The behavior of micropiled raft foundations subjected to combined vertical and lateral loading: numerical study

The micropiled raft offers a foundation system that combines the advantages of the conventional piled raft and the efficient installation of micropiles. In this paper, a comprehensive numerical analysis was conducted on the behavior of micropiled rafts under combined vertical and lateral loading using finite element modeling. A numerical model calibrated against full-scale axial and lateral field tests is used to conduct the analysis. The soil profile was soft clay soil underlain by a layer of dense sand. Numerous cases were analyzed to assess the lateral performance of micropiled rafts while considering several factors that may affect the performance, such as micropiles spacing, raft thickness, the magnitude of vertical loading, micropiles length, and their arrangement. The difference between the lateral performance of a primary micropiled raft and that of an existing raft enhanced by underpinning micropiles was also investigated. The lateral load capacity of the micropiled raft, the bending moment, and the shear force along the micropiles depth were estimated. Moreover, the load-sharing ratio between the micropiles and the raft was assessed. Based on the parametric study results, significant guidelines for choosing suitable micropiled raft configurations for initial design purposes were provided.


Introduction
A micropile is a small diameter "cast-in-place" pile. Micropiles were initially used to repair historic buildings damaged during World War II, which required installing micropiles by drilling through the existing foundation and filling the holes with cement grout and a steel bar (Lizzi 1982). In current practice, the diameter of a micropile is typically less than 300 mm. The use of micropiles was introduced in North America in 1973 through several underpinning applications in the New York and Boston areas, and their use has been rapidly growing ever since. Their construction methods have been improved. The advancements in drilling equipment have resulted in the ability to drill through almost any ground condition to install micropiles at any angle with minimum noise and disturbance. In addition, the relatively small size of the drilling equipment has allowed the underpinning of existing foundations even in restricted access situations (Bruce et al. 1995). Based on their construction methods, micropiles are classified into four categories by FHWA (2005). Type A: the grout is concreted without any injection pressure. Type B: injection pressure is used in pouring the grout into the hole and typically ranges from 0.5 to 1 MPa. Type C: the grout is poured first under the gravity head. Then, after the hardening of the poured grout, additional grout is poured using a sleeved pipe at a pressure of at least 1 MPa. Type D: similar to Type C, but a packer can be used at specific depths inside the sleeved pipe. Using pressurized grout as one of the installation methods has some advantages, such as densifying the surrounding soil (especially for granular soil) and increasing the shear strength of the soil along the grout-ground interface. Due to the high applied pressure, the grout will penetrate the soil, increasing the micropile cross-section (Alnuaim et al. 2016). In recent construction techniques, micropiles have been used to construct primary foundation systems or to enhance existing raft foundations for many applications, such as high-rise buildings. Strengthening the existing foundation and increasing its load-bearing capacity may be required for several reasons. Additional vertical, lateral, or vibratory loads may be applied to the foundation, increased magnitude of applied loads, or the addition of vibrating machinery (FHWA 2005). Practically, structures are often subjected to lateral loads due to wind, ship impact, wave loading, etc. In the case of onshore structures, this lateral load can be 10-15% of the vertical load and exceeds about 30% of the vertical load in any offshore structure (Rao et al. 1998;Palammal and Senthilkumar 2018;Elsawwaf et al. 2022a). Although micropiled rafts combine the advantages of micropiles and piled rafts, no attempt has been made to investigate their response under combined vertical and lateral loading. Even the studies on micropiled raft foundations' response to pure static lateral load are minimal. Hence, in this paper, the study aims to assess the performance of micropiled rafts under combined loading and determine if micropiles play the same typical behavior of large-diameter piles under combined loading or not.

Prime objectives of the study
The soil profile used in this study was soft clayey soil underlain by a layer of dense sand. An attempt has been made to investigate the impacts of the clay undrained shear strength, thickness of soft clayey soil layer, micropiles length, and magnitude of vertical loading, on micropiled raft performance under combined vertical and lateral loading. In addition, the effects of micropiles arrangement, micropiles spacing to diameter ratio, and raft thickness were evaluated. The difference between the lateral performance of a primary micropiled raft and that of an existing raft enhanced by underpinning micropiles was also investigated. The performance was investigated in terms of the lateral response of the micropiled raft, vertical and lateral load sharing between the micropiles and the raft, and the micropiles bending moments and shearing forces.

