Human drivers naturally balance the risks of different concerns while driving, including traffic rule violations, minor accidents, and fatalities. However, achieving the same behavior in autonomous driving systems remains an open problem. This paper extends a risk metric that has been verified in human-like driving studies to encompass more complex driving scenarios specified by linear temporal logic (LTL) that go beyond just collision risks. This extension incorporates the timing and severity of events into LTL specifications, thereby reflecting a human-like risk awareness. Without sacrificing expressivity for traffic rules, we adopt LTL specifications composed of safety and co-safety formulas, allowing the control synthesis problem to be reformulated as a reachability problem. By leveraging occupation measures, we further formulate a linear programming (LP) problem for this LTL-based risk metric. Consequently, the synthesized policy balances different types of driving risks, including both collision risks and traffic rule violations. The effectiveness of the proposed approach is validated by three typical traffic scenarios in Carla simulator.