‘Lessons learnt from recent deep excavation projects about ground and structural stiffness’

The accuracy of underground structural analysis is reliant on estimating the stiffness of the materials resisting and imposing loads; the ground and the structure, and their interaction over the design life.

My upcoming presentation at the GE Basements and Underground Structures Conference will focus on some lessons learnt from recent projects involving deep excavations that highlight the importance of both ground and structural stiffness.

Lesson 1: Stiffer ground can govern design

When analysing embedded retaining walls to Eurocodes, it is typical to select a characteristic value for the ground stiffness that represents a moderately conservative point less than the mean of the data. For most aspects of the wall design this cautiously “inferior” stiffness will be appropriate, but consideration should be given to scenarios where stiffer ground may introduce more onerous demands.

For example, when constructing a basement by a top-down methodology the base slab, which is connected to the retaining wall, is installed without any axial load. Early age thermal shrinkage will result in the slab "pulling" on the wall and creating tension in the element, which will be increased further by long-term shrinkage as well as decommissioning of any de-watering system within the excavation, which can produce a net outward load on the wall. Such tension in slabs can be problematic for watertightness and in terms of the demands to be carried by reinforcement across the joint with the wall.

The magnitude of this tensile stress will be determined by the restraint provided by the walls, which is directly affected by the ground it is embedded in. Therefore, when determining the demands in basement slabs and wall connections, I would recommended that a check is undertaken using “superior” characteristic stiffness parameters to capture this “high restraint” behaviour. This may be particularly important to consider in soft rocks where the intact insitu stiffness may be significantly higher than values estimated from disturbed sampling.

Lesson 2: Potential efficiencies from assessing concrete flexural stiffness

The flexural stiffness of reinforced concrete is the product of the concrete modulus and second moment of area of the section and is a fundamental property when designing elements using classical beam theory. Selection of this value will have direct impact on demands on the wall and therefore quantities of reinforcement specified, often governed by serviceability requirements, i.e. crack width.

Ciria Guide C760 recommends a reduction in flexural stiffness for analysis, from an uncracked initial value, of 70% during construction and 50% in long term conditions. This is a sensible starting point, and the approach has stood the test of time, but the guide does acknowledge that the value of stiffness adopted should strictly be determined for the reinforced section itself. In my opinion, it is worth designers undertaking more detailed assessment of the flexural stiffness for large and/or heavily reinforced elements to identify where the general rules of thumb might err on the conservative side.

The modulus of the concrete when first loaded can be higher than the 28-day value used in design for embedded retaining walls on large scale linear infrastructure projects, as construction of all embedded elements can take a relatively long time. Additionally, "long-term" quasi-permanent conditions can be achieved relatively early in the context of the overall construction programme.

If time of first loading and establishment of long-term loading is adequately considered alongside the environmental conditions, i.e. relative humidity, it is possible to build a profile of modulus against time using the estimations of creep provided in the Eurocode. Alongside this variability in modulus over time the effect of cracking on the second moment of area of the section is difficult to assess, although relationships have been proposed by the American Concrete Institute that provide a basis for this.

Back-analysis of a recently built cut and cover structure showed the as-built flexural stiffness of the wall has dropped to below 50% of its uncracked value within two years of excavation, with further reduction predicted due to long term creep. This aligned well with a flexural stiffness predicted using direct calculation using the formulations suggested above.

However, a larger body of case studies are required before this could be used as a reliable means of assessing flexural stiffness during design.