Internal friction angle of soil varies with the density of soil. Angle of repose is the angle of friction of sand in loosest state.For sands angle of repose is equals to the residual friction angle.
If you consider the ultimate state of a soil, often called the critical state, there is no difference between critical state friction angle and the angle of repose. Critical state is the state of failure when stresses (normal and shear) do not change any more during shearing and volume is also constant. Only distortion (shear strain) continues to increase. The ratio of shear stress over normal stress at any stage of shearing equals to the tangent of so called mobilised friction angle. When you look at the shear curve (shear strain vs. shear stress) for a loose sand or normally consolidated clay it increases monotonically to the ultimate value of shear stress. The stress path (normal stress vs. shear stress) goes straight up during shearing at constant normal stress. So the mobilised friction angle increases monotonically to the critical (or residual) value of friction angle.
When you have dense sand or overconsolidated clay, the shear curve goes up at the beginning and then drops. The stress path firstly goes up, then drops to the failure line (Coulomb line). This means that the mobilised friction angle increases to the peak value and then drops to take the critical state value.
You can find clear explanations for all of this e.g. in the book of Atkinson "The mechanics of soils and foundations" or http://environment.uwe.ac.uk/geocal/geoweb.htm.
In practical application it is safer to take the critical state (or residual) value.
Shamas, both sands and clays have the internal friction angle. It characterizes their strength. What you write about clays is undrained shear strength (cu or su). It can be measured in e.g. unconfined compression test. In undrained conditions the friction angle for clays is approximately 0 provided that the clay tested is saturated. In drained conditions the friction angle for clays at failure (in the critical state) is somewhere between 20 and 30 deg.
Certainly, we cannot speak about the angle of repose for clays unless a clay sample is remoulded (its structure is destroyed, thus bonds are broken) and is submerged in water to overcome negative pore water pressure and resulting suction.
Unconfined compression test gives the short term shear strength called also undrained shear strength. It can be used in case of rapid loading of clays (e.g. earthquake). In such conditions the friction angle is 0 and the strength is expressed only by cohesion.
Hi,
Please look at this interesting paper:
Santamarina, J. C., and Cho, G. C. (20001). Determination of critical state parameters in sandy soils- simple procedure. ASTM Geotechnical Testing Journal, 24(2), 185-192.
In simple words; there is no relationship between them unless in very limited cases. In my publication here I mention why is that:
https://www.sciencedirect.com/science/article/pii/S0032591018301153
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