Probabilistic model for stress in buried mains


Water mains in the Netherlands suffer failures many times every day. These events cause a nuisance in the surrounding areas. The pipes fail because they are loaded beyond what they can bear. Moreover, as the pipes age their load resistance diminishes. The mains need to be replaced in time to prevent failures.

Establishing an effective mains replacement strategy requires a clear picture of the existing loads and aging processes. The Comsima model (COMputation of Stresses In MAins) was developed to calculate the stresses in buried mains. Comsima uses data from the pipe, soil, settling, and traffic and ground loads. Calculations can be done for pipes with both rigid and flexible joints. The tool calculates the stress in the pipe as well as the angular displacement of a joint. Failures occur when the allowable stress (in this case the pipe material’s fluid stress) or the allowable angular displacement are exceeded. Since 2017, Comsima also offers the option of including in its stress calculations the effects of aging, such as a decrease in pipe-wall thickness in AC pipes, or a decrease in resistance to slow crack-growth in PVC pipes.

Importance of physical models in relation to other information sources

Comsima is a physical probabilistic model. This means that the model describes the physical condition of a pipe and that the model’s operation (calculation) is based on probabilities. These probabilities are determined by the probability density functions for the parameters in the model, such as wall thickness, settling and traffic loads. By conducting multiple calculations, and thus constantly establishing parameters from the probability density functions (Monte Carlo analysis), a picture emerges of the probability of a pipe’s failure (and its uncertainty), given the pipe’s properties and its surrounding environment.

The modelling of physical processes (stress, aging) in pipes is useful because it offers the possibility of determining whether individual pipes are critical and should be replaced. This cannot currently be done with the failure data. In order to achieve a complete and cost-efficient picture of pipe degradation, a combination of physical modelling (Comsima), analyses of failure data, and the results of pipe inspections is required.

Validation of Comsima with USTORE failure data

In 2018 a validation process was conducted to assess the extent to which the Comsima results for a large group of mains agreed with the USTORE failure data for the same group. To this end, Comsima was used to conduct stress calculations for more than 10,000 kilometres of water mains based on precise soil settling information taken from satellite data. The validation showed that there is a clear relationship between the Comsima results and the failures reported in USTORE over the last few years.

The accuracy of the Comsima results naturally depends on the accuracy and precision of the information used in the model.

Overview of the external loads on the pipe and stresses within the pipe. For the circumferential stress caused by vertical loads, the stress within the pipe is shown. This is the same stress division established in the NEN 3650 standard. The stress on the outside is precisely the opposite.