A simplified numerical approach to the evaluation of residual shaft friction induced by concrete curing in drilled shafts on granular soils

Porto Alegre, RS, Brasil Abstract: Conventional interpretation procedures of load tests on instrumented piles rely upon measurements of strains that assume as zero for strains measured at the instant immediately before starting the test as reference configuration. However, some experimental evidence shows that concrete in drilled shafts undergoes strains induced by the curing process comparable in magnitude to the strains measured during the load tests. It is therefore expected that mobilization of shaft friction takes place before the load test. Several authors have performed experimental and numerical analyses aiming to quantify the influence of those pre-load test concrete volumetric strains on the measured bearing capacity using different approaches. The present work aimed to establish a reference framework for the existing and future works on this topic. In order to assess the influence of concrete strains induced by curing process on the shaft friction before the start of the load tests in drilled shafts, several finite element numerical simulations are performed, considering the thermal, autogenous and drying strains. The analyses consider concrete as an isotropic linear-elastic material and the soil as an elastic-plastic material using the Mohr-Coulomb constitutive model natively implemented in the software ABAQUS. The results are interpreted focusing on the relevancy on the bearing capacity and load distribution along drilled shafts considering or not the strains


INTRODUCTION
The consideration of shaft friction mobilized during the installation of driven piles, prior to load test procedures, is a fundamental issue in foundation engineering [1]. In the context of drilled shafts, variations of normal stresses as well as associated mobilized shaft friction at the pile-soil interface, prior to external load application, should be also properly evaluated [2]. These distributions are expected to be notably governed by concrete volumetric shrinkage or expansion strains during pre-load test phase.
Measurements during pre-load stage of instrumented pile load tests revealed significant variations in the strain profile, which would alter the reference configuration for the instrumentation zero readings [3]- [5]. In particular, Viggiani and Vinale [4] and Pennington [5] reported strain measurements along the shaft of instrumented piles, illustrated in Figure 1 and Figure 2, where negative strains refer to swelling, while positive strains reflect shrinkage. The results emphasized that the concrete undergoes significant volumetric shrinkage strains in a pre-load test phase.  Strain measurements during the curing period for a drilled pile with 1.5 m diameter [5].
Based on strain measurements together with temperature rising profiles induced by the concrete curing process recorded immediately after concrete casting in large diameter drilled shafts, Pennington [5] estimated the mobilized shaft friction. Calculated values for the unit shaft friction for both residual stresses prior to test and during pile load tests are shown in Figure 3. For residual shaft friction, the volumetric strains in the pile due to the curing induced contraction in the upper portion of the pile, generating downward relative movements and consequently positive shaft friction. On the contrary, the residual shaft friction is negative along the lower part. Although it may appear that the average of the residual stresses tends to a vanishing value, it is however expected to modify the equilibrium stress distribution along the pile during loading.

