Calculation Approach for Lateral Bearing Capacity of Single Precast Concrete Piles with Improved Soil Surrounds

Precast concrete (PC) piles with cement-improved soil surrounds have been widely used for soft ground improvement. However, very few calculation approaches have been proposed to predict the lateral bearing capacity. *is study aims at investigating the lateral capacity of a single PC pile reinforced with cement-improved soil through a series of 3D finite element analyses and theoretical studies. It is revealed that application of cement-improved soil around the PC pile can obviously reduce the induced lateral deflections and bending moments in the pile and can significantly increase its capacity to resist lateral loading. To account for the reinforcement effect of cement-treated soil, a modified m approach is proposed by introducing a modified coefficient to enable the predictions of the lateral bearing capacity for such reinforced PC piles. It is revealed that the modified coefficient is approximately linearly related to the compressive bearing capacity of improved soil surrounds.


Introduction
Deep cement-mixing (DCM) column has many advantages, such as a large volume, limited environmental disturbance, rapid construction, and low cost, so it is extensively used in soft ground improvement.However, the DCM column strength is significantly affected by soil conditions, which results in a low column uniformity and poor reinforcement effect [1].Although a precast concrete (PC) pile has many advantages with various applications, the strength of the concrete pile cannot be sufficiently utilized under either vertical or lateral loading, and failure caused by soil failure can always occur, which makes it uneconomical for use in soft ground improvement [2].To solve the abovementioned problems, the PC pile with improved soil surrounds, produced by inserting a PC pile into a DCM column before the initial setting of cement-improved soil (Figure 1), has recently been proposed [1,2].In this way, the high-strength PC pile is designed to bear a load, and the improved soil surrounds act to transfer axial force into the surrounding soils by skin frictions [2].To date, this new type of composite pile has attracted considerable attention owing to its low cost and high effectiveness and has been successfully applied to soft ground improvement [3][4][5].
To investigate the vertical bearing characteristics of PC piles with improved soil surrounds, a series of pile load tests, numerical simulations, and theoretical models have been carried out [5][6][7][8][9].ese studies verified that the application of cement-improved soil surrounds could greatly improve the vertical bearing capacity of the PC pile and reduce its settlement.However, further studies are also needed to evaluate the contribution of improved soil surrounds to the lateral performance of PC piles.Liu [10] performed full-scale lateral load tests on several PC piles with improved soil surrounds.e test results showed that owing to the presence of outer improved soil surrounds, the lateral bearing capacity and the lateral stiffness of the PC piles are significantly increased.Rollins et al. [11] performed lateral loading tests on an existing pile group modified with jet-grouting and cementmixing column reinforcement around the pile caps.It was observed that the lateral resistance of the existing pile group foundations could be significantly increased with jetgrouting and cement-mixing reinforcement.Based on the field tests of Rollins et al. [11], Lin et al. [12] used the finite di erence simulation method to model the laterally loaded pile groups in soft clay with or without the jet-grouting columns.In addition, Wang et al. [13] and He et al. [14] carried out monotonic and cyclic lateral loading tests to investigate the contributions of the jet-grouting column reinforcement to improve the lateral performance of the single cast-in-place pile.
Although eld observations and numerical modeling of laterally loaded piles with jet-grouting or cement-mixing column reinforcement have been reported, systematic studies pertaining to the contributions of cement-treated soil surrounds to the lateral capacity of PC piles are still somewhat lacking.Indeed, there is still much that is not well understood about the lateral capacity of PC piles with such improved soil surrounds.In addition, there has generally been a limited amount of theoretical studies pertaining to the lateral bearing capacity of single PC piles with improved soil surrounds, so this requires further investigation.
is paper aims at conducting a comprehensive study on the lateral response of PC piles with improved soil surrounds as well as the m approach for predicting the bearing capacity under lateral loading.To achieve the research objectives, three-dimensional (3D) numerical analyses that were rst validated against eld test results were performed using Midas/GTS nite element software.
e e ect of outer improved soil surrounds on the lateral response of PC piles was further assessed.Moreover, a modi ed m approach accounting for the cement-improved soil reinforcement was proposed for the reinforced piles within the cohesive soil, and the suitability of the proposed m approach for predicting the lateral bearing capacity of such reinforced piles was also assessed.

