# Is there a standard formula available to calculate lateral concrete pressure from the measurements of lateral concrete strain?

As shown in the image, I have done a vibrating wire type strain gauge and pressure cell (not shown in the image) instrumentation on full scale form. the objective is to measure the lateral pressure of the concrete on the form while concrete was poured and until later initial setting time. Though the interest was to measure only the concrete pressure. As an additional information I measured strain too.

There is a doubt in the measured pressure. I checked the calibration and raw data. It seems everything is OK. But the measured values are far less than the expected theoretical value. Fortunately, We have concrete strain measurement. But unfortunately I do not know how to use the strain data to back calculate and get the lateral pressure.

Is there a standard formula available to calculate lateral concrete pressure from the measurements of lateral concrete strain?

Poured concrete after the initial plastic stage changes volume for a large number of reasons. Some changes are small like autogenous volume change ( 0.001 range), some large which can cause cracks and strain in the concrete like plastic shrinkage.

There are many studies on the concrete Volume change and ways to mitigate its undesired effects and take advantage of desired effects.

The forms will deflect a bit and give rise to the expansion of the concrete as well.

Hypothetically though ignoring all the above effects, one could try to establish the stiffness of the concrete forms by measuring the formwork under the load and finding the counterpart of its "modulus of elasticity", $$E_{formwork}$$.

Then one can use the $$\sigma=\epsilon E_{formwork}$$ This will be the stress of the concrete due to its confinement by the forms.

The pressure is simply derived from the classical Stress-strain relationship, $$\delta = E\epsilon$$. However, some materials do not have a linear portion (for example, cast iron and fluid-like, or semi-rigid concrete) to their stress-strain diagrams. To do accurate stress analysis studies for these materials, it is necessary to construct the stress-strain diagram to determine the modulus of elasticity at the stage of interest. Note $$E$$ will vary with the viscosity of the fresh concrete, which varies with time, and it may vary with temperature.

Without knowing the appropriate/actual $$E$$, the discrepancy between the pressures derived and calculated is understandable, especially the strain reading is taken at a stage (initial set) the bond strength of the concrete has not adequately developed yet, but the $$E$$ derived from the properties of the hardened concrete (such as 21 days strength) was used in the calculation.

Note the direction of the discrepancy is logically correct. With the presence of significant pore pressure in the wet concrete, it will have an effective $$E$$ that is much lower than the typical $$E$$ value due to the lower strength attained but large displacement (strain) present at the initial setting stage (the concrete is considerably less stiff).

ADD: The strain gauge setup and accuracy are questionable if there are other support mechanisms other than the gauge that exist.