Crews have reported that the work of clearing the backlog has been "slow and arduous" due to pavement conditions and volume of waste.
Work to clear the city streets is also continuing, with a council spokeswoman saying category-three roads were being gritted from early yesterday.
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Hide AdShe added that the council plans to clear snow and grit from all category-three routes by the weekend.
The Met Office said temperatures were expected to remain sub-zero throughout the Christmas periods.