Numerical Simulations
In order to evaluate the e ect of cement-improved soil surrounds on the lateral bearing performance of a PC pile, the Midas/GTS software was used to establish threedimensional models of PC piles with and without improved soil surrounds under lateral loading, according to the full-scale pile load tests.e test project was performed in Nantong, which is located along the southeast coast of China.Extensive eld tests and laboratory tests were performed to characterize the subsoil conditions.Specifically, conventional laboratory soil tests were carried out to determine the unit weight, compression modulus, and relevant shear parameters of the soil mass.Moreover, a cone penetration test (CPT), which is one of the most commonly used eld test approaches in geotechnical investigations, was performed to determine the ultimate unit skin friction and tip resistance.e soil pro le and engineering properties of the test site are presented in Figure 2. It can be seen that the soil pro le near the ground surface consists of a marine silty clay layer underlain by a silty sand deposit.e de ection and bending moment distribution of the two types of piles are then investigated in detail.e detailed information of the test piles is shown in Table 1.

Numerical Modeling.
In general, there are di erent numerical approaches for analysis of the lateral bearing capacity of a single pile [15].One approach is to establish the pile-soil model based on the lateral pile-soil interaction.
e other is to establish the pile-spring model by replacing the pile-surrounding soil with equivalent spring and damping based on the Winkler elastic foundation beam theory.Although the pile-spring model can simulate the compressive and nontensile behavior of pile-surrounding soil, it cannot re ect the plasticity of pile-surrounding soil.It is well known that with a gradual increase in the lateral load applied at the pile head, the pile-surrounding soil changes from behaving elastically to plastically, and the plastic zone around the pile is gradually extended.In addition, in the pile-spring model, the size of the pile-soil contact surface is assumed to be constant under di erent loading conditions.In the pile-soil model, however, the contact surface may change with varying loading conditions, which is more consistent with the actual pile-soil interaction.erefore, the pile-soil model was adopted in this study.2 Advances in Civil Engineering e typical 3D finite element models used for the analyses are shown in Figures 3(a) and 3(b).In the horizontal direction, the surrounding soil was extended by 10 times greater than the pile diameter.Meanwhile, in the vertical direction, the surrounding soil was the same length as the pile.e soil and pile were modeled using 3D eight-node linear brick elements, with a refined mesh of 33,600 elements.Particularly, the mesh used for the soil was sufficiently fine in the region close to the pile.Regarding the meshing convergence issue, a numerical test shows that further halving the current mesh size can only result in a change of numerical results of no more than 0.6%. is suggests that sufficiently accurate simulation results can be achieved with the mesh size adopted in this study.
A total stress analysis under undrained conditions was adopted in this study to simulate the field lateral load tests on the PC pile with improved soil surround, which did not account for the pore water pressure response.Such a modeling technique has been used by many scholars [16][17][18][19][20] in investigations of the behavior of a single pile subjected to lateral loading.Accordingly, the total stress parameters for both the undrained modulus and shear strength of the cement-treated and untreated soil were assigned in this numerical study.e Mohr-Coulomb failure criterion was adopted to compute the failure loads of pile-surrounding soils deforming under undrained conditions.e undrained shear strength C u � 20 kPa and undrained Young's modulus E u � 750C u for the silty clay were then determined through the undrained shear tests and the work of He et al. [20], respectively.e cement-treated soil was also assumed to obey the Mohr-Coulomb failure criterion.Specifically, the undrained shear strength and Young's modulus of the cement-treated soil were obtained from the work of Jamsawang et al. [21] and Tyagi et al. [22].According to Jamsawang et al. [23], the tensile strength (σ t ) of cementtreated soil can be defined as 0.15 times the compressive strength.e constitutive models and parameters used in this study are listed in Table 2.It is worth noting that the cement-improved soil is considered as homogeneous without varying with depth.
e interaction between the PC pile and the improved soil surrounds was modeled by defining zero-thickness interface bond-slip elements at their contact surfaces, so as to allow for the relative shear displacement between, and the separation of the two objects.e interface cohesion and friction coefficient between the pile and cementtreated soil were derived as 200 kPa and 0.65, respectively.Considering that slippage and gapping occurs during lateral loading, the interaction between the cement-improved soil and the surrounding soil was modeled using the Coulomb friction model.An interface friction coefficient of 0.35 was applied in this study.e finite element analyses were comprised of two primary steps.First, the initial stress field of the pile-soil system was balanced.In the next step, lateral loads were applied at the pile head by multiple-step loading.Advances in Civil Engineering surrounds, respectively.It can be seen that the computed pile-head de ections agreed well with the numerical results in the case of a lateral load less than 100 kN.However, when the lateral load exceeded 100 kN, the computed results were signi cantly di erent from the corresponding measured values.For laterally loaded exible piles, failure of the pilesoil system can always be a result of the plastic damage of the pile following yielding of the pile-surrounding soil [20,24].Additionally, the lateral bearing capacities of these two types of piles were determined to be 125 kN and 95 kN, respectively, according to Technical Code for Building Pile Foundations [25].erefore, in this study, once the lateral load was applied up to 100 kN, the severe tension-induced damage in the pile occurred and its exural rigidity obviously decreased, resulting in a steep increase in the pile de ection.However, the numerical modeling does not take the pile damage into account, which leads to the foregoing di erence.It is worth mentioning that the lateral bearing capacity of the PC pile with cement-treated soil reinforcement was approximately 30% larger than that of the unreinforced PC pile, which indicates an essential strengthening e ect with the application of cement-improved soil around a PC pile.

