged.  You just have to design the wall to hold up.I know that this has come up in the last year somewhere. . .f-d ¡papá gordo ain't no madre flaca!
 BigH (Geotechnical) 6 Dec 08 0:01
 This has acatually been discussed in other threads - but my first step, I suppose, would be to treat it like pressures in a silo.  One of the other threads linked to a paper on this.  As for the rock contributing - if you just cut the rock, then I suppose there could still be some "expansion" due to the stress relief.  If it is an "old" face, it is likely not unless there are joint sets that might be contributing to creep.
 danyul (Geotechnical) 8 Dec 08 16:45
 fattdad -  i was figuring something like what you wrote... problem is that the rock wall will be built onto a rock ledge and the rock face behind the rock wall will be staring at the back of the wall at a steep angle.  so the 45-(phi/2) is "into" the rock face at the start. the height of backfill is about 18 feet and the width at the top is 5 feet... and zero at the base of the wall.
 fattdad (Geotechnical) 8 Dec 08 17:06

#### Quote:

so the 45-(phi/2) is "into" the rock face at the start.

There is a Rankine wedge at any depth from the top also.  Call that the start.  If you are at a depth of 1 ft, you can strike off an angle for the Rankine wedge, just like you can at the depht of 2 ft.

Your problem is interesting as between the depths of 17.9 ft and 18.0 ft there is no soil (trivial) in the zone between the two lines for each of these Rankine wedges.

I bet you could think through how to handle that. If it was my problem, I believe I could work up something to account for your case.  It seems like fundamental earth pressure stuff.  (I'm not trying to make light of your question at all.  It is a unique case, but I just seem to think after some pondering it'll become apparent how to handle the problem.  Work up a sketch, make a pdf and post it to this forum.  I'd be glad to look at what you've come up with.)

¡papá gordo ain't no madre flaca!

