*A study was commissioned to analyze the internal stability of the Ohio River Greenup Locks and Dams, utilizing @RISK. The findings of the project would serve as a guide for additional rehabilitation of the system.*

The Ohio River serves as a vital area of shipping transport for the coal, petroleum and iron and steel industries. The Greenup Locks and Dam, located at Greenup County, Kentucky and Lawrence County, Ohio (and 24 miles downstream from Huntington, West Virginia) raises and lowers water levels to allow large vessels to pass through unnavigable waters. More than 62 million tons of materials (which translates to nearly $10 billion) pass through Greenup annually, with that weight expected to reach 113 million tons by 2030. For obvious reasons, proper maintenance of the Greenup Locks and Dam is critical to the financial well-being of the industries that ship materials through the area.

The middle wall of the Greenup Locks and Dam—which forms the water barrier separating two lock chambers— was constructed in 1967, and began to crack almost immediately. In 1976, steel anchors were installed in the cracked monoliths to stabilize the concrete elements. A portion of the monoliths did not crack and were not internally anchored. In 2011, a study was commissioned to analyze the internal stability of the monoliths utilizing @RISK. The findings of the project would serve as a guide for additional rehabilitation of the system.

### About the Researchers

Perry Cole—now of A&D Engineering-was the Project Manager and Lead Structural Engineer; Chirag Mehta, P.E., PMP—now of Black and Veatch-was the Senior Risk Engineer. Perry and Chirag performed this work while they were at a previous employer, INCA Engineers, Inc. (now part of Tetra Tech).

*Monte Carlo simulation allowed us to determine the probability of performance with a known level of confidence. @RISK provided all the tools to accomplish the Monte Carlo simulation and communicate the results in a manner that could be easily understood.*

*"**"*

*Perry Cole
President, A&D Engineering*

**Determining Internal Structural Stability**

The project was commissioned to investigate the performance of the lock monoliths in support of a major rehabilitation program. The questions the analysis sought to answer were:

- What is the probability of unsatisfactory performance throughout the planning horizon, through the year 2070?
- When is rehabilitation work anticipated to be necessary?
- What should be done to insure continued safe operation of the locks?

Three monolith conditions were analyzed: cracked and anchored, cracked and not anchored, and not cracked and not anchored. For this analysis, Monte Carlo simulation was used to calculate the probability of unsatisfactory performance for each year of the planning horizon. The probability of unsatisfactory performance for a component is the conditional probability of failure for a year, given that the component survived up until the previous year.

In this application, the lead engineers calculated the performance of the structural system by determining the demand on the structure from environmental loads and the structural capacity, based on material properties and geometries. The performance function was defined as structural capacity minus structural demand. When the demand on the structure exceeded the structural capacity, the performance is unsatisfactory.

The structural demand was modeled using environmental loads and load cases described in the U.S. Army Corps of Engineer Manual EM 1110-2-2602, “Planning and Design of Navigation Locks,” which considered:

- Lateral loading due to water in the lock chambers
- Uplift due to water pressure in the filling and emptying culvert
- Lateral loading due to soil contained within the monolith
- Hawser load on the monolith
- Barge impact

Then, the lock wall geometry and reinforcement configuration, size and location were modeled, based on the design drawings from the lock construction records. For the Monte Carlo analysis, the following probabilistic variables were considered:

- Concrete strength, as measured by 28-day compressive strength
- Tensile strength of the reinforcing steel
- Soil angle of internal friction
- Soil unit weight
- Tensile strength of the anchor rods

For the concrete 28-day compressive strength, reinforcing steel tensile strength and anchor rod tensile strength models, truncated normal distributions were utilized. Typically, distributions that are used in reliability models are developed based on a limited number of data points, because it is often difficult to fit “simple” distributions, where a mean and standard deviation can be interpreted and implemented into reliability models. However, during the design of U.S. Army Corps of Engineers civil works structures, minimum requirements are often specified for the materials and construction techniques that are used.

For example, the yield strength of steel or the compressive strength of concrete is always specified as a guaranteed minimum strength. Therefore, if a structure was built with minimum yield strength of 36-thousand pounds per square inch (1 ksi = 1,000 psi) for the steel, then a normal distribution would not fit correctly if the mean was 44 ksi because the yield strength would obtain values less than 36 ksi. Truncating a distribution was the proper way to handle this type of problem, as it permitted the calculated mean and standard deviation to be maintained, but did not yield values below either set lower or upper limits.

Cell references were used in the distribution definition to enhance readability of the computations and to identify the input values specific to each variable. For example, the minimum concrete compressive strength and coefficient of variation were known and the mean and standard deviation were calculated for use in the definition of the normal distribution.

“We find that the most useful feature of @RISK is the ability to define the distributions by using cell references. This allows us to clearly communicate the parameters used,” said Perry Cole, President of A & D Engineering. “Another useful feature is the ability to name the inputs and outputs, which help with keeping track of complex models.”

**The Findings**

Utilizing @RISK, the analyses for the Greenup Locks and Dam planning horizon revealed the following results:

- The monoliths that had cracked and were anchored were expected to perform satisfactorily throughout the planning horizon.
- The monoliths that are cracked and not anchored were predicted to perform unsatisfactorily for all years in the planning horizon.
- The monoliths that are not cracked and not anchored had an increasing probability of unsatisfactory performance, requiring mitigation during the planning horizon to assure continued safe operation of the locks.

The analysis provided the owners of Greenup Locks and Dam the critical information they needed to keep system functional, and continue the flow of commercial vessels through the area.

“The @RISK software was essential in modeling the change in structural performance through the planning horizon. The stability of the monoliths is based on a number of variables, each with a level of uncertainty,” said Perry Cole, President of A & D Engineering. “Monte Carlo simulation allowed us to determine the probability of performance with a known level of confidence. @RISK provided all the tools to accomplish the Monte Carlo simulation and communicate the results in a manner that could be easily understood.”