Background
The performance of the micropiled raft foundation under lateral loading or combined loading is entirely different from that of the raft foundation. The lateral and vertical loads in the micropiled raft are partially shared between the micropiles and the raft through the interface frictions. The interface forces developed in the micropiled raft and the soil are shown in Fig. 1.
El Kamash and Han (2017) conducted a numerical investigation of existing foundations underpinned by micropiles to resist additional vertical loads applied on the raft. It was observed that micropile installation after the initial loading stage causes more vertical displacements and less percent load taken by micropiles. Moreover, the vertical displacement of the raft decreases with decreasing the initial pressure ratio (before underpinning) and the increase of micropiles length. Alnuaim et al. (2018) performed 26 different FE analyses and used Mohr-Coulomb soil constitutive Fig. 1 Interface forces developed in the micropiled raft model to study the vertical performance of micropiled rafts in clay with undrained cohesion of 30 kPa . The tolerable bearing pressure of the micropiled raft was 100% greater than that of the isolated raft. The differential settlement was only reduced when the micropiles were positioned close to loaded areas. Borthakur and Dey (2018) investigated the vertical loadcarrying capacity of the micropile group on highly plastic soft clay soil with cohesion in the range of 18-20 kPa. The loadcarrying capacity increased with increasing the micropiles' spacing and their number. Many other studies were performed in order to evaluate the vertical performance of micropiles and micropiled rafts, for example, Jeon and Kulhawy (2001), Tsukada et al. (2006), Han and Ye (2006), Farouk (2009), Hwang et al. (2017), and El Kamash et al. (2022. Abd Elaziz and El Naggar (2015) conducted two monotonic and six cyclic lateral loading tests on single micropiles in stiff to very stiff silty clay. A numerical analysis was also conducted. It was concluded that the micropile lateral capacity should be evaluated after carefully considering the micropile connectivity into the pile cap. Kyung and Lee (2018) conducted a parametric study on the lateral-load carrying capacity of micropiles in order to assess the effect of micropile inclination and load direction. The study included model load tests, finite-element analysis, and full-scale field tests. The performance of both single and group micropiles was investigated. Moreover, the micropile mechanism of lateral load-carrying was observed through the FEA. Estimated load capacities were compared to measured ones by the full-scale field load tests. Sharma and Hussain (2019) conducted a parametric study on the performance of vertical and inclined micropiles through model testing. It was observed that the ultimate lateral load tends to increase significantly for increasing the micropile length-to-diameter ratio up to 30 for vertical micropiles. A number of other studies were conducted to assess the micropiles and piles lateral behavior (e.g., Teerawut (2002), Shahrour andAta (2002), Long et al. (2004), Richards and Rothbauer (2004), Abdelhalim et al. (2020), El Sawwaf (2006). From all the studies mentioned above, it is observed that only vertical loads or lateral loads were considered in the analysis of micropiles or micropile groups. Thus, this paper aims to study the effect of combined vertical and lateral loading on micropiled rafts. Moreover, many previous studies assessed the lateral response of micropiles but in a single soil layer. Hence, an attempt has been made in the present study to consider the possible effect of the soil stratum in the lateral response of micropiled rafts.

Numerical model
The 3D model used to conduct the analysis was established using the computer program PLAXIS 3D. The model's validity was checked by using the results of full-scale field loading tests and comparing them with those obtained from the FE analysis. The advantage of the symmetry across the x-axis was taken, and half of the micropiled raft foundation was modeled to decrease the computation time. Based on the results of an incentive sensitivity analysis shown in Fig. 2, appropriate model dimensions and element size were specified by conducting a number of initial trial analyses considering different widths (18 m, 25 m, 35 m, 45 m, and 55 m), depths (25 m, 35 m, 45 m, and 65 m), and numbers of elements (214535, 305937, and 474686). The model dimensions were increased successively until the maximum horizontal displacement of the raft did not change significantly with a further increase in the model size.
The horizontal side boundary was kept at 3.2 B r (where B r is the raft width), and the vertical side boundary was maintained at 4.6 B r , as shown in Fig. 3. Vertical side boundaries with normal in the x-direction were fixed in the x-direction only, whereas vertical side boundaries with normal in the y-direction were fixed in the y-direction only. The bottom side boundary was fixed in all directions, while the top side boundary was free in all directions. 3D 10-node tetrahedral elements were used to model the soil and micropiles, while the raft foundation was modeled using 6-node triangular plate elements. In order to ensure the high accuracy of results, a denser mesh was used at locations where highstress concentration was expected (e.g., raft base, micropile The raft and micropiles were assumed linear elastic materials considering the mechanical properties (elastic modulus and Poisson's ratio). The Mohr-Coulomb model (elastic perfectly plastic behavior) was chosen for simulating the behavior of the soil. The Mohr-Coulomb model requires conventional soil parameters, including unit weight, cohesion, friction angle, dilation angle, and Poisson's ratio. In finite element analysis, interface elements are used to simulate the interaction between the micropile or the raft and the adjacent soil. These interface elements follow the Mohr-Coulomb failure criterion; as the shear stress reaches the maximum shear strength of the soil, slippage happens at the interface. In PLAXIS 3D, an interface reduction factor, R int , is used to model the interface element. R int represents the strength of the interface element as a percentage of the shear strength of adjacent soil.

