Keywords: concrete, fire, heat, prediction, strength.

Strength estimation of concrete in fire-damaged structure enables engineers to propose appropriate repair strategies, if repair is practical and economically visible, or recommend demolishing. In the field, strength is estimated either using concrete cores (obtained from heat-damaged structures) or by employing certain non-destructive techniques. Concrete coring is destructive and expensive whereas current non-destructive techniques are limited in their ability to detect damage and hence estimate concrete strength accurately. In this paper, a non-linear statistical model is proposed to predict the residual compressive strength for Portland cement concrete (without pozzolanic additives). The parameters of the model include exposure temperature, water-cement ratio, type and weight fraction of aggregates, relative humidity, and testing conditions.

The model developed is based on literature data which were mainly concerned with mechanical behavior of ordinary and high strength concretes under high temperatures in the range (100-1000^oC). The data used covers water-cement ratios of (0.25-0.7), weight fraction for two types of aggregate (siliceous: basalt and granite, and carbonic: limestone), relative humidity (50-100%), two testing conditions (testing while hot, and after cooling) and different volumes of test specimens.

The predictability of the model may be ranked as very good. The multiple coefficients of determination (R²) and the proportion of variance accounted for were found to be 0.96 and 0.93, respectively. Moreover, the trend behaviors of the model's residual strength versus temperature are in agreement with those obtained experimentally and with Eurocode and CBE designing curves.

The sensitivity of the residual compressive strength to the model's parameters can be summarized as follows:

• The RCS is slightly affected by temperature in the range (20-100^oC). A sever reduction in PRCS occurred mainly in the temperature range 400-1000^oC.
• The effect of water-cement ratio is more pronounced at relatively low exposure temperatures, and becomes minimal as the temperature exceeds 400^oC. The effect for mixtures at w/c >= 0.45 is negligible over the entire temperature spectrum.
• A higher resistance to heat up to 800^oC can be achieved by incorporating calcareous instead of moderate-to-high silica aggregates.
• The relative humidity of concrete has a pronounced effect on the concrete resistance to heat especially when exposed to temperatures of up to 600^oC.
• At temperatures below 600^oC, the RCS is higher for specimens tested after cooling as compared to those tested while hot.

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