Rock Anchor Tendon Design

[CosSin]

Can anyone help me in regards to the tendon design for rock anchors used in retaining wall?
I am using AS4678 and wondering what tensile strength fp below refer to? Is it breaking strength or yield strength?

I used yield strength but 3x15.2 tendons only gives me less than 500kN. In this case I wonder how other engineers use 3x15.2 (even just 2x15.2) tendons for 6m retaining walls where the tension is greater than 500kN easily?


I also want to clarify the concept of working load and proof load.
Say the design tension is 450kN and I am using 3x15.2 tendons with 470kN capacity (with fp = fpy for the above formula). Now the working load Pw as per AS4678 is 60% of its yield strength which is 386kN and proof load is 1.1*Pw = 425 kN which is lower than the design tension. Is it acceptable that the proof load is lower than ultimate design tension in anchor?

 

[Ingenuity]

I am not familiar with AS4678, so my comments below are more based upon rock anchors to PTI-USA.

Is it breaking strength or yield strength?

Ultimate strength. There is no well defined yield strength of high-carbon content prestressing steel.

For low-relaxation (and therefore stress-relieved) 7-wire strand f_pu = 1860 MPa (check your code or local supplier).

Usually you would stress and lock-off the tendons (P_j) to say 70%, or 75% or 80% of ultimate tensile capacity. This is jacking force/load.

For 3 each 15.2mm ø (@ 140 mm² area each) = 3 * 140 mm² * 1860 MPa = 781 kN.

I also want to clarify the concept of working load and proof load.

Proof load usually refers to the magnitude of the load applied at time of load testing the anchor. Other codes (like USA) refer to both Proof and Performance testing loads, with differing requirements on load, duration, and acceptance etc.

'Working load' is a bit of a misnomer - they may refer to the jacking load (i.e. 70%, 75% or 80% of the ult strand capacity). Check the code for its definition of 'working'.

Is it acceptable that the proof load is lower than ultimate design tension in anchor?

Everything should be less than the ultimate tendon strength BUT your proof test load should be greater than the 'stressing/jacking' load.

You need to also check you other failure limit-states for the tendon capacity, like ground/rock bond, uplift/pullout cone, grout strength, anchorage bearing stresses etc.

 

[Agent666]

Usually you would stress and lock-off the tendons (Pj) to say 70%, or 75% or 80% of ultimate tensile capacity. This is jacking force/load.

This percentage really depends on the wall design (the amount of preload needs to be baked into the wall analysis), I've never seen more than 50% preload specified, more usually down to 30%. But there is some practical minimum requirement to set the wedges which I cannot recall off the top of my head.

We don't design to AS4678 in NZ, we instead follow BS8081 standard for grouted anchors. We take the ultimate load from the wall analysis, and test the anchors to anywhere from 1.25 to 1.5 times the critical design load with seismic being at the lower end of the scale and ULS gravity cases at 1.5 factor.

This usually means from the sizing of the strands perspective and anchored bond length we are equating the test load to the max jacking load which is approx 70% of ultimate tensile strength. This means the test load is always the critical design case for sizing the strands and the anchored length. There is no point testing to less than the actual design load, you want to establish the performance at the design load (i.e. establish geotechnical side of the design works (skin friction strength)). There is no option to not test permanent anchors.

Two types of testing, acceptance testing, and proof testing. One is ramping load up and down several times and holding for 15 minutes and measuring slip. Other is one cycle and 5 minute hold on load. Usually for larger numbers of anchors you might do the longer test on 5-10% of the anchors, and the rest the shorter test.

 

[CosSin]

Thank you for your response.

AS 3600 define the yield strength as below.

If I use the breaking strength, doesn't that mean the tendons are allowed to yield? Won't it cause increased displacement issue?

Does the lock-off load and proof load need to be greater than the design tension? ie. S* < min (Phi_k*Phi_t*Phi_n*Ap*fp, (0.7 to 0.8)*Ap*fp)？

 

[CosSin]

Thank you Agent666.

This is where I got confused. Proof load (and working load) is defined by yield load as per AS 4678 while the tension capacity is defined by breaking strength (not sure about this)？
Does that mean the capacity of tendons need to be more than 1.5 times the design tension cause otherwise it might fail when applying the test load (proof load)?

 

[Agent666]

Yes, as I noted, test load is almost always the critical load case for the tendon and grout bond checks. Also need to ensure the wall elements can also take this larger load depending on how you are testing. Usually you're using the wall or capping beam to react the test loads.

The method we use is sort of a fudge to ensure we more or less meet the intent of BS8081, being that a factor of safety of 3 is achieved on permanent anchors. Though in reality we do see all sorts of things being suggested by geotechnical engineers since we don't have a standard like AS4678. Sometimes we agree with them, sometimes not.

 

[Agent666]

The lockoff load is whatever preload you need for your wall design. Needs to be less than the maximum design capacity of the anchor limit states.

 

[Agent666]

There should be some other limits in AS3600 related to max applied loads in terms of the ultimate strength times some factor, which of applied will mean sufficient margin to ensure limiting the permanent deformation to acceptable limits given there is no yield plateau for the strands when you look at the stress/strain plot for the strands.

Usually it's critical for the jacking load, which is the test load if you're locking off at a lower load to suit the wall design (usually deformation based criteria will drive this).

 

[CosSin]

So if I understand you correctly. lock-off load doesn't needs to be greater than design tension but increasing the lock-off load will be beneficial in wall deflection?