Modeling of micropiles
In order to ensure that the micropile behavior is simulated in an accepted manner, its composition and construction method must be considered when modeling micropiles. First, the large portion of steel area installed in micropiles induces high elastic modulus compared to conventional reinforced concrete cast-in-place piles. The elastic modulus of the micropile can be estimated as an average weighted modulus using the relationship proposed by FWHA (2005) as (1) E micropile = (A grout * E grout + A steel * E steel )∕A micropile where E micropile = elastic modulus of the micropile; A grout = section area of grout; E grout = elastic modulus of grout; A steel = section area of steel; E steel = elastic modulus of steel; and A micropile = section area of the micropile. According to the FHWA (2005), the use of E grout = 31,000 MPa for confined grout and E grout = 23,000 MPa for unconfined grout can provide reasonable results for micropiles. Second, R int value is expected to be higher than 0.80 to simulate the rough surface condition for micropiles of Type B, Type C, and Type D since these micropiles construction techniques cause the soil surrounding the micropiles to densify (Alnuaim et al. 2016;Kyung and Lee 2018). Third, the pressurized grout for micropiles of Type B, Type C, and Type D causes a high confining pressure to the soil around the micropile, which would increase the lateral earth pressure coefficient ( K s ) (Farouk 2009;Alnuaim et al. 2018). The trend of K s variation agrees to a great extent with the variation of grout to ground bond strength given by FHWA (2005) against different grouting methods.

Comparison and validation of the model
The developed numerical model was validated through two stages to ensure the reliability and accuracy of the current FE analysis, as evident from Figs. 4 and 5. In the first stage, the results of full-scale field axial loading tests of micropile group as well as a single micropile by Kyung et al. (2017) were compared with those obtained from the FEA. Table 1 shows basic soil properties at the test site. Type C micropiles with a diameter of 0.165 m and a length of 9.00 m were used. For the micropile group, a 2.52 m × 2.52 m × 1.00 m raft supported on four micropiles with a spacing of 1.26 m was used. The average value of elastic modulus (E) of upper silty sand, middle clay, and lower silty sand was 5000 kN/m 2 , 14,000 kN/m 2 , and 14,000 kN/m 2 , respectively. Since the Type C grouting technique was used in the micropiles construction, R int tended to be high in the lower silty sand layer (uncased bond zone) and was assumed to be 0.95 (Alnuaim et al. 2016;Kyung and Lee 2018). Moreover, high confining pressure of the soil was expected, which would, in turn, cause an increase in the K s value in the lower silty sand layer (uncased bond zone). The variation of the vertical load versus displacement behavior using different values of K s for the lower silty sand layer for the micropile group and the single micropile is presented in Fig. 4a and b, respectively. Since an increase in the K s value was expected, the studied values began from a value of 1.00. Then, the K s value was increased in successive runs till there was an acceptable matching between the estimated results and the field test results at a K s value of (2.00 to 3.00). A similar approach was used by Farouk (2009) and Elsawwaf et al. (2022a) to evaluate the optimum value in K s .
In the second stage, the results of full-scale field lateral loading tests of Type C micropile group and single Type A micropile by Kyung and Lee (2018) were compared with those obtained from the FEA. The single micropile was 0.165 m in diameter and 8 m in length, and it was tested in Gongju, where the soil was found to be silty sand with a total unit weight of 18 kN/m 3 and internal friction angle of 36.3°. The used soil elastic modulus was 1800 kPa, and it was increased over depth with a rate of 1600 kPa. Since the Type A gravity grouting technique was used in the micropile construction, R int was assumed to be 0.7. Moreover, no increase in the K s value was expected. Table 2 presents basic soil properties at the test site in Gochang city for the micropile group. A 2.52 m × 2.52 m × 1.00 m raft supported on four micropiles with a spacing of 1.26 m and length of 10 m was used. The average value of E of upper silty sand, middle clay, and lower silty sand was 5000 kN/m 2 , 8000 kN/m 2 , and 8000 kN/m 2 , respectively. R int was assumed to be 0.95 in the lower silty sand layer (uncased bond zone) (Alnuaim et al. 2016;Kyung and Lee 2018). A sensitivity analysis emphasized that the R int value of 0.95 best fits the  field results. Moreover, high confining pressure of this soil layer was expected, which would in turn cause an increase in the K s value which was taken 3.0. The lateral load versus displacement variation for the micropile group and the single micropile is presented in Fig. 5a and b, respectively. It should be noted that the used value of E mp was 85 × 10 6 kN/m 2 for the four verification studies. The high stiffness of micropiles was due to the large portion of steel area due to placing a 65-mm diameter steel rod reinforcement and a permanent upper steel casing. From Figs. 4a-b and 5b the load-displacement plots obtained from the field tests and the FE analysis were in good agreement with each other. For the laterally loaded micropile group presented in Fig. 5a, FE results tended to produce a more or less overestimated load-displacement curve. However, the compared results show that FE results are in reasonable agreement with field results since they offer similar tendencies in the load-displacement curves. Roh et al. (2019) gave similar notes for calibrating their numerical model. It is worth noting that the dimensions of the calibrated micropiled raft were modified to allow for a wider raft and conduct a comprehensive numerical study on full-sized micropiled rafts. A similar trend of extending the calibrated model for further analysis was followed by (Alnuaim et al. 2018(Alnuaim et al. , 2016Kumar et al. 2017; Russo 2013, Deb and Pal 2019).

