###### Abstract
[11] presented a numerical study evaluating the performance of UHPC (90-190 MPa) under ogive-nosed projectile impacts with striking velocities from 300 m/s to 1000 m/s, where the effects of the compressive strength, projectile striking velocity, and projectile CRH on the DOP and cratering damage of targets are discussed by applying a calibrated and validated K&C material model. An empirical equation for the DOP prediction was proposed. In this work, the numerical results of projectile impacts lack sufficient experimental comparisons and verifications, and it was found that the empirical equation overestimates the penetration resistance of the UHPC. [PERSON] et al. [12] established a novel dynamic constitutive model for UHPC based on the KCC model, which was applied to numerically predict the resistance and damage pattern of UHPC subjected to projectile impacts and achieved good accuracy. [PERSON] et al. [13] numerically explored the effects of steel wire mesh on the penetration resistance of reactive power concrete (RPC). An empirical equation was proposed to predict the DOP of steel wire mesh-reinforced RPC targets subjected to high-velocity projectile penetrations. Generally, UHPC is treated as a homogeneous material when conducting simulations on UHPC targets subjected to projectile impacts, which has shown some shortcomings in reproducing and explaining the dynamic response. In fact, UHPC should be regarded as a two-phase composite material consisting of matrixes and reinforcing fibers. The addition of fibers is an important contributor to the high performance of UHPC [14]. Hence, treating UHPC as a homogeneous material is no longer appropriate, and a three-dimensional model that models the matrix and fibers discretely should be established. [PERSON] et al. [15], [PERSON] et al. [16], and [PERSON] et al. [17] built a mesoscale model to simulate the mechanical properties and failure characteristics of UHPC under static and dynamic loadings. The numerical results are in excellent agreement with corresponding experimental results, and the mesoscale model provides a mesoscopic perspective to analyze the responses of UHPC. [PERSON] et al. [18] carried out simulations of UHPC slab penetration and perforation experiments using a mesoscale discrete particle model. It was found that the mesoscale model perfectly reproduces cratering damage, spalling damage, and the crack-bridging effect in UHPC slabs. Although the mesoscale model performs better than the homogeneous model in the penetration simulation, the computational cost of the mesoscale model is too high to be used in some large-scale penetration simulations. The main reason of the high cost of the mesoscale model is that the number of established fiber elements is too large. Therefore, some equivalent treatment must be performed on fibers to reduce their quantity in the penetration model to improve computational efficiency. The mesoscale equivalent treatment on fibers in UHPC has rarely been studied before. In the present study, an efficient mesoscale equivalent model based on the bond-slip constitutive between steel fibers and matrixes is first developed for simulating the dynamic response of UHPC under projectile impacts and is verified by the uniaxial tests and penetration tests. Then, the validated numerical model is applied to numerically investigate the effects of the projectile striking velocity, UHPC compression strength, and volume percentage of steel fibers on the DOP of UHPC targets subjected to projectile impacts. Moreover, a modified Young equation for predicting the DOP of UHPC subjected to the projectile penetration is fitted in terms of the simulated data.