This achievement can be a bit misleading at first. by "smashing through" the roadblock it means you need to hit / do damage to a Cop car in a roadblock and make it past (without wrecking) to earn the achievement.
If you simply find a weak point such as a gap between the barricade, or an alternate route you can drift through to get past then it doesn't count towards the achievement.
Having impact body mods or high toughness rating on your car will increase your chances of not wrecking when you make contact with a roadblock at high speeds.
(Try aiming for either the front or rear of the cop car. Hitting in the middle is almost always an instant wreck.)