Analysis outline
When investigating the lateral performance of a primary micropiled raft, the numerical analysis was conducted through a number of stages. In the first stage, the initial stress field was calculated for the initial geometry configuration. In the second stage, the micropiled raft was installed. In the third stage, vertical loading was applied at the top of the raft. In the final step, a lateral displacement of 0.1d (where d is the micropile diameter) was applied at the micropiled raft to assess the combined loading effect (Zormpa and Comodromos 2018;Deb and Pal 2019;Elsawwaf et al. 2022a). When investigating the lateral performance of an existing raft enhanced by underpinning micropiles, the numerical analysis was conducted through several different stages that simulate the current practice. In the second stage, a conventional surface raft was installed after calculating the initial stress field. In the third stage, initial vertical loading was applied at the top of the raft. Then in the fourth stage, in order to increase the foundation bearing capacity, micropiles were installed. In the fifth stage, the vertical loading was increased. In the final step, a lateral displacement of 0.1d was applied to the micropiled raft (Elsawwaf et al. 2022b).

Model configuration and parametric study
In this study, a 14 m × 14 m raft supported on 250 mm in diameter micropiles was used. A 6 × 6 micropile group was connected to the raft. The soil profile was soft clay soil underlain by a layer of dense sand. Table 3 shows micropiles and raft input parameters used in the FEA. Two types of loadings were adopted in the study. First, a uniformly distributed pressure that simulates the load of a water tank, an oil tank, or a large storage area. Second, concentrated loads that simulate loads of 16 columns of a multistory building. The studied parameters included the undrained shear strength of the upper clay soil layer ( S u ), its thickness (t), micropiles length (L), the magnitude of vertical loading (V), micropiles spacing to diameter ratio (s/d), and raft thickness ( t r ) as shown in Table 4. However, not all these parameters were investigated in the case of concentrated loads.
The difference between the lateral performance of a primary micropiled raft and that of an existing raft enhanced by underpinning micropiles was also investigated. The value of vertical loads applied on the existing rafts before underpinning was considered in the analysis. The ratio of the initial vertical pressure before underpinning to the final applied pressure after underpinning, p*, is defined as the initial vertical pressure ratio. At p* = 0, this means that micropiles are used to construct a primary micropiled raft. That's why the initial vertical load before installing micropiles equals zero. However, at p* = 0.4, a surface raft will be first loaded vertically with 40% of the final vertical load. Then, micropiles underpinning takes place to enhance the raft, after which 60% of the final vertical load is applied. Furthermore, the effect of micropiles arrangement was studied. In current practice, when micropiles are used to enhance existing raft foundations, some design engineers prefer to install the micropiles concentrated around the columns (Elsawwaf et al. 2023), as shown in Figure 6a. Some engineers tend to establish the micropiles uniformly under the whole raft (Fig. 6b). An attempt was made in a single series to study the best arrangement of micropiles when used to underpin existing rafts.

Soil parameters
The Mohr-Coulomb model was chosen for simulating the soil behavior in the FEA. Table 5 summarizes the input parameters used in the numerical model for different soil layers. Bowles (1996) stated that the field values range of modulus of elasticity of soft clays and dense sands varies between 5000 and 25,000 kPa and between 50,000 and 81,000 kPa, respectively. Moreover, the values range of Poisson's ratio of saturated clays and sands varies between 0.4 and 0.5 and between 0.3 and 0.4, respectively. Considering these values ranges, the modulus of elasticity and Poisson's ratio of the soil layers were selected, as shown in Table 5. It is worth noting that the clay was considered soft in the whole study with S u = 25 kPa. However, a single analysis series was conducted with a wide range of S u values as shown in Table 4, since the lateral behavior of micropiles is known to be mainly affected by the state of the upper 3-5 m in the soil profile (Richards and Rothbauer 2004). When conducting this series, the clay elastic modulus was changed and correlated to the undrained cohesion using the relationship proposed by (Bjerrum 1973).
where E = elastic modulus of clay and S u = undrained shear strength of clay. Dense state only of the lower sand layer was adopted in the study. As for R int , the suggested value between sand and concrete ranges between 0.8 and 1.00, whereas the recommended one between clay and concrete ranges between 0.7 and 1.0, depending on the state of the surrounding soil. R int was assumed to be 0.95 to simulate the rough surface condition for the micropiles of Type C. This assumption agrees with the validation process of the current study and with previous studies by Alnuaim et al. (2016) and Kyung and Lee (2018) who emphasized the necessity of taking a high value of R int due to the pressurized grouting technique in micropiles installation.
(2) E = (500 to 1500)S u The most critical parameter that affects the shaft resistance of the micropiles is the lateral earth pressure coefficient K s . It depends on soil conditions, the pile geometry and material, and the construction method (Bowles 1996). Kim et al. (2018) stated that K s could be in the range of 4-7 for sandy soils (the passive stress state). Olgun et al. (2019) stated that K s could be between at-rest earth pressure coefficient ( K o ) and passive earth pressure coefficient ( K p ) . Therefore, choosing the proper K s value for the soil layers in the current study was quite challenging due to the construction method of Type C micropiles. Hence, the validation process results of the model were utilized to choose an appropriate value of K s for sand and was taken 3.0. In the case of the upper clay layer, the K s value was expected to be lower than that of sand. According to the FHWA (2005), the shaft resistance of Type C micropiles in clay could reach 1.7 times the shaft resistance of Type A micropiles. This could indicate that K s in the case of Type C micropiles in clay could reach 1.7 K o . A value of 1.2 was adopted by Alnuaim et al. (2018) who studied micropiles of Type B in clay. Hence, a value of 1.4 is selected throughout the current study which adopts micropiles of type C.