Figure 3.
Comparison of residual shaft friction with shaft friction establish from load test for a 1.5 m diameter pile [5].
It comes from the above experimentally based analyses that the concrete curing phenomena can be viewed as an important component of pile-soil interaction, thus affecting the mechanical state in the soil around the pile.
Concerning the available shaft resistance in drilled shafts, rational procedures for its evaluation in granular soils are classically based on the assumption that the shaft friction mobilized at the pile-soil interface follows the linear Coulomb friction model. In the simplified framework in which the residual stresses are disregarded and the geostatic state of stresses is preserved, the shaft friction at any depth z along the pile-soil interface may be expressed as: It comes from the above experimentally based analyses that the concrete curing phenomena can be viewed as an important component of pile-soil interaction, thus affecting the mechanical state in the soil around the pile.
Concerning the available shaft resistance in drilled shafts, rational procedures for its where τ is the unit shaft friction, σ′h is the acting effective horizontal stress, δ is the interface friction angle, σ′v0 is the effective initial vertical stress, Ks = τ/(σ′v0tanδ) = σ′h/σ′v0 is a measure of the acting lateral earth pressure, and β = τ/σ′v0 = Ks tanδ is a shaft friction design parameter.
Although this assumption might appear at first glance questionable from the mechanical viewpoint, Burland [6] highlighted that this expression represents a simple and logical starting point evaluating the pile shaft friction from well-established soil mechanics properties.
Parameters Ks(z) and β(z) seek to encompass in a global manner the essential soil characteristics and associated uncertainties in pile analysis and design. This formulation takes implicitly into account the stress history of the soil, mobilized friction angle and pile-soil interface properties, grain-size distribution, as well as changes in lateral stresses induced by pile installation procedures and straining at the pile-soil interface caused by concrete curing process. To illustrate the importance given to stress history and related K0 profile Mayne and Kulhawy [7] and Kulhawy [8], using Ks = K0 for β, considers that if overconsolidation is disregarded at shallow depths (constant value of K0 -Normally Consolidated soil), the respective β profiles would also be constant with depth (dashed lines in Figure 4). Considering δ constant with depth, one can note that the main influent factor on the increase of β at shallow depth should precisely be the preexisting K0 profile. The mobilized interface friction angle δ(z) has been the subject of several studies pointing out its dependence on the pile-soil interface roughness. Typical δ(z) values range from the critical state friction angle ϕ′crit, for smoothed interfaces, to the peak friction angle ϕ′peak, for rough interfaces. Drilled shafts always exhibit high roughness at the pile-soil interface and failure yielding is likely to occur in the soil mass, following a simple shear mode governed by ϕ′crit angle.
According to Kulhawy [8] and [9], the typical profiles for β and Ks decreasing with depth ( Figure 4) can be explained as reflecting the reduction in K0 with depth together with the decrease in soil friction angle as confining stresses increase.
Focusing the analyses on the effects induced on the shaft friction of floating drilled shafts embedded in granular soils, in the pre-load test stage, Mascarucci [10] and Mascarucci et al. [11] performed axisymmetric numerical simulations in axially load piles considering curing strains coupled with evolving stiffness during the curing process. Both approaches used the standard finite-difference FLAC 2D software with a strain softening behavior for the interface constitutive model and a Strain Softening Model for the soil [12]. These studies emphasized that restarting the strain measurements in instrumented piles immediately before the load test would introduce significant errors in the distribution of shaft friction along the pile-soil interface.
Based on a simplified but consistent formulation, the present work aims at presenting a reference framework for existing and future numerical analyses. Restricting the subsequent analysis to concrete drilled shaft embedded in granular soils, this work focuses on the effects induced on the shaft friction by concrete curing strains during pre-load test stage. In that respect, the analysis is undertaken in the context of fully drained conditions, indicating that pore pressure effects are not relevant for the proposed approach.

