Consolidation Effect on the Behavior of Micropiled Rafts Under Combined Loading: Case Study

This paper used finite element modeling to evaluate the consolidation effect on the performance of existing rafts underpinned with micropiles under combined vertical and lateral loads. For this purpose, a real-life case study was discussed, in which micropile underpinning was used to stop the continuous tilt of a 13-floor residential building supported by a surface raft. It was found that the building tilted towards the northeast direction because of the consolidation of a deep soft clay layer under the northeast building corner. After discussing the as-built micropiling system, a 3D numerical model, developed using the PLAXIS software, was used to conduct the numerical research. The time-dependent behavior of the raft with and without the consideration of micropiles was assessed. Moreover, the variation of load-sharing ratios with time was investigated. The numerical results emphasize that the underpinning process was effective and reduced the final raft rotation and maximum settlement by 79.9% and 73.9%, respectively, compared to the case of the absence of micropiles. The consolidation process under a steady level of vertical loads enhanced the performance of the micropiled and unmicropiled rafts against upcoming lateral loads. The vertical load-sharing ratio increased during a life span of 20 years by 10.4% due to the consolidation process, but the increase was at a decreasing rate. Comparing all the four directions in which the lateral load was applied, the micropiles carried (57.4–76.6%) of the lateral load.

Lateral load-sharing ratio 1 Introduction

Background
The micropile is a cast-in-situ bored pile of less than 300 mm in diameter.In the case of already existing foundations, micropiles can be easily installed by drilling through the reinforced concrete foundation and filling the holes with cement grout and steel reinforcement.The advancements in drilling equipment nowadays have resulted in the ability to install micropiles at any angle with minimum noise and disturbance through almost any ground condition.The relatively small size of the drilling equipment gives a chance to underpin existing foundations easily, even in low-headroom conditions or restricted access situations [1].
A better understanding of repairing methods of existing foundations has become a great demand due to the growing number of buildings subjected to excessive settlement or tilt.In most cases, the tilt of an entire building occurs due to the increase in applied contact stresses which exceed the bearing capacity of the soil.In some cases, foundations can face settlement problems because of the overestimation of the soil-bearing capacity or the absence of a geotechnical investigation, leading to an improper foundation design.
The use of micropiles in retrofitting applications is not only limited to underpinning rafts, but micropiles can also be used as a kind of vertical or inclined soil reinforcement.A growing research trend confirms that installing unconnected micropiles under or around footings can enhance the soil-bearing capacity [2][3][4][5].In addition, numerous case histories were documented to demonstrate how micropiles were successfully utilized to underpin existing foundations.For instance, AbdelSalam [6] described a micropiling system used on a tilted building supported on deep soft clay in Alexandria, Egypt.The repair system included sixty micropiles to stabilize the 16-floor building.Elsawwaf et al. [7] described three different approaches for designing the micropile configuration for the restoration of a tilted building in Egypt.Gutierrez [8] presented the strengthening of existing foundations for the Arts and Science Museum in the USA by installing 62 micropiles with a compression capacity of 250 kN each, which was done to accommodate the growing needs of the museum.The first documented case history of micropiling existing shallow foundations in China was of an old building with three floors in order to make it resistant to additional applied vertical loads caused by the construction of two additional floors [9].Lopes et al. [10] reported a Brazilian case study in which two columns in the unoccupied area of the hospital building of the Federal University of Rio de Janeiro failed in 2010, leading to its demolition, after which the adjacent block settled.Hence, micropiles were installed under a number of existing footings.Three different micropile retrofit cases were also discussed by Edens and Fisher [11].
Apart from documented case studies, few researchers tried to assess the improvement in the vertical behavior of underpinned foundations through experimental and numerical analyses.For example, El Kamash and Han [9] conducted a numerical investigation of existing foundations underpinned by micropiles to resist additional vertical loads.The vertical displacement of the raft was found to decrease with decreasing the initial pressure ratio and the increase of micropiles length.Azzam and Basha [12] examined the advantages of using bearing micropiles by installing them in parallel rows on both sides of a strip footing under a newly added area.The underpinning process proved to be effective in increasing the bearing capacity of the strip footing by 260%.
As for the behavior of micropiles subjected to lateral loads, Abd Elaziz and El Naggar [13] conducted two monotonic lateral loading tests on single micropiles in stiff to very stiff silty clay.A numerical analysis was also conducted.Kyung and Lee [14] conducted a parametric study on the lateral-loadcarrying capacity of micropiles.The performance of both single and group micropiles was investigated.Kaur et al. [15] performed a 3D numerical investigation of the lateral behavior piles embedded in a layered-soil system consisting of upper soft clay overlying dense sand.The lateral capacity of piles was found to decrease with the increase in the thickness of the soft clay, which was also reported by Elsawwaf et al. [16] and [17] on micropiled rafts subjected to lateral loads.Shawky et al. [18] investigated how a lateral load would affect the negative skin friction of circular and square piles.The square piles exhibited lower negative skin friction values than circular piles, and the existence of lateral loads reduced these values.
The necessity and innovation of the present article can be briefly discussed as follows.Firstly, onshore and offshore structures are subjected to lateral loads that can reach 15% and 30% of the vertical load, respectively [19][20][21].However, it is observed that only vertical loads were considered in the analysis and design of the retrofitting micropiling systems for documented case studies [7,22,23].Secondly, research on the performance of existing rafts underpinned by micropiles is limited [9,24] since most research on micropiles dealt with primary micropiled rafts, in which the micropiles were connected to the raft before applying vertical loads [25][26][27].Thirdly, most past studies dealt with the behavior of micropiles and piles under pure lateral loads [13,14,16,[28][29][30] or pure vertical loads [3,31,32].A limited number of investigations were carried out about the effect of vertical loads on the lateral response of piles in clay [20,33,34].In these studies, the lateral load was applied immediately after imposing the vertical load, and the consolidation process induced by the vertical load was not considered in the analysis.In fact, the raft could be loaded laterally after a long period of dissipation of the excess pore pressure.
Considering these issues, the current paper aims to offer a better understanding of rafts underpinned with micropiles under combined loading with the consideration of consolidation, through conducting numerical modeling of a real-life case history in which the foundation raft of an inclined building was micropiled.After discussing the as-built micropiling system, a 3D numerical model, developed using the PLAXIS software, was used to conduct the numerical research.The time-dependent behavior of the raft with and without the consideration of micropiles was assessed to examine the applicability and the level of improvement obtained in the field after micropiling the raft.Moreover, the variation of load-sharing ratios with time was investigated.