Applied vertical loads
When applying vertical loading, forced-based approach was adopted in order to have a constant controlled vertical load value. One case model having the following parameters (t = 7 m, L = 13 m, s/d = 8, t r =0.8m , S u = 25 kPa ) was first tested under pure vertical loading to obtain its ultimate vertical capacity ( V u ) . The performance-based design method was adopted to estimate V u . In this method, a tolerable settlement that will induce a functionality problem or maintenance issue for the building under working loads is specified. Then, the foundation system is designed such that the applied working loads cause settlement within the tolerable value (Roberts et al. 2011). The maximum overall settlement of piled rafts reported for several case histories was found to be between 60 and 100 mm (Alnuaim et al. 2016). Therefore, V u was estimated as the vertical pressure corresponding to the settlement of 7.5 cm and was found to be 422 kPa. Different ratios of this value were adopted throughout the study. In the case of concentrated vertical loading, the loads were modeled such that they caused net contact stresses equal to 0.5V u =211 kPa.

Evaluation of the lateral response of micropiled raft under uniform vertical loading
It is significant to specify a reasonable displacement level that corresponds to lateral load capacity due to the small  (2015) selected displacement levels of 6.25, 12 mm, and 5% of micropile diameter to define the lateral load capacity of micropiles. Kyung and Lee (2018) specified the lateral load capacity of micropiles and micropiled rafts at a lateral displacement of 0.1 micropile diameter. Throughout the current study, the lateral load capacity was determined at 0.1d lateral displacement, which agrees with the trends of previous studies and is often used in practice.

Effect of undrained shear strength of clay soil layer
The effect of clay undrained shear strength on the lateral response of micropiled raft systems was studied by changing the value of S u and the corresponding value of E. The elastic modulus of clay was correlated to S u value using Eq. 2 and was taken at 20,000 kPa, 40,000 kPa, 60,000 kPa, and 100,000 kPa at S u values of 25 kPa, 50 kPa, 100 kPa, and 200 kPa, respectively. Figure 7 presents the lateral response of micropiled raft systems under combined vertical and lateral loading with different undrained shear strength values of the clay layer. Figure 8 shows that the maximum lateral load increases with the increase in S u of the clay. However, the rate of increase of the lateral capacity decreases with the increase in S u . The maximum lateral load for S u = 200 kPa reaches 4.33 times the maximum one for S u = 25 kPa . This can be attributed to the increase in the passive soil resistance in front of the micropiles as well as the adhesion between the clay and micropiles sides. The ratio of lateral capacity to the applied vertical load was found to be 16.5%, 31.8%, 49%, and 71.4% at S u values of 25 kPa, 50 kPa, 100 kPa, and 200 kPa respectively.

Effect of thickness of soft clay layer
The effect of the thickness of the soft clay layer on the lateral response of micropiled raft systems was studied. The micropiles length was kept constant at 13.0 m while the clay thickness was changed. Figure 9 shows that the lateral load capacity decreases with increasing the ratio of t/L . However, Fig. 10 demonstrates that this reduction is obvious with increasing t/L ratios up to around 0.54, beyond which the decrease was found to be not significant. The decrease in the lateral load capacity with increasing the clay thickness can be attributed to its low undrained shear strength and the decrease of the micropiles portion length embedded in the dense sand. Hence, the passive soil resistance in front of the micropiles decreases. The ratio of lateral capacity to the applied vertical load was found 18.2%, 17.2%, 16.5%, and 16.2% at t/L ratios of 0.25, 0.38, 0.54, and 0.75, respectively.