Numerical Model
As the problem of cylindrical piles axially loaded in homogeneous soil (usual configuration for drilled shafts) complies with the revolution symmetry with respect to the pile axis, axisymmetric modeling is adopted for bearing capacity analyses. The overall dimensions of the model in terms of the pile length L and pile diameter D, together with model boundary conditions are shown in Figure 5. The different zones in Figure 5 were established for mesh control and refinement. The typical finite element model discretization used is shown in Figure 6. Four-node axisymmetric quadrilateral elements with bilinear displacement CAX4, available in the ABAQUS finite element library, were used for both pile and soil. Due to the roughness classically observed along drilled pile shaft [13], resulting from drilling and casting concrete processes, a perfect bonding condition is assumed at the pile-soil interface.
The width and height of the geometric model are respectively fixed as B = 25D and H = 2.5L, according to standard discretization used in foundation analyses [14]. As regards material constitutive characteristics, concrete was modeled as an isotropic linear-elastic material, with Young's modulus Ec = 30 GPa (corresponding approximately to fck = 30 MPa [15]) and Poisson's ratio νc = 0.2, whereas the behavior of the homogeneous soil is described by means of an non associated elasto-plastic Mohr-Coulomb model, with Young's modulus Es = 50 MPa, Poisson's ratio νs = 0.2, friction angle ϕ = 29° and dilatancy angle ψ = 1°. Physical material parameters of Ottawa sand defined in Han et al. [16] as specific gravity Gs = 2.65, minimum void ratio emin = 0.48 and maximum void ratio emax = 0.78 were used. The value of the coefficient of earth pressure at rest is fixed to K0 = 0.4. For the purpose of numerical model validation, a convergence analysis was performed to define the finite element mesh configuration, comparing the results obtained using the model with those presented by Han et al. [16] in analogous analysis involving a 300 mm diameter and 10 m long pile. Dry sand conditions were assumed, with relative density ID = 50%, corresponding to a void ratio e = 0.63 and an effective specific weight γ′ = 15.95 kN/m 3 (density d = 1,625.77 kg/m 3 ). For sake of simplicity, the same density was used for both soil material and pile concrete in all subsequent analyses.
The numerical simulations, including the validation analysis, were performed following a three steps procedure ( Figure 7): geostatic step, in which the dead load is applied by acceleration of gravity g = 9.81 m/s 2 using an automatic time increment scheme under small deformations conditions; curing_process step, for pile thermal volumetric strains that are imposed following fib Model Code recommendations [17]; and load_test step, in which a prescribed displacement of w = 10%D is incrementally applied.
For the preliminary numerical validation and convergence analysis, the concrete step curing_process was not accounted for, disregarding curing strains. Comparison of model predictions obtained herein and results from Han et al. [16] are shown in Figure 8. The numerical values for ultimate total (Qult), lateral (Ql,ult) and base (Qb,ult) resistances are presented in Table 1. The perfect agreement observed between the present simulations and results provided in Han et al. [16] validate the proposed modeling.

Numerical assessment of residual shaft friction
A The purpose of this section is to perform a series of finite element simulations to investigate the effects of concrete curing on the mobilized shaft friction of drilled shafts. Keeping the pile length fixed to L = 20 m, assessment of pile slenderness L/D effects were investigated varying the pile diameters in the range of 0.5 m to 1.5 m (L/D ranging from 40 to 13.33) for both dry (S = 0) and saturated (S = 1) sand. Appropriate effective specific unit weight of γ′ = 15.95 kN/m 3 (d = 1,625.77 kg/m 3 ) and γ′ = 9.93 kN/m 3 (d = 1,012.27 kg/m 3 ) were respectively adopted for the dry ad saturated conditions. General characteristics of the numerical finite element discretization used in each configuration are summarized in Table 2.

Simulation of concrete curing process
Due to microstructural mechanisms, concrete shrinkage is classically separated into autogenous and drying shrinkage [17], [18]. Hydration of the cement compounds involves mainly exothermic reactions that raise the temperature of the concrete mass (Figure 9), inducing thermal volumetric strains (εth). The total volumetric strains (εcs) resulting from the concrete curing process εcs is a sum of those three strain components (Equation 2): autogenous shrinkage εcas, drying shrinkage εcds, and thermal shrinkage εth. cs cas cds th ε = ε + ε + ε (2) Figure 9. Temperature change with time. Adapted from Mehta and Monteiro [19].
The development of the autogenous and drying shrinkage during the curing period of 28 days was calculated following fib Model Code recommendations [17]. Physically, these shrinkage components are a function of factors such as water-cement ratio, cement type and content, strength class, environmental conditions, type of aggregate, among others. In the model, these components are computed using the concrete compressive strength as a design parameter accounting at macroscopic scale for concrete strength class, aggregate type, cross-section geometry, relative humidity and duration of drying. The thermal shrinkage resulting from the temperature change Δθ induced by curing process is calculated from concrete thermal expansion, with a thermal expansion coefficient αc = 1×10 −5 K −1 as: [19] th c θ ε =α ∆ , where Δθ ∈ [0 K, 28 K] is considered in the analysis. The distribution of temperature variation raising in concrete during the curing varies with depth and is heteronomous within the cross-section of the pile. For simplicity, however, a spatially uniform temperature profile was assumed, using the temperature profile measured in a large diameter drilled shaft by Pennington [5] (Figure 10), for the entire pile. The temperature is assumed to remain constant after 20 days, with further curing strains calculated by fib Model Code recommendations [17]. In the thermal analysis it is assumed that concrete sets at maximum temperature, so that the development of differential strains between the contracting pile and the soil can be estimated from this reference time. Strains due to the thermal expansion of the pile before the maximum temperature is reached are therefore disregarded, as well as associated loading that is transferred to the soil.
Note that, in the numerical simulation of the curing process, the evolution of the strains in the concrete is imposed in the curing_process step. The temperature change Δθ was used as a kinematic time for assessing the mechanical state of the system, since material properties can be expressed as a function of temperature through a thermo-mechanical coupling. To meet the model of thermal strains proposed in fib recommendations, as displayed in Figure 11, the curing strains that are actually imposed to the pile have been evaluated considering an appropriate fictitious non-linear coefficient of expansion αc,fic for each Δθ ∈ [0 K, 28 K] by means of Equation 3. Figure 11. Imposed curing strains in the curing_process step.

