A method for maintaining a hard, smooth floor surface comprising a polymer material, the method comprising: treatment of the surface with a flexible pad comprising an open, lofty, three dimensional non-woven web of fibers, in the presence of abrasive particles, bonded to the pad, on a contact surface between the pad and the hard surface, wherein the abrasive particles comprise diamond particles of an average diameter of 0.1 to 30 μm, preferably 0.1 to 15 μm or 3 to 6 μm, and wherein the treatment is performed using said pad having: abrasive particles bonded to it only in the vicinity of the contact surface, the fibers of the pad bonded to each other by a primary binder and/or by being melt-bonded, and having the abrasive particles bonded to it by means of a secondary binder, the abrasive particles present throughout the secondary binder, a first portion wherein said abrasive particles are present in a first concentration, and a second portion having a second, lower concentration of said abrasive particles, and said second concentration being zero, such that the second portion is free from diamond particles; and wherein the pad consists of a disc-shaped body having a thickness and a first surface, wherein said abrasive particles are present on said first surface and down to a depth from said first surface, which depth is less than said thickness, such that said first portion is at said first surface and said second portion is at a second surface, opposite said first surface. treatment of the surface with a flexible pad comprising an open, lofty, three dimensional non-woven web of fibers, in the presence of abrasive particles, bonded to the pad, on a contact surface between the pad and the hard surface, wherein the abrasive particles comprise diamond particles of an average diameter of 0.1 to 30 μm, preferably 0.1 to 15 μm or 3 to 6 μm, and wherein the treatment is performed using said pad having: abrasive particles bonded to it only in the vicinity of the contact surface, the fibers of the pad bonded to each other by a primary binder and/or by being melt-bonded, and having the abrasive particles bonded to it by means of a secondary binder, the abrasive particles present throughout the secondary binder, a first portion wherein said abrasive particles are present in a first concentration, and a second portion having a second, lower concentration of said abrasive particles, and said second concentration being zero, such that the second portion is free from diamond particles; and wherein the pad consists of a disc-shaped body having a thickness and a first surface, wherein said abrasive particles are present on said first surface and down to a depth from said first surface, which depth is less than said thickness, such that said first portion is at said first surface and said second portion is at a second surface, opposite said first surface. abrasive particles bonded to it only in the vicinity of the contact surface, the fibers of the pad bonded to each other by a primary binder and/or by being melt-bonded, and having the abrasive particles bonded to it by means of a secondary binder, the abrasive particles present throughout the secondary binder, a first portion wherein said abrasive particles are present in a first concentration, and a second portion having a second, lower concentration of said abrasive particles, and said second concentration being zero, such that the second portion is free from diamond particles; and wherein the pad consists of a disc-shaped body having a thickness and a first surface, wherein said abrasive particles are present on said first surface and down to a depth from said first surface, which depth is less than said thickness, such that said first portion is at said first surface and said second portion is at a second surface, opposite said first surface.