Effect of micropiles length
The effect of the micropiles length on the lateral response of micropiled raft systems was investigated. At L/d ratios of 13, 20, and 28, micropiles were entirely embedded in the soft clay, while at ratios of 39 and 52, a portion of the micropile was placed in the soft clay whose thickness was kept at 7.0 m, and the rest of  Figure 11 shows the variation in the lateral performance of micropiled rafts at different values of L/d . It can be observed that increasing the L/d ratio enhances the lateral capacity of the micropiled raft. However, Fig. 12 demonstrates that the lateral load capacity increase rate is much higher for micropiles wholly placed in the soft clay (floating micropiles) compared to end-bearing micropiles. Furthermore, increasing the micropile length causes enhancement in the lateral capacity of micropiled rafts with increasing L/d ratios up to around 39, beyond which the increase is found to be not significant. The maximum lateral load increases by about 44% in the case of L/d = 39 compared to the case of L/d = 13. The ratio of lateral capacity to the applied vertical load was found to be 25%, 29.3%, 33.5%, 36%, and 36.6% at L/d ratios of 13, 20, 28, 39, and 52, respectively. It should be noted that the analysis was conducted on micropiled raft systems subjected to vertical pressure of 105.5 kPa not 211 kPa to avoid early soil failure in case of shorter micropiles under the action of vertical load.
Similar behavior was reported in several studies. For example, Reese and Van Impe (2010), Abdrabbo and Gaaver (2012), and Sharma and Hussain (2019) reported that increasing a pile length beyond a particular length will not enhance the lateral capacity.

Effect of magnitude of vertical loading
The variation of the lateral performance of micropiled rafts at different values of vertical loading is presented in Fig. 13. It can be seen that increasing the vertical loading pressure causes a continuous decrease in the lateral capacity of micropiled rafts resting on soft clay, as shown in Fig. 14. The maximum lateral load decreases by about 22% in the case of V = 379.8 kPa compared to the case of pure lateral loading. The ratio of lateral capacity to the applied vertical load was found to be 36.5%, 16.5%, 10.4%, and 8.4% at V values of 105.5 kPa, 211 kPa, 316.5 kPa, and 379.8 kPa, respectively. This reduction may be attributed to the early failure of the micropile-soil interface in the upper soft clay layer under the vertical load action. In this case, the further lateral deformation in the micropile group will not cause increased lateral soil resistance. Hence, this will result in a considerable  decrease in the lateral load capacity. This trend is similar to that presented by (Rajagopal and Karthigeyan 2008;Hazzar et al. 2017).

Effect of micropiles spacing to diameter ratio
In the case of ordinary piles, it is well known that the group interaction significantly varies for pile group with close spacing or pile group with higher spacing. Figure 15 shows the variation of lateral load response for the micropiled rafts with s/d ratios considering that the number of micropiles is constant at 36 micropiles. It can be seen that the lateral load capacity increases with increasing the s/d ratio, as shown in Fig. 16. This trend is similar to that presented by El Sawwaf (2008). There is almost an 18% increase in the lateral load capacity when the s/d is increased from 6 to 8, whereas the lateral load increased by 31% by increasing s/d from 6 to 10. The ratio of lateral capacity to the applied vertical load was found to be 14%, 16.5%, and 18.3% at s/d ratios of 6, 8, and 10, respectively. This can be attributed to the "micropile-micropile" interaction among the micropile group under the raft. For closely spaced micropiles, the developed stress fields for the micropiles overlap each other, and the resisting zone in front of every single micropile becomes smaller. When the spacing between the micropiles increases, this overlapping gets insignificant, causing a larger resisting zone. Figure 17 shows the variation of the lateral load response with different values of raft thickness ( t r ) . It is observed that the lateral load capacity increased by 6.5% as t r increased from 0.4 to 0.8 m, beyond which the increase was insignificant, as shown in Fig. 18. The ratio of lateral capacity to the applied vertical load was found to be 15.5%, 16.5%, 16.7%, and 16.8% at t r values of 0.4 m, 0.8 m, 1.2 m, and 1.6 m, respectively. This slight increase in the lateral load capacity can be attributed to the slight increase in the portion of the load share taken by the micropiles, which allows the micropiled raft to sustain a higher lateral load.

Evaluation of the lateral response of micropiled raft under concentrated vertical loads
In this section, the lateral performance of micropiled rafts was studied under concentrated vertical loads of 16 columns of a multistory building. The rafts were supported by micropiles that were uniformly distributed (Fig. 6b).

Effect of undrained shear strength of clay soil layer
The analysis was performed on different micropiled rafts by changing the undrained shear strength of the clay layer and the corresponding value of E, as explained before. The same variation discussed earlier in the case of uniform vertical loading has been observed. The maximum lateral load increases with the increase in S u of the clay layer, as shown in Fig. 19, and there was hardly any difference in the value of maximum lateral load when the vertical loading was applied as concentrated loads. Figure 20 presents the variation of the lateral load taken by micropiled rafts under combined lateral and concentrated vertical loading at different values of raft thickness ( t r ) . The maximum lateral loads were compared to the values obtained in the case of uniform vertical loading. It can be observed that the lateral load capacity decreases by only 2.25% at t r =0.4 m , but there is no significant difference in the lateral load capacity for the relatively rigid rafts.