 danyul (Geotechnical) 8 Dec 08 19:47
 fattdad - i see, thanks... how bout this... this may be way off base but what if instead of using the phi angle in solving for the Ka, use the rock face angle from horizontal (a forced failure line).
 fattdad (Geotechnical) 8 Dec 08 19:53
 You have described a potential failure surface (i.e., the rock face to aggregate backfill interface) that is a triangle with an 18 ft leg and a 5 ft leg.  That triangle has two acute angles.  Find the smallest angle and set that value to 45-(phi/2) and solve for "phi".  That may more likely be the replicate angle to use for calculating a "Rankine-like" active earth pressure.  I'd try it to see if you get a reasonable result.f-d ¡papá gordo ain't no madre flaca!
 danyul (Geotechnical) 8 Dec 08 20:43
 well... using different methods (note there is a batter on the inside of the wall of about 1H:13V and flat backfill) Rankine- with a typical wedge using soil phi=40 the EFP = 29 pcfwith the potential failure surface with an angle of 16.5 between the inside face of the wall and rock face the new "phi" is 57 which equates to EFP = 12 pcf.Coulomb- normal wedge EFP = 37 pcf         new "phi" EFP = 22 pcfthese seem "reasonable"...
 dgillette (Geotechnical) 8 Dec 08 20:57
 Danyul - I sure wouldn't rely on that until you have checked the "silo" model (which involves arching), potential for hydrostatic pressure, and compaction pressures.I heard what I thought was a tall tale when told to me by a farmer I worked for, but later reconsidered when I heard it from a geotech prof.  It was about a tall, narrow bin full of corn, which blew out when the door was opened at the bottom and the corn arched across the bin, creating very large lateral pressures.Aeoliantexan: Recall how far back Handy's paper was?  I have the Journal going back to 1984 in my cabinet, but don't feel like plowing through the December indexes.tan-1(18/5) = 74.5 degrees.  74.5=45+(59/2), and 59 seems a little high for an equivalent phi to apply to a modified Coulomb (not Rankine) wedge.  (Rankine active assumes the whole soil mass is at failure, with sigma3 horizontal and sigma1 vertical.)
 fattdad (Geotechnical) 9 Dec 08 11:16
 danyul (Geotechnical) 9 Dec 08 14:09
 fattdadif im reading this right, and id like to think that i am...case b would be the most accurate for my situation... not taking arching into account.thanks
 fattdad (Geotechnical) 9 Dec 08 14:42
 I think I'd evaluate the earth pressures using case B.  I think the earlier idea of using the rock-slope angle and back-calculating some equivalent phi is shown to be incorrect by the sketch.I think case B does take "arching" into account as the earth pressures actually decrease below the depth of 10 ft. To my way of thinking this frictional response is fundamental to the concept of arching (i.e., not acting as a hydrostatic force).Interesting problem and it was fun to noodle through what I might do if the problem was mine.Good luck.f-d ¡papá gordo ain't no madre flaca!
 dgillette (Geotechnical) 10 Dec 08 10:37
 I don't think B actually does account for arching, which would increase the horizontal pressure, rather than decrease it.
 fattdad (Geotechnical) 10 Dec 08 11:31
 dgillette:  I'd like to comment to your thought, but may not be fluent enough on the subject of soil arching.  To me when soil pressures fail to increase in proportion to Z*density*(some factor), arching is to blame.  I think  Spangler's equations get to the root of this.While my sketch of "Case A" shows Rankine failure planes headed toward the wall, you could also show these failure wedges headed toward the rock.  After all the rock face will "feel" an equal and opposite horizontal pressure, eh?  If you were to draw these opposing failure planes, at the bottom of the backfill you'd have some triangle that would be formed.  To me (again, I may be wrong), that is some form of arching in the graphical sense.I like these topics as it requires engineering judgement and creativity.  I'd like to know your thoughts on how you'd derive the earth pressures and if you feel some scaler or alternate solution is needed to throttle up the loads to account for some "arching" affects.  This would be a new concept to me.f-d ¡papá gordo ain't no madre flaca!
 dgillette (Geotechnical) 11 Dec 08 15:44
 Do you have Winterkorn and Fang?  In the 1975 edition, it's in Chapter 5 by Arpad Kezdi.  On page 216, see "Pressure of Sand Located Between Two Rough Vertical Walls."  The newer work by Handy, mentioned by aeoliantexan, could give different results - I have thus far been too lazy to dig through the journals to track it down.  Regardless, the lateral force from arching is roughly analogous to the very large normal force that an arch dam puts on the walls of the canyon, in addition to the shear forces that keep the dam from moving downstream.DRG
 fattdad (Geotechnical) 11 Dec 08 21:38
 I am familiar with the arch-dam analogy (I've actually worked on a few arch dams in Alaska many years ago).  Haven't looked at your references and I don't have Winterkorn and Fang.  I'd like to learn more and have always solved the problem as shown herein.  When I was in grad school (this was over 20 years ago, so I may have lost some of the details), Duncan lectured on arching related to buried conduits - actually with some interesting guidance for design of culvert shapes.  I think much of this is also shown by Spangler (others too I'm sure).  There is a distinction in vertical force for pipes constructed in trenches v. embankment conditions.  It's the trench sidewalls and the arching of the backfill to either sidewall that affects these vertical forces.  This can only imply that for the vertical force to be something other than gamma*Z there must be some increased shear/horizontal forces acting on the sidewall.I may be mixing concepts here, but if I recall correctly, log spirial earth pressures account for friction along the backfill-to-retaining-wall interface.  Maybe there is some design method to look at the O.P.'s concern using log spirial.  Something to ponder, eh?f-d ¡papá gordo ain't no madre flaca!
 escrowe (Geotechnical) 12 Dec 08 14:11