I don't have British Standard. Is tension capacity defined by breaking strength? Cause AS 4678 doesn't say whether it is yield or breaking as shown in the very first pic I attached. (Lock-off load as per AS 4678 is not greater 0.75 of yield strength. Working load, proof load & lock-off load are all in related to yield strength).

Below is the breaking strength from AS 3600.

If I use 3x15.2 tendons. The capacity according to AS 4678 (the first pic with breaking strength) is 0.9*0.9*0.9*250*3 = 550 kN. ie. 0.73*Ap*fp, which is similar to 1.5 times the design action.

Even tendon is not designed to proof load but design action only, does it still sound reasonable for retaining wall with 6m retaining height, 2.4m pier spacing with 3x15.2 anchor installed at 2m below NGL? I have done the quick check with rectangular soil pressure and 20 kPa surcharge and 0.5Ka. The tension will be greater than 600kN. I have reviewed some plans from other firms and 3x15.2 have been used even their comps shows 600+kN tension in anchor. Don't know why. Maybe I missed something or it was just aggressive design?

 

[Agent666]

I don't have British Standard. Is tension capacity defined by breaking strength? Cause AS 4678 doesn't say whether it is yield or breaking as shown in the very first pic I attached. (Lock-off load as per AS 4678 is not greater 0.75 of yield strength. Working load, proof load & lock-off load are all in related to yield strength).

For strands it say tensile strength in the standard. This is the ultimate tensile strength. Strand strength is almost always a function of the ultimate strength.

So if I understand you correctly. lock-off load doesn't needs to be greater than design tension but increasing the lock-off load will be beneficial in wall deflection?

Yeah, it does not need to be greater, nor does it need to have any real relationship to the ultimate design load. Level of preload may be beneficial to the deflection. Totally depends on the configuration you're looking at and why the anchors were required in the first place. Crank it up too much and you're influencing your wall design actions more than you need to. You're looking for some sort of middle ground between limiting horizontal and therefore vertical settlements and ending up with a fairly neutral effect on the design actions.

Maybe I missed something or it was just aggressive design?

It's generally a function of not knowing what they are doing and not designing to any recognised standard. Generally I'd say they are eroding the actual safety factor implied in your standard of choice.

We'd usually get the design done by the geotechnical engineer, as they are better placed to assess the configuration with specialist software (wallap usually) that accounts for the soil cohesion in some non linear manner. Doing some elastic hand method using active pressure is not very efficient design as you'll overcook the design.

 

[CosSin]

Okay. Thank you for your help.

 

[Retrograde]

I find AS4678 confusing as they do not define what they exactly mean by working load. In your original post, when you say the design tension is 450kN, is that 450kN a working load or an ultimate load?

Ingenuity is correct in that 15.2mm 1830MPa strand has a minimum breaking load of 262kN. The 0.1% proof force (yield load) is 214kN. So your working load would be 0.65 x 214 = 139kN.

The rule of thumb I was given by an anchoring subcontractor is that each strand is good for 150kN working load and a typical lock-off load would be 100kN. They also install their anchors such that the geotechnical capacity is greater than strand breaking load. They typically proof load to 1.25 x working load which is about 190kN.

 

[CosSin]

450kN is the design action from ULS analysis (it is conservative as I didnt use FEA)

This where I find it weird. The working load in AS 4678 is defined by 60-65% of yield strength "Max" , which means it can be lower than 60% to even 10%. And then proof load depends on the working load. So proof load can be lower than the design action, which is pointless, like Agent666 pointed out.

 

[Agent666]

I just had an actual look through AS4678, for a permanent anchor the minimum ratio of proof load to working load is 1.5, not the 1.1 you inferred in the original post (see table B1). What am I missing here? Or have you possibly misread the standard? For a temporary anchor the minimum factor is 1.1. Keep in mind these are minimums.

This is inline with the test load (proof load) being at least equal to the ultimate limit state on the basis that the ultimate limit state load is usually governed by 1.25G+1.5Q from AS4678, so 1.5 factor on unfactored loads is maybe a margin higher test load than the ULS load.

 

[CosSin]

It is temporary (will be removed when ground floor is in place).

So if I understand correctly, working load Pw is unfactored resultant tension in anchor (Dead + Surcharge) from analysis result right? Then
Pw <= 0.6Ap*fpy. Lets take take the max. 0.6Ap*fpy

For proof load, lets take 1.5 (lets say it is permanent) or even greater then we have Pp >= 1.5 Pw, which is greater than ultimate design tension.
But then we have Pp >= 0.9 Ap*fpy

Tendon capacity PhiT = Phi_k * Phi_n * Phi_t * Ap *fp = 0.9*0.9*0.9Ap*fp = 0.73Apfp = 0.89Ap*fpy

Looks like proof load might be greater than tendon capacity since AS 4678 doesn't mention Pp < PhiT, or is it just common sense to avoid proof load greater than PhiT?


For example, say we have permanent anchor, and the tension under soil is 400kN and 200kN for surcharge. So working load is 600kN and ultimate is 800kN. Then we adopt tendons such that Ap*fpy = 1000kN,
Pw = 600 = 0.6Ap*fpy, ok;
Capacity PhiT = 0.89*Apfpy = 890kN > 800kN, ok
poof load >= 1.5*Pw = 1.5*600 = 900kN, which is greater than PhiT.
Do I miss anything?