Validation and Results.
Figure 5 shows the computed lateral de ection along the PC pile with and without improved soil surrounds in the case of a lateral load of 100 kN.It can be observed that both types of piles behaved as exible piles, and the pile de ection decreased nonlinearly from the pile head, with the de ection primarily distributed at the upper part of the pile body. is suggests that the shallow soil layer, which ranged from 0 m to approximately 5 m below the ground surface, played a key role in the bearing performance of the PC pile subjected to lateral loading.A comparison indicates that the lateral deection along the PC pile with improved soil surrounds was obviously smaller than that of the PC pile alone in the soil.
is is because the pile de ection at a certain depth was closely related to the pile-soil modulus ratio.When a PC pile   was concentrically inserted into the cement-improved soil surrounds, the greater constraint e ect provided by the outer cement-improved soil undoubtedly caused a noticeable decrease in pile de ection.
Figure 6 shows the computed bending moment along the PC piles with and without improved soil surrounds in the case of a lateral load of 100 kN.It is evident that the variations in the bending moment along the PC pile with improved soil surrounds were consistent with that along the PC pile alone in soil.To be speci c, the bending moment increased monotonically to a peak and then gradually decreased, which had also been reported by Liu [10].It is clearly observed that the maximum bending moment of the PC pile with improved soil surrounds was signi cantly smaller than that of the PC pile alone in soil. is can be attributed to the fact that the presence of the improved soil surrounds resulted in a large equivalent diameter of the pile, which could generate greater soil resistance to the pile de ection, thus signi cantly reducing the bending moment in the PC pile.e reduction is also in agreement with Voottipruex et al. [6] and Liu [10], who found that the outer improved soil surrounds may play a critical role in load transfer and can e ectively transfer the lateral load from the PC pile to the surrounding soil.
Although the application of cement-improved soil around a PC pile could greatly reduce the accumulation of pile de ection and bending moment, both types of piles experienced similar trends when subjected to lateral loading. is suggests that the lateral bearing behavior of the PC pile with improved soil surrounds was similar to that of the PC pile alone in soil.erefore, the m approach applicable to a single PC pile without improved soil surrounds can still be used to calculate the lateral bearing capacity of a single PC pile with improved soil surrounds.But related parameters in the existing m approach need to be modified so as to reflect the reinforcement effect of improved soil surrounds on the lateral bearing performance of PC piles.