RESULTS AND DISCUSSION
In the load_test step, a total displacement of 10%D was prescribed at the pile head, linearly applied during the time step. Although this maximum value of displacement has been adopted to ensure the validity of small strain framework, it is often assumed a representative of ultimate state in foundation design. For comparison purposes, numerical simulations were performed with and without accounting for the curing process for each selected slenderness L/D and saturation condition. The numerical load test simulation consisted in applying incrementally a total displacement of 10%D to the pile head after completion of the curing process.
The mobilized shaft friction τ along depth obtained from the simulations of the six different configurations defined in Table 2 are presented in Figure 12. Results correspond to the ultimate pile load obtained for 10%D total displacement. Solid lines represent simulations carried out with account for concrete curing and dashed lines stands for simulation disregarding this process (suppressing the curing_process step).
In Figure 12, τreal refers to shaft friction computed from the initial reference configuration when concrete curing starts, whereas τvirtual is computed considering the configuration reached after completion of the curing process (immediately before the start of the load test) as the reference configuration. Deviation between τreal and τvirtual can be quantified by means of: which represents the error τr introduced when volumetric concrete curing strains are disregarded in the analysis. The most important feature of numerical predictions lies in the fact that the actual distribution in shaft friction τreal at ultimate state coincides with the values calculated when the curing process is disregarded. This fact is consistent with general theorems of plasticity stating that the stress field at ultimate state is insensitive to initial stress distribution state [20], [21].
In addition, Figure 12 emphasize that significant errors can be induced when the unit shaft friction is evaluated based on the so-called virtual reference configuration. This is mainly explained as follows. The volumetric strains in the pile due to the curing induce contraction in the whole pile, generating downward relative movements in the upper part of the pile and upward relative movements in its lower part. These relative movements between the contracting pile and the adherent soil elements mobilize shaft friction in the soil elements (considered positive upwards and negative downwards). It is therefore demonstrated that "zeroing" the instruments immediately before starting a load test may reveal mechanically inconsistent for stress pile analysis. In order to observe the impact of the concrete curing strains on the total load distribution along the pile at ultimate state, normalized load distribution curves are shown in Figure 13 for the cases described in Table 2.
It is observed from curves in Figure 13 that although the normalized load distribution computed from both real and virtual conditions differ along the shaft, the corresponding values of base resistance are close to each other. It implies that the predicted ultimate shaft and base load components are not affected by the procedure adopted regarding the reference configuration in instrumented load tests. Going back to unit shaft friction analysis, the pile equilibrium expressed under real and virtual conditions respectively read: where Qb real and Qb virtual are the base resistance computed for real and virtual conditions, respectively. Combining the above Equations 5 and 6, and observing that ΔQb = Qb real − Qb virtual ≈ 0, yield ( ) Equation 7 indicate that the distribution of τr shall always exhibit a neutral point where a change in signal occurs. The location of this neutral point depends on soil and pile parameters. In homogenous soils, as considered in the present analysis, the neutral point approximately lies at a depth of z = 2/3L, which is in accordance with previous numerical works performed by Mascarucci [10] and Mascarucci et al. [11]. Numerical predictions for distributions of τr and τvirtual are in agreement with experimental data measured from instrumented piles, such as the results previously displayed in Figure 3. It is emphasized that experimental works [22]- [24] give evidence that τvirtual distribution along depth can significantly differ from the actual τ distribution, although both yield the same bearing capacity.
The calculated load-displacement curves for each case are presented in Figure 14 with and without consideration of the curing process and associated pre load-step strains. It can be noted from Figure 14 that consideration of curing strains has little effect on the ultimate load (Qult) distribution. The results summarized in Table 3 are in accordance with limit analysis theory [21], as already mentioned when discussing unit shaft friction distribution. This set of results demonstrates that curing strains slightly affect the ultimate state design of drilled shafts. However, this phenomenon is expected to influence the shaft friction distribution and bearing load-strain behavior at earlier stages, such as loads controlling serviceability limit state.

