Apparatus and test procedure for measuring the cohesive, adhesive, and frictional properties of bulk granular solids

A method of testing bulk solids to determine an unconfined yield strength fc, an angle of internal friction phi and an effective angle of internal friction delta at a major principal consolidation pressure sigma 1 comprising the steps of:

• placing bulk solid in a test apparatus comprising an upper plate, a lower plate parallel to the upper plate and the upper plate rotatably attached to a load application bracket such that the lower and upper plate may rotate about an axis substantially parallel to a planar surface of the upper plate;
• applying a known consolidation force CF to the upper plate while the direction of applied force CF is substantially perpendicular to a planar surface of the upper plate;
• rotating the test apparatus with respect to the direction of the applied force until a steady state movement of the bulk solid occurs between the parallel upper and lower plates of the apparatus;
• recording an angle of rotation alpha 1 between the
• force direction and an axis perpendicular to a planar surface of the upper plate of the apparatus necessary to just maintain steady state movement;
• reducing the angle alpha 1 slightly to stop the steady state movement and maintain the force CF for a desired time of consolidation;
• reducing the applied force CF to near zero;
• increasing the angle alpha 1 to a failure angle;
• increasing the applied force CF to a condition of failure of the specimen;
• and
• recording the applied force CF at the condition of failure of the specimen value as the failure force FF;
• and
• calculating phi, fc, delta and sigma 1 as follows:
• phi=Arc tan((CF Sin(alpha1)−FF Sin(alpha2))/(CF Cos(alpha1)−FF Cos(alpha2)))
• fc=2(FF/A) Sin(alpha2)Cos(phi)−Cos(alpha2)Sin(phi)/(1−Sin(phi))
• delta=Arc sin(Sin(alpha1)/Cos(alpha1−phi))
• sigma1=(CF/A)Sin(alpha1)(1+Sin(delta))/(Cos(phi)Sin(delta)).

A method of testing bulk solids to determine an unconfined yield strength fc and an angle of internal friction phi after the bulks solids being consolidated under a uni-axial compressive stress sigma1 comprising the steps of:

• placing bulk solid in a test apparatus comprising an upper plate, a lower plate parallel to the upper plate and the upper plate rotatably attached to a load application bracket such that the lower and upper plate may rotate about an axis substantially parallel to a planar surface of the upper plate;
• applying a consolidation force CFU while the direction of force CFU is substantially perpendicular to a planar surface of the upper plate and such that CPU/A=sigma 1, where A is the area of the upper plate;
• maintaining CFU for a desired length of consolidation time;
• reducing CFU to near zero;
• increasing an angle between an axis perpendicular to the parallel plates of the test apparatus and the direction of the force CFU to an angle alpha 1 greater than an effective angle of internal friction delta;
• increasing the force CFU to a failure condition of the specimen;
• recording the value of force at the condition of failure as FF1;
• placing a new sample in the test apparatus;
• applying the consolidation force CFU while the direction of force CFU is substantially perpendicular to a planar surface of the upper plate and such that CPU/A=sigma 1;
• maintaining CFU for the same length of consolidation time as used previously;
• reducing the force CFU to near zero;
• increasing an angle between the axis perpendicular to the parallel plates of the test apparatus and the direction of the force CFU to a new angle alpha2 greater than alpha1;
• increasing the force CFU to a failure condition;
• recording the value of force at the condition of failure as FF2;
• and
• calculating phi and fc as follows:
• phi=Arc tan((FF1 Sin(alpha1)−FF2 Sin(alpha2))/(FF1 Cos(alpha1)−FF2 Cos(alpha2)))
• fc=2(FF2/A)Sin(alpha2)/Cos(phi).

A method of testing bulk solids to determine an adhesive and kinematic friction angle between a bulk solid and a plate of material on which the bulk solid may be required to slide comprising the steps of:

• placing bulk solid in a test apparatus comprising an upper plate, a lower plate parallel to the upper plate wherein the lower plate surface in contact with the bulk solid is roughened and wherein the upper plate is rotatably attached to a load application bracket such that the lower and upper plate may rotate about an axis substantially parallel to a planar surface of the upper plate;
• applying a force CFA in a direction substantially perpendicular to a planar surface of the upper plate to a magnitude such that CFA/A represents the impact pressure sigma_i of material at the upper plate, where A is the area of the upper plate;
• reducing the magnitude of the applied force CFA to a desired value FFF;
• increasing an angle between an axis perpendicular to the parallel plates of the test apparatus and the direction of the force CFU until failure occurs at which point the value of the angle is the adhesion angle for a bulk solid consolidated under impact pressure sigma_i with normal pressure FFF/A;
• reducing the angle between an axis perpendicular to the parallel plates of the test apparatus and the direction of the force CFU to a value just required to keep the bulk solid moving on the lower plate at a constant steady rate, at which point this value is the kinematic friction angle of the bulk solid on the lower plate.