Modified m Approach for PC Piles with
Improved Soil Surrounds

m Approach.
e m approach was proposed based on the Winkler elastic foundation model and Euler-Bernoulli beam theory, and it is assumed that the lateral soil resistance at a certain depth equals the product of the corresponding lateral resistance coefficient and pile deflection.Moreover, the lateral resistance coefficient linearly increases with the depth and is equal to zero at the ground surface.
According to the Technical Code for Building Pile Foundations [25], the calculation formula for the lateral bearing capacity of a single PC pile is expressed as where R ha � design value of the lateral bearing capacity of single PC piles (kN); β � reduction coefficient, generally taken as 1.0; χ 0a � allowable lateral deflection at pile head (m); v x � pile-head deflection coefficient; EI � flexural stiffness of pile (kN•m 2 ); and α � lateral deformation coefficient of pile, which is given as where b 1 � calculation width of pile (m) and m � proportional coefficient of lateral resistance coefficient (kN/m 4 ), which can be determined by the Technical Code for Building Pile Foundations [25], as summarized in Table 3.
It should be noted that for the PC piles with improved soil surrounds, the flexural stiffness and tensile strength of the outer cement-improved soil are significantly lower than that of the inner PC pile, and severe cracking in cementimproved soil can be easily induced under lateral loading.In other words, slippage and separation is likely to occur at the interface of the PC pile and the cement-improved soil during loading.us, the two parts of the reinforced piles cannot work together to support and transfer the lateral load effectively, especially in cases of cement-improved soil with low strength.Based on the above analysis, it is reasonable to treat the outer improved soil surrounds as the pilesurrounding soil with greater soil resistance, rather than as the extended diameter of a PC pile.As a result, the parameters EI and b 1 of the PC pile were used to predict the lateral bearing capacity of a PC pile with improved soil surrounds.
It is well known that the proportional coefficient, m, is a key parameter for analysis of laterally loaded piles when using the m approach.However, the m value is closely dependent on soil properties, pile material, loading conditions, and so on [26].Hence, in order to determine the m value applicable to PC piles with improved soil surrounds, it is required to consider the reinforcement effect of improved soil surrounds on the lateral PC pile.

Back-Calculation of m Value.
In cases of the lateral load on the free-head pile is applied at the ground surface, the coefficient, m, is determined from ( 1) and ( 2) as follows: where P and Y 0 � lateral load (kN) and pile-head deflection (m), corresponding to R ha and χ 0a , respectively.From (3), it can be seen that the variation of m with Y 0 can be deduced according to the P-Y 0 curve derived from pile load tests.In general, at a pile-head deflection of 10 mm, the applied load, P, is defined as the design value of lateral bearing capacity of single piles.As a result, the m value used to determine the lateral bearing capacity of single piles can be obtained from the m-Y 0 curve.
Figure 7 shows the deduced m-Y 0 curves for single PC piles with and without improved soil surrounds based on  1 and 4. Generally, under large de ection levels, the m value gradually decreased with the increasing deection.At a pile-head de ection of 10 mm, the backcalculated and recommended m values (shown in Figure 7 and Table 3, resp.)are compared in Table 5.From these results, it is clearly demonstrated that the back-calculated m value for the PC pile without improved soil surrounds was very close to the recommended m value.However, the back-calculated m values for PC piles with improved soil surrounds were 1.6 to 5.0 times larger than the recommended values for PC piles alone in soil. is denotes that the improved soil surrounds led to an obvious increase in the m values of the PC piles.

Modi ed Coe cient.
In order to clearly distinguish the signi cant di erence between the back-calculated and recommended m values, a modi ed coe cient, ξ m , is de ned as follows: Table 6 shows the modi ed coe cients for di erent test piles and several parameters of outer improved soil surrounds.It can be seen from Table 6 that the strength of  Advances in Civil Engineering cement-treated soil with the wet spraying method was generally lower than that with the dry spraying method.It is known that the improvement of the soil with cement treatment is referred to as the chemical reactions between cement and the soil particles, and the water-cement ratio has an important influence on the mechanical properties of cement-treated soil.Once the water-cement ratio exceeds the optimum level, the strength of cement-treated soil obviously decreases with the increasing water-cement ratio [27,28].It is worth noting that, in practical engineering, the initial water content of the natural clay undoubtedly increases the water-cement ratio of the cement-treated soil.us, it can be concluded that the lower strength of a DCM column can always occur when constructed using the wet spraying method, especially in coastal areas with a high groundwater level and water content.
It can be observed that the m value for PC piles with improved soil surrounds was not only dependent on soil properties but also closely related to the compressive strength and cross-sectional area of outer improved soil surrounds.e larger the cross-sectional area and the higher the compressive strength of the improved soil surrounds, the larger the modified coefficient.is can be attributed to the different reinforcement effects of outer improved soil surrounds.Fortunately, the reinforcement effect of outer improved soil surrounds was found to be positively related to its compressive bearing capacity (denoted as Q u (kN)).us, a correlation relationship between ξ m and Q u can be established.As shown in Figure 8, for PC piles with improved soil surrounds, ξ m exhibited an In summary, for laterally loaded single PC piles with improved soil surrounds, the m value can be obtained by introducing the modified coefficient.us, a modified m approach is proposed by modifying the m value based on the existing m approach, that is, by substituting the modified m value into the existing equation.e proposed m approach can account for the cement-treated soil reinforcement.