The response comparison between primary micropiled raft and enhanced existing raft
The following comparison has been conducted to help design engineers decide if it is preferable to choose the primary micropiled foundation system or delay the installation of micropiles when needed for strengthening the surface raft. The value of vertical loads applied on the existing rafts before underpinning was considered in the analysis.
The analysis included one primary micropiled raft and three enhanced existing rafts with p*=0.2, 0.40, and 0.60. Figure 21 shows that the lateral load capacity of primary micropiled rafts is higher than that of enhanced existing rafts. Moreover, the lateral load capacity increases with the decrease of p* in the case of enhanced rafts. The ratio of lateral capacity to the applied vertical load was found 16.5%, 15.7%, 14.7%, and 13.2% at p* values of 0, 0.2, 0.4, and 0.6, respectively. The maximum lateral load decreases by about 20% in the case of p*=0.6 compared to the case of p*=0. This behavior can be attributed to the soil's early yielding during the raft's initial loading with vertical loads before micropiles installation. Figure 22 was taken from the FEA prior to the installation of micropiles at p*=0.2, 0.40, and 0.60. The green-colored soil zones present the areas where the ratio of shear stress to shear strength ranges from 0.85 to 0.95 along a vertical cross-section at the center of the raft. A larger greencolored area should mean a larger soil area tending to yield. It is obvious that the case of p*=0.6 has the largest soil area close to yielding compared to the two other cases of p*=0.2, 0.4. This finding is similar to that of El Kamash and Han (2017) who studied micropiled rafts under vertical loads and stated that vertical displacements of the micropiled raft increase with increasing the initial vertical pressure ratio before underpinning.

Effect of micropiles arrangement
Micropiles may be installed concentrated around the columns or uniformly under the whole raft when they are used to underpin an existing raft to improve the foundation system, as shown in Fig. 6. The following comparison has been conducted in order to know the best arrangement in terms of lateral performance. Both rafts were initially loaded vertically with 84.4 kPa (p*=0.4) before micropile installation. Figure 23 shows the variation in the lateral response of the two arrangements. It is observed that the lateral load capacity is 11% higher in the case of concentrated micropiles than that of uniform micropiles. The ratio of lateral capacity to the

Evaluation of the lateral load carried by each micropile in a micropiled raft
When a micropiled group is subjected to combined loads, the micropiles will offer different load capacities depending on their position and the lateral loading direction. In this study, 36 micropiles were divided into six rows with six piles in each row. The lateral load capacity of each row is determined as the mean of the lateral load values carried by micropiles of that row at 0.1d lateral displacement. Figure 24 shows the lateral load response for different rows for the case of primary micropiled raft under concentrated vertical loads. It can be seen that the lateral load capacity subsequently increases from row 1 to row 3, i.e., row 1 takes the least part of the lateral load while row 3 carries the largest amount of lateral load. In order to discuss the lateral load distribution among individual micropiles at 0.1d lateral displacement, the ratios of the lateral load of each micropile in the row relative to the total lateral load carried by micropiles are plotted in Fig. 25. According to the current design practice of conventional pile foundations, all piles are designed assuming that they take the maximum horizontal pile load in the group. Considering the results of this study about the variation of the lateral load taken by every micropile could lead to a more economical micropile foundation design. Moreover, based on common knowledge, the leading piles should carry more lateral forces than the trailing ones. However, Fig. 25 demonstrates that the load distribution among the micropiles tends to be more uniform, and the most trailing micropile could carry the highest lateral load in its row. This can be attributed to the presence of vertical loading, which may help redistribute the lateral loads among the micropiles compared to the case of pure lateral loading. These findings are similar to those of Hazzar et al. (2017).

Evaluation of load sharing ratio between micropiles and raft
Applied loads are shared by both the raft and micropiles connected to the raft. The lateral load-sharing ratio a h can be defined as the proportion of the lateral load taken by the micropiles to the total lateral load carried by the micropiled raft, while the vertical load sharing ratio a v can be defined as the proportion of the vertical load taken by the micropiles to the total vertical load carried by the micropiled raft. Figure 26 shows the proportion of the lateral load carried by micropiles with normalized horizontal displacement (y/d) The impact of the raft flexibility, the magnitude of vertical load, and the micropiles length in controlling a h and a v ratios are investigated. Figure 27 presents the values of a h and a v ratios with different values of s/d, t r , V, and L/d. The figure depicts that a h is affected by the variation of s/d. a h increases from 56 to 68% when s/d is changed from 6 to 10. However, the other studied parameters hardly have any influence on a h , as its value seems to remain constant with the variation of t r , V, and L/d. A quite different trend takes place when considering a v which seems to be affected by all the studied parameters except t r . At V = 211 kPa and L/d = 52, a v increases from 59 to 74% when s/d increases from 6 to 10. In addition, the variation of a v with the value of V demonstrates that a v is vertical displacement-dependent. At s/d = 8 and L/d = 52, a v increases from 63 to 76% when V increases from 105.5 kPa to 379.8 kPa. This indicates that a v increases with the increase of vertical displacement.
The most governing factor on a v for micropiled rafts on layered soil is found to be L/d. Considering the fact that the micropiles were embedded completely in the soft clay layer when L/d ≤ 28, Fig. 27d depicts that a v for end-bearing micropiles is much higher than that for floating micropiles.
At V = 105.5 kPa and s/d = 8, a v increases from 17 to 63% when L/d increases from 28 to 52. Comparing all the configurations, it is observed that the raft carries 24-92% of the vertical load, whereas the micropiles carry 8-76%. Regarding the applied lateral load, the load carried by the raft varies between 32 and 44% of the total lateral load, while the micropiles carry 56-68%.

