14.1 Introduction
477
data, the strain-rate effect parameters based on dynamic tensile and compressive
test data and the damage parameters based on repeated trials. The calibrated set of
parameters were then used to numerically simulate the low-velocity impact tests of
UHPCC columns and beams and reasonable agreements with test data were observed.
However, the damage parameters were obtained by adjusting the relation of the yield
scale factor h and the damage function l, which affected both the compressive damage
and tensile damage accumulation, leading to a dilemma situation that the compressive
behavior cannot be well modelled if the h-l relation was adjusted according to the
tensile behavior and vice versa. The other important issue is that in the K&C model
the elastic modulus E is determined by a built-in formula (E = 57000
√
f c /145, both
E and f c are in MPa units) and cannot be modified by users. This formula always
underestimates the elastic modulus of UHPCC, which may result in underestimation
of structural stiffness. To model the dynamic response of UHPCC subjected to a lowvelocity impact, Guo et al. (2017) calibrated the parameters of continuous surface cap
model (CSCM) (Murray 2007) in detail based on existing experimental data, such
as the parameters for failure surface functions and the strain rate effects in tension
and compression. However, for the intensively dynamic loading concerned in this
study, the CSCM model has some limitations as pointed out in (Wu et al. 2012),
e.g. the inaccurate description of compressive behavior under high pressure and
inaccurate consideration of high strain-rate effect (Kong et al. 2017b).Othman and
Marzouk (2018) presented a set of parameters of concrete damage plasticity (CDP)
constitutive model available in ABAQUS for UHPCC material. The CDP model
separately considers the compressive damage and tensile damage and supports userdefined damage input, consequently, it could predict both the compressive and tensile
behavior well. The predictive capability of their calibrated parameters was validated
by numerical simulation on two slabs subjected to repeated drop-weight impact.
However, it is known that the CDP model was originally developed for structural
responses at relatively low pressures. At high pressures, the EoS that governs the
compaction behavior becomes important, and consequently, the CDP model may
not be suitable for intensively dynamic loadings concerned in this study.
The present study aims to establish a material model for UHPCC material that
can well capture its dynamic behavior under impact and blast loadings. This involves
proposing a new tensile damage model for UHPCC which is then incorporated into
a recently proposed concrete material model (Kong et al. 2018a) (named Kong-Fang
model for simplicity), and calibrating parameters of this modified material model
based on existing and our test data. After a brief description of the original KongFang concrete material model, a new tensile damage model suitable for UHPCC
material is presented in Sect. 14.2, followed by detailed parameter calibration of
the modified material model. Then in Sect. 14.3, the improved performances of
the proposed damage model and modified set of parameters are demonstrated by
single element tests. Experimental validations and corresponding discussion will be
presented in Sect. 14.4, which is followed by conclusive remark in Sect. 14.5.
477
data, the strain-rate effect parameters based on dynamic tensile and compressive
test data and the damage parameters based on repeated trials. The calibrated set of
parameters were then used to numerically simulate the low-velocity impact tests of
UHPCC columns and beams and reasonable agreements with test data were observed.
However, the damage parameters were obtained by adjusting the relation of the yield
scale factor h and the damage function l, which affected both the compressive damage
and tensile damage accumulation, leading to a dilemma situation that the compressive
behavior cannot be well modelled if the h-l relation was adjusted according to the
tensile behavior and vice versa. The other important issue is that in the K&C model
the elastic modulus E is determined by a built-in formula (E = 57000
√
f c /145, both
E and f c are in MPa units) and cannot be modified by users. This formula always
underestimates the elastic modulus of UHPCC, which may result in underestimation
of structural stiffness. To model the dynamic response of UHPCC subjected to a lowvelocity impact, Guo et al. (2017) calibrated the parameters of continuous surface cap
model (CSCM) (Murray 2007) in detail based on existing experimental data, such
as the parameters for failure surface functions and the strain rate effects in tension
and compression. However, for the intensively dynamic loading concerned in this
study, the CSCM model has some limitations as pointed out in (Wu et al. 2012),
e.g. the inaccurate description of compressive behavior under high pressure and
inaccurate consideration of high strain-rate effect (Kong et al. 2017b).Othman and
Marzouk (2018) presented a set of parameters of concrete damage plasticity (CDP)
constitutive model available in ABAQUS for UHPCC material. The CDP model
separately considers the compressive damage and tensile damage and supports userdefined damage input, consequently, it could predict both the compressive and tensile
behavior well. The predictive capability of their calibrated parameters was validated
by numerical simulation on two slabs subjected to repeated drop-weight impact.
However, it is known that the CDP model was originally developed for structural
responses at relatively low pressures. At high pressures, the EoS that governs the
compaction behavior becomes important, and consequently, the CDP model may
not be suitable for intensively dynamic loadings concerned in this study.
The present study aims to establish a material model for UHPCC material that
can well capture its dynamic behavior under impact and blast loadings. This involves
proposing a new tensile damage model for UHPCC which is then incorporated into
a recently proposed concrete material model (Kong et al. 2018a) (named Kong-Fang
model for simplicity), and calibrating parameters of this modified material model
based on existing and our test data. After a brief description of the original KongFang concrete material model, a new tensile damage model suitable for UHPCC
material is presented in Sect. 14.2, followed by detailed parameter calibration of
the modified material model. Then in Sect. 14.3, the improved performances of
the proposed damage model and modified set of parameters are demonstrated by
single element tests. Experimental validations and corresponding discussion will be
presented in Sect. 14.4, which is followed by conclusive remark in Sect. 14.5.