Evaluation of the Modified and Existing m Approach for Piles with Improved Soil Surrounds
According to the pile load test data presented in this study, the lateral bearing capacities of these test piles were calculated using the modified and existing m approach, as shown in Figure 9.It is clearly seen that the lateral bearing capacities obtained by the modified m approach were all in good agreement with the measured results, with a relative error range of 15%.ese results also indicate that the modified m approach was able to effectively account for the reinforcement effect of outer improved soil surrounds.erefore, it is feasible and appropriate to predict the lateral bearing capacity of PC piles with improved soil surrounds by using the modified m approach.However, the calculated bearing capacities from the existing m approach were obviously smaller than that measured, indicating that the existing m approach would significantly underestimate the lateral capacity of such reinforced piles. is implies that designs of laterally loaded single PC piles with improved soil surrounds using the existing m approach would tend to be conservative.
To further assess the suitability of the modified m approach for the analysis of laterally loaded piles with improved soil surrounds, the deflection and moment responses derived using the modified and existing m approach were compared with the numerical results (from Figures 5 and 6), as demonstrated in Figures 10 and 11, respectively.It is evident that both the pile deflection and moment from the existing m approach were significantly larger than those from the numerical results.However, compared with the numerical results, the modified m approach can accurately predict the lateral response of a reinforced PC pile. is also further indicates that the proposed m approach is applicable for laterally loaded single PC piles with improved soil surrounds and would be especially useful in practice.

Conclusions
In this paper, the numerical and theoretical investigation on the lateral bearing capacity of a single PC pile with improved soil surrounds was presented.
e existing m approach (recommended by Technical Code for Building Pile Foundations (JGJ 94-2008)) was modified by taking into account the reinforcement effect of outer improved soil surrounds.e primary conclusions that can be obtained from this study are summarized below: (1) By applying cement-improved soil around a PC pile, the lateral deflection and the maximum bending moment of the PC pile are significantly reduced.Nevertheless, the lateral performance of the PC pile with improved soil surrounds is similar to that of the PC pile alone in soil.us, the lateral bearing capacity of a single PC pile with improved soil surrounds can still be calculated using the m approach.(2) To account for the reinforcement effect of improved soil surrounds on the laterally loaded single PC piles, a modified m approach was proposed by introducing a modified coefficient based on the existing m value.e modified coefficient, ξ m , is approximately linearly related to the compressive bearing capacity of cement-improved soil surrounds.
(3) Compared with numerical results, the proposed m approach can accurately predict the lateral bearing capacity of single PC piles with improved soil surrounds.In addition, the existing m approach obviously underestimates the lateral bearing capacity of such reinforced PC piles, thus leading to a conservative prediction of their lateral performance.

Figure 1 :
Figure 1: (a) Schematic diagram of PC pile with improved soil surround; (b) photo of eld excavation.
Figure 4  compares the measured and computed lateral load (P) versus the deflection (Y 0 ) curve at the head of the piles with and without improved soil

Figure 2 :
Figure 2: Soil profile and engineering properties of the test site.

Figure 3 :
Figure 3: 3D nite element models of (a) entire pile-soil system and (b) pile with improved soil surround.

Figure 8 :
Figure 8: Correlation between the modified coefficient and compressive bearing capacity of improved soil surrounds.

Figure 9 :Figure 10 :Figure 11 :
Figure 9: Comparison of lateral bearing capacity using the modified and existing m approach and measured results.
Note.PCI � PC pile with improved soil surround; PC � PC pile without improved soil surround.

Table 2 :
Material models and parameters used in this study.

Table 6 :
Modified coefficients for different test piles and several parameters of outer improved soil surrounds.

Table 5 :
Back-calculated and recommended m values at a pile-head deflection of 10 mm.
u � 0 (corresponding to the PC pile without improved soil surrounds), the modified coefficient, ξ m , should be determined as 1.0.us, the linear correlation function is fitted as follows: