Dear Masoud,

Attached you can find a spreadsheet and original article to estimate safety factor against toppling.

http://geogroup.utoronto.ca/xe/geogroup/PDF/Tatone_2009_Computers-&-Geosciences.pdf

Regards

Thanks Mr. Ramos,

But as you see even for kinetic analysis we dont have "height, width and other required parameters of the slope...

[ I think the only way to estimate the safety factor is using required condition for toppling which has been provided by Goodman and Bray (1976). As you know, the equation is:

(90-phi (p))+phi(joints)

Without the full geometry of the slope defined, you cannot calculate a Factor of Safety. The check you performed above appears to be the best you can do given the available information.

Dear Bryan,

Thanks. It was really helpful.

I agree with Bryan that in order to find the factor of safety you need more information about the slope geometry, nature and dip of joints and the type of rock. In general, toppling failure is of two types: Block toppling and Flexural toppling. In my opinion, it is difficult to apply limit equilibrium method to flexural toppling .Limit equilibrium methods has been used to analyse block toppling mainly with the aim of determining loads required to anchor individual blocks. Friction (Goodman, 1976) and numerical models (FLAC-Itasca; UDEC) have also been used for block toppling. 

Toppling could be of two types: Flexeral and Direct toppling.

Direct toppling – occurs when the centre of gravity of a block lies outside the outline

of the base of the block, with the result that a critical overturning moment develops.

Flexural toppling – occurs under certain circumstances when a layered rock mass

outcrops at a rock slope, and the principal stress parallel to the slope face induces

inter-layer slip which causes the intact rock to fracture and the resulting blocks

to overturn.

Simple thumb rule is -- For a toppling failure to occur, the dip direction of the discontinuities dipping into the face must be within about 10° -   20°of the dip direction of the face so that a series of slabs are formed parallel to the face. Also, the dip of the planes must be steep enough for interlayer slip to occur (Hoek and Bray, 2005).

Factor of safety against toppling can be estimated from the DIPS program of RocScience software.

Another technique can be evaluated potential toppling failure by stereo-net. It must be known discontinuity orientation and not necessary slope geometry value. 

Mr Tonnayopas,

Thanks for your contribution. As you could see, dip direction is not known in this case. 

To evaluate toppling failure we should plot stereonet and depending upon the mutual relation of slope and orientation you will get the probability or clue about degree of any possible toppling failure.

Madhavi Latha Gali Thank you for your explanations. I have a quastion about DIPS..How can I calculate of find safety factor with DIPS software againist to toppling. It gives only probabilistic results.

Toppling Failures may be categorised into A) Primary and B) Secondary. The first one encompasses Flexural, Block and Block-Flexural while the latter class encompasses toppling types such as Slide base, Slide head, Tension crack types of toppling. The pre-requisite condition being the strike of dominant discontinuity, basal plane of separation and that of slope face be parallel or skewed at most by 10 degree to each other. Kinematic analysis of discontinuities/ joints may extend info about probable zones of toppling failures by following certain steps in stereo-net analysis. DIPS, nonetheless, is helpful in basic kinematic analysis. For FOS, however, one needs to have much more site specific information, dimensions etc. in addition to the data pertaining to structural discontinuities.

Dear Masoud,

These articles might help:

Article Numerical analysis and stability assessment of complex secon...

Article Application of fuzzy expert decision-making system for rock ...

Article Key-block based analytical stability method for discontinuou...

Bests,