 Arching is critical to design of pier walls for landslide stabilization, specifically pier spacing.  Many pier walls have been constructed in California (for instance).  Day discusses some of the design issues.   Sect. 16.12http://books.google.com/books?id=65EB8JQXJxcC&pg=PT507&lpg=PT507&dq=design+of+pier+walls+for+landslide+stabilization&source=web&ots=_CDA2q4a3F&sig=ymoQerBtGeK5LP1ulCWqermfC1E&hl=en&sa=X&oi=book_result&resnum=2&;ct=result#PPT507,M1
 fattdad (Geotechnical) 12 Dec 08 17:25
 The pier wall reference (above) reminds me of the lateral pile capacity term "Cp", typified by phi/2, as this directly relates to arching also, and a very similar concept as used for pier spacing.f-d ¡papá gordo ain't no madre flaca!
 Mumbo (Geotechnical) 14 Dec 08 21:08
 Soil Engineering by Spangler and Handy, 4th Edition has exactly what you are looking for regarding a rock face.  It is not covered in earlier editions though.Full earth pressure usually occurs to a depth of approx. 2 x space between wall and rock face and then levels off assuming a certain friction between the backfill and rock face.Note: Rock is never where it is supposed to be and this calculations is totally dependent on the space between wall and rock. If you assume 3 feet and it is actually 5 feet,  the pressure calculation is off by quite a bit.Note 2: some of this may not apply real well in a seismic zone where the pressures may increase due to a reduction in frictional factors.
 fattdad (Geotechnical) 15 Dec 08 8:27
 Just to correct an error in my earlier posting:  Cp is typified by phi/10.f-d ¡papá gordo ain't no madre flaca!
 palmahouse (Geotechnical) 14 Jan 09 19:42
 Why don't you draw the flatest failure plane that could form - assuming linear surface, assign strength parameters to it, and run a simple wedge analysis.  Calculate the unbalanced force required to give you a safety factor of one.  Then, distribute that unbalanced load over the wall as a triangular distribution.  This method is pure soil mechanics and assumes no friction between the backfill and the back of wall plus the backfill and the basalt (hence, it is conservative).  I did this before and came up with 15 to 20 pcf equivalent fluid pressure (which was great - much less structure required).  That wall has been up for 15 years, is 12 feet high, and there is no distress.If you want to model in the friction between the backfill and the back of wall (but still ingnore the friction between the backfill and the basalt), you could use Coulomb for the prescribed failure plane.  Esentially, Coulomb is the same as doing the simple wedge analysis, but adds in the boundary friction.If you are not comfortable with that - there is a design procedure for "facia walls."  I don't have it handy - you could try a google search.  I think the facial wall procedure will give you a similar result anyway.
 aeoliantexan (Geotechnical) 16 Jan 09 14:11
 The Handy reference is "ASCE J. Geotech .Eng. 111(3), PP 302-316:.If you Google "fascia walls" you can get to a preview of Geotechnical Engineering by Handy and Spangler, Page 544, which presents the same solution.  Handy did use Spangler's theory for conduits in trenches in developing his derivation.I would be cautious in using the low lateral earth pressures thus derived in designing a retaining wall. It's not that the theory is not sound; it just might not cover all the things that can happen to the wall.  My mentor used to tell me never to design a retaining  wall that could not support water, at least at a safety factor of 1.0.  He had looked at a building on a daylight basement that had been shoved downhill when water got into the backfill.  The soil was loess, which can stand vertically, and the water table was probably at least 40 feet deep.  I believe that Handy got interested in the subject after consulting on a tall stone wall that toppled, flattening a car and occupants.  The wall was constructed close to a vertical rock face. I don't know the details.
 palmahouse (Geotechnical) 26 Jan 09 14:33
 aeoliantexan,Your mentor seems very wise.  However, if you think your wall backfill will become undrained, the horizontal stresses on it will actually be higer than that imposed by the unit weight of water (check your soil mechanics on this - the horizontal stresses will be the boyant weight of the backfill times the coeficient of lateral earth pressure PLUS the unit weight of water).  If anything, and you want to be conservative, I would design for a F.S. of 1 using this undrained loading.I would suggest, however, that you should just focus on providing adequate drainage behind the wall so the undrained stress conditions will likey never occur.  This means granular backfill, an adequately wide collector pipe, and discharge to a suitable location that cannot get flooded or comprimised.Perhaps in your mentor's case, the failure occured because of poor drainage, or there was no drainage combined with a design that could not accomodate undrained conditions.Of course, basement walls that extend below the water table should be designed for the undrained conditions I describe.  The funny thing is, lots of old walls in San Francisco are below water and waterproofed, have hardly any reinforcement, and have never failed, even during earthquakes.  Arching apparently happens.
 aeoliantexan (Geotechnical) 29 Jan 09 13:48
 Palmahouse, I have no quarrel with anything you said.  Certainly the soil will add some pressure to the water pressure.  I just wanted to contrast the very real 62 pcf water pressure with the calculated 25+/- pcf soil pressure.Yes, the failure I mentioned probably involved roof runoff going directly into an uncompacted silty clay backfill during a storm and no perimeter drain.  That would have been common local  construction at the time, because of the deep water table.  As it became more common to recompact 2 or 3 feet of the loess under the building to prevent collapse settlements, we learned that any water that entered the backfill was likely to become trapped there and began to provide perimeter drains no matter how dry the site was.I can't explain the San Francisco walls you described, unless they are load-bearing walls that can take quite a bit of bending moment due to the axial load.
 jbenway (Civil/Environmental) 6 May 09 17:33
 You may want to check out "Earth Pressure on Retaining Walls near Rock Faces" in the Journal of Geotechnical Engineering Vol. 113, No. 6, pages 586-599.

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