Evaluation of bending moments and shear forces of micropiles
The proper estimation of the bending moment and the shear force acting on the micropile is critical during its design under a lateral load. When a lateral load is applied to a micropiled raft, a negative bending moment is produced at the micropile head due to the rigid connection between the micropile group and the raft (Deb and Pal 2019). The structural forces produced in the micropiles depend on the micropile position and the lateral loading direction. As shown earlier, row 3 carries a higher lateral load than the successive rows. That is why a similar trend has been seen in the case of bending moment and shear force. The mean value of the structural forces in each micropile of a specific row is determined. Then, this mean is used to show the row's bending moment and shear force. Figure 28 presents the variation of structural forces obtained in different rows of a micropiled raft under pure lateral loading at 0.1d lateral displacement. It can be seen that the maximum negative bending moment and the maximum positive shear force are produced at the micropile head. The maximum positive bending moment is produced at a depth of 0.16-0.2L  from the micropile head at the position of zero shear. Row 1 presents the least structural forces, while row 3 shows the highest structural forces. In addition, the lateral movements of the micropiles with depth were checked by plotting the lateral deflection of micropile no.1 of the three different rows versus the depth at 0.1d lateral displacement, as shown in Fig 29. Overall, the micropile of row 3 shows lower lateral displacements than that of the successive rows. This can be attributed to the fact that row 3 is the furthest row from the applied lateral point load, whereas row 1 is the nearest one. While the difference between the displacement values for the three rows is very low at the micropiles' head and tip, this difference was evident in the middle third portion of the micropiles' depth.
In order to discuss the impact of the vertical loading at 0.1d lateral displacement, the absolute values of the maximum negative bending moment of micropiles in row 3 are plotted in Fig. 30a, whereas the absolute values of the maximum positive shear force of micropiles in row 3 are plotted in Fig. 30b, with the variation of the magnitude of vertical loading. It is observed that the structural forces decrease with the increase in vertical loading. The bending moment of pile 6 decreased by 55% when the applied vertical load was 379.8 kPa compared to the pure lateral case, whereas the shear force decreased by 52%.

Design guidelines
Considering the fact that onshore and offshore structures are subjected to lateral loads that can reach 15% and 30% of applied vertical loads, respectively (Rao et al. 1998;Palammal and Senthikumar 2018), and based on the findings of this paper, the major guidelines for designing micropiled foundations on soft clay underlain by dense sand under combined loading are proposed below: 1. It is preferable to construct a primary micropiled raft from the beginning instead of underpinning an existing raft with micropiles. 2. In the case of underpinning existing rafts, design practitioners are encouraged to install the micropiles concentrated around the locations of columns. 3. For S u = 25 kPa, the micropiled raft offers a reasonable lateral load capacity that exceeds 15% of the applied vertical load, whatever the soft clay thickness. However, the minimum undrained shear strength required for offshore structures is 50 kPa. 4. For offshore structures, end-bearing micropiles should be adopted in the design to offer a reasonable lateral load capacity and high a v . Much care must be taken when adopting floating micropiles, as they provide a reasonable a h , but offer much lower a v than that offered by end-bearing micropiles. 5. In general, the micropiles spacing is preferable to be chosen not less than 8d. 6. The raft thickness doesn't govern the lateral load capacity of the micropiled raft. Load-sharing ratios are not affected by t r as well. Therefore, t r can be estimated in order to satisfy other structural design requirements.
These guidelines, however, are based on various idealized conditions for a micropiled raft, a specific soil profile, and a specific level of vertical loading. Hence, they are for initial design purposes only. Care must be taken when dealing with micropiled rafts under a much higher level of vertical loading or different soil profiles.
Author contribution Eng. Ahmed Elsawwaf, Prof. Dr Ashraf Nazir, and Prof. Dr. Waseim Azzam contributed to the study's conception and design. Data collection and numerical analyses were performed by Eng. Ahmed Elsawwaf. The manuscript was written and reviewed by Eng. Ahmed Elsawwaf. Prof. Dr. Ashraf Nazir, Prof. Dr. Waseim Azzam, and Prof. Ahmed Farouk helped to develop the idea and reviewed the manuscript.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
Data availability All data, models, and code generated or used during the study appear in the submitted article.

Declarations
Ethical approval and consent to participate Not applicable.

Competing interests The authors declare no competing interests.
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