Research Methodology
Section 2 discusses the current case study.The available field measurements are described, and the soil profile is presented.Section 3 discusses the adopted micropiling system, one of several available proposed restoration solutions.This section is particularly helpful to engineers dealing with similar cases of tilted buildings since it shows how the number, location and depth of micropiles were determined.Section 4 presents the numerical modeling and how the 3D model was developed.The numerical model was validated by comparing the FE results with the available field results.Section 5 presents the analysis of results which mainly focus on the time-dependent behavior of the raft with and without the consideration of micropiles.In addition, load-sharing ratios are

Case Study Description
The tower structure described in the current case history is located in Tanta, Egypt.It consists of one basement, a ground floor and 11 typical floors; the tower height above the foundation level is about 40.0 m.The foundation system consists of a 1.1-m-thick reinforced concrete raft supported on a 0.3m-thick plain concrete raft.The estimated total load of the tower, including the raft's own weight, is about 99,165 kN.The building construction began in December 2010 and was completed in July 2012, with a total area of about 572 m 2 .As shown in the layout in Fig. 2, the building has an irregular trapezoidal shape, and there is an old 6-storey neighboring building to the west.Moreover, a 2.0-cm settlement joint separates the investigated building and an adjacent modern 13-storey structure to the south.In August 2012, as soon as concreting works had been completed, the tower structure was noticed to tilt towards the northeast direction.The tilt took place before any brick masonry, flooring, or finishing work were conducted.

Visual Inspection
A visual in-situ inspection was carried out in August 2012.The major observations are listed below: (1) No cracks were detected along any structural elements; all beams, columns and slabs were in good condition.(2) There was a noticeable tilt in the building towards the northeast.As shown in Fig. 2, the settlement joint width between the investigated building and the southernmost neighboring building at the roof elevation increased to be largest at the southwest zone and equal to 14.0 cm, resulting in an inclination ratio of around 1H:333.33 V, which was observed afterwards to increase over time.(3) Due to difficult access circumstances, the increasing horizontal distance between the building and the western neighboring building couldn't be measured accurately.
A monitoring survey program was arranged to be performed starting in August 2012 using total station survey measurements.Moreover, a detailed soil investigation program was arranged to be conducted to specify the main reasons leading to the building tilt.

Monitoring Survey
In order to see how far the structure was moving over time, a complete monitoring survey program was conducted.Simultaneously, brick masonry work was being conducted.Knowledge of the vertical and lateral displacement rates over time was of great importance since accelerating rates could eliminate any chance of foundation repair and force the project team to take down the tower.
Seven monitoring targets were attached to the structure at predetermined spots.Targets No. 1 and 5 were located near the northeast building corner, whereas targets No. 2 and 6 were located near the northwest corner.The plan positions of the seven targets are presented in Fig. 3. Table 1 presents the initial coordinates of the 7 target points and the results of survey observations.It is worth noting that the raft repair system was conducted in late October 2012, leading to a noticeable settlement rate cut afterwards, as shown in Table 1.
Figure 4 shows the movements of