This question was posed to me recently, and the short answer is “yes.”
This is called a premises liability case. In Texas, a customer can prevail in a premises liability case against a business if the customer can prove several things: (1) that the condition (here the broken pavement or sidewalk) posed an unreasonable risk of harm; (2) the business owner knew or reasonably should have known of the danger; (3) the business failed to use reasonable care to make the condition safe; and (4) the business failed to use reasonable care to warn the customer about the condition.
While these questions may seem simple, there are a lot of difficult issues hidden inside of them. For instance, almost all premises cases have disputes about whether the condition was unreasonably dangerous. This often requires expert witnesses who can talk about building codes or other rules and regulations that might apply and why failing to comply with those regulations is dangerous.
Additionally, when proving whether the business owner knew or should have known of the danger, arguments arise over how long the condition had been present. In this type of case, where broken pavement or sidewalk is likely to occur slowly over time, the issue might not be important. But if you’re suing a business over a spilled drink on a floor or something similar, then you have to prove how long the drink had been on the floor. As you might imagine, that can be difficult.
There are other similar difficult issues that make this a much more complicated question than it might normally seem. That’s why it’s so important to have a competent lawyer on your side when you’re hurt in these situations.