Influence of concrete curing on design parameters
The influence of concrete curing on the Ks and β parameters (related by Equation 1), which control the distribution of shaft friction in conventional pile design, has been evaluated by mean of a series of numerical simulations with consideration for the virtual and real cases. The obtained Ks profiles are shown in Figure 15 and computed for an interface friction angle δ = 29°. It should be recalled that perfect bonding condition at the pile-soil interfaced has been assumed throughout the paper and the interface friction angle is used only to calculated Ks. The distribution of coefficient β can be directly deduced from Ks since the soil profile is considered homogeneous with constant interface friction angle (β = Ks tanδ).
Referring to Figure 15, the following comments may be made to guide engineering design of drilled shafts: a) The singularity associated with the high values of Ks computed in the upper soil layers is reflecting vanishing vertical stresses in this region. b) Disregarding this upper crust, the values of Ks exhibit a slight reduction with depth and rapidly tends to a constant value. c) Referring to the so-called virtual case, it appears that Ks,virtual = τ/(σ′v0tanδ) with δ = ϕ constant along the depth and Ks,virtual = σ′h/σ′v0 exhibit close profiles along the region laying above the neutral point, whereas they progressively deviate from each other as depth increases. Except in a narrow zone located beneath the upper surface, the ratio Ks,virtual = σ′h/σ′v0 reveals close to K0 value. The latter can therefore be conveniently used in drilled pile design to characterize the initial stress state. d) The estimates of Ks,real and Ks,virtual for the earth pressure coefficient could significantly differ, indicating that disregarding the concrete curing effect amounts, the initial horizontal stress distribution at shallow depths tends to be underestimated. e) Ks is a valuable design parameter for shaft resistance, but it has no physical meaning limiting Ks value by active (Ka) and passive (Kp) earth pressure coefficient values, given that Ks always refers to the initial condition and not the current condition in the soil. f) The pile slenderness L/D has only some effect on Ks distribution close to the upper surface, without affecting its asymptotic value. g) For the two limiting saturation conditions (S = 0% and S = 100%) evaluated in this paper, it is found from the numerical simulations that saturation has qualitatively similar effects on Ks than L/D.

CONCLUSIONS
It is widely accepted that load test performed at relatively large prescribed displacements to reach the ultimate limit state is the most reliable procedure to analyze the behavior of piles, although technological factors, such the method of construction, are expected to affect the measured response. Based on these premises, numerical analyses were performed to assess the effect of curing process on the shaft friction regarded as a major parameter in pile design. The numerical analyses indicate that ultimate resistance is in fact not significantly affected by the curing process-imposed strains. The same trend is observed for base and lateral mobilized resistances.
The volumetric strains in the pile due to concrete curing induce contraction in the whole pile, generating downward relative movements in the upper part of the pile and upward relative movements in its lower part. This phenomenon explains the errors that can be introduced by "zeroing" the instruments immediately before starting a load test.
In regard to pile analysis and design, the distribution of the stress parameter Ks along the pile shaft, classically used to evaluate ultimate shaft friction profile, could be significantly affected by concrete curing while pile slenderness ratio or saturation conditions in homogeneous soils are not.