effct of ground, and gap to design monopole antenna

effct of ground, and gap to design monopole antenna,what should be the dia of radiation box in hfss

Radiation boundary is typically 1/4 wavelength away.

increasing the gap can decrese the impedance mathching of the second resonat, so the gap between grond and patch must be optimized to achive the best impedance matching.
width of the gnd has negligible effect on monopole.

The size of the ground plane will affect the radiation pattern. In infinite ground plane will allow radiation orthogonal to the monopole. As the plane is reduced the radiation will tilt up.