4.2 Barrier Design and Length of Need

Barrier Design and Length of Need

When a roadside hazard cannot be eliminated, relocated, or designed with a breakaway base, engineers must shield it using a traffic barrier. Although barriers prevent vehicles from striking rigid hazards, they are also obstacles. A barrier should only be installed if a collision with it is expected to be less severe than hitting the unshielded hazard.

Barrier Classification and Structural Options

Traffic barriers are classified into three categories based on their lateral deflection during an impact:

1. Flexible Barriers (e.g., Cable Barrier)

   • Characteristics: Consist of tensioned steel cables on weak posts, with dynamic deflection of 6 to 10 feet.
   • Advantages: Impart the lowest deceleration forces on occupants, resulting in fewer injuries. They are inexpensive and maintain sight lines.
   • Disadvantages: Require significant lateral clearance for deflection. They must be repaired (posts replaced and retensioned) after most impacts.

2. Semi-Rigid Barriers (e.g., W-Beam and Thrie-Beam Guardrails)

   • Characteristics: Consist of corrugated steel rails on steel or wood posts, with blockouts to prevent wheel snagging. Deflection is 2 to 5 feet.
   • Advantages: Offers a good balance of cost, deflection, and deceleration forces. Standard W-beam is the most common barrier in the US.
   • Disadvantages: Requires moderate maintenance after impacts. Improper mounting height (standard is 31 inches) can lead to vaulting or underrunning.

3. Rigid Barriers (e.g., Concrete Safety Shapes)

   • Characteristics: Standard concrete structures (Jersey, F-shape, or single-slope) with virtually zero deflection.
   • Advantages: Withstands multiple impacts with minimal maintenance. Excellent for narrow medians or shielding rigid structures where deflection is intolerable.
   • Disadvantages: Imparts the highest deceleration forces on occupants and has high initial costs.

---

Length of Need (LON) Calculations

The Length of Need ($LON$) is the total length of the barrier system required upstream of the hazard to shield it from an errant vehicle. Determining the correct $LON$ ensures that a vehicle leaving the road at the designated runout angle cannot travel behind the barrier and strike the hazard.

Key Variables in LON Design

To calculate the $LON$, designers must identify several geometric parameters:

• $L_R$: Runout Length (feet). The distance an errant vehicle travels after leaving the traveled way. It is determined from AASHTO tables based on design speed and volume.
• $L_A$: Lateral Distance to Hazard (feet). Distance from the traveled way edge to the far side of the hazard. If the hazard extends beyond the clear zone, $L_A$ equals the clear zone width.
• $D_C$: Lateral Distance to Barrier (feet). The distance from the edge of the traveled way to the face of the barrier.
• $\theta$ (or Flare Rate $a:b$): The rate at which the barrier is flared away from the roadway. The flare rate is expressed as a ratio $1/a$ (e.g., a 1:15 flare means for every 15 feet along the road, the barrier moves 1 foot laterally). Thus, $\tan \theta = 1/a$. If the barrier is parallel to the roadway, the flare rate is 0.

Parallel Barrier LON Formula

For barriers installed parallel to the roadway (no flare, $\tan \theta = 0$), the formula for the upstream length of need ($X$) is:

$X = \frac{L_R(L_A - D_C)}{L_A}$

This is the most common equation tested on the PE Civil Transportation exam.

Flared Barrier LON Formula

If the barrier is flared away from the roadway to reduce the required length of barrier or to terminate it further from the traveled way, the formula becomes:

$X = \frac{L_A - D_C}{\frac{L_A}{L_R} + \tan \theta}$

If the flare rate is given as a ratio $a:b$ (where $b = 1$ and $a$ is the run along the road), then $\tan \theta = 1/a$, and the equation is written as:

$X = \frac{L_A - D_C}{\frac{L_A}{L_R} + \frac{1}{a}}$

Sample Calculation

Suppose a roadway has a 60 mph design speed ($L_R = 300$ ft). A bridge pier is offset 16 feet ($L_A = 16$ ft), and a parallel guardrail is offset 6 feet ($D_C = 6$ ft).

Using the parallel barrier formula:

$X = \frac{300 \times (16 - 6)}{16} = \frac{300 \times 10}{16} = 187.5\text{ feet}$

Using the parallel formula, at least 187.5 feet of guardrail must be installed upstream to shield the pier.

---

Barrier End Treatments and Crash Cushions

The upstream end of a guardrail is a major hazard because it can spear a vehicle during a head-on collision. Therefore, all barrier terminals must be fitted with crashworthy end treatments.

End Terminals

Modern end terminals are designed to either absorb the energy of a head-on impact or guide the vehicle away.

• Gating vs. Non-Gating: A gating terminal allows a vehicle striking it at an angle to pass ("gate") through the terminal and enter the area behind the guardrail. A non-gating terminal will redirect the vehicle along its face during an angled impact.
• Energy-Absorbing Terminals: These terminals feature an impact head that slides down the W-beam during a head-on collision, flattening the steel rail and extruding it away from the vehicle. This process controlledly absorbs the vehicle's kinetic energy.

Crash Cushions (Attenuators)

Crash cushions are used to shield rigid, wide hazards such as toll booths, gore areas at freeway exits, or concrete barrier ends.

• Compression-Based (Redirective): Consist of steel or plastic cells that compress under impact. They contain internal cables that guide the vehicle and prevent it from pocketing or vaulting, redirecting side impacts.
• Inertial Barriers (Sand Barrels): A series of plastic barrels filled with sand. They are non-redirective and work by transferring momentum from the vehicle to the sand. The mass of sand increases closer to the hazard to provide controlled deceleration. Sand barrels are destroyed upon impact and must be completely replaced.