What properties should I use for geogrid and geotextile reinforcement?

Tensile strength is published by the manufacturer.  The only issue is whether you use ultimate or allowable tensile strength.  A good reference for ultimate versus allowable strength for support in slope stability analyses can be found in Duncan and Wrights Soil Strength and Slope Stability text.  Chapter 8 in particular deals with support. 

In the text, their Method A is the same as Slide's Active model, while their Method B is the same as Slide's Passive method.  Wright and Duncan suggest that one should use the allowable capacities for their Method A, and suggest ultimate capacities for Method B.

As far as shear strength is concerned, you may want to start off with the linear model.  This is straight Mohr-Coulomb behaviour and is what most people use.  When dealing with adhesion and friction angle, this is the shear strength of the interface between the soil and the geotextile.  This is discussed in the attached document.  What people generally do is take a percentage of the soil strength in which the geotextile resides.  This is called the interaction coefficient.  The interaction coefficient is simply a factor that is applied to the tangent of the friction angle of the material in which the geosynthetic is embedded.  See page 7 of the attached document.  Basically it's a shear strength reduction factor.  To use an interaction coefficent (Ci), set:

Adhesion = cohesion*Ci

Friction angle = arctan(Ci*tan(phi))

 

Cohesion and phi are the Mohr-Coulomb parameters of the soil in which the geosynthetic is embedded.  If the geosynthetic is in more than one material, use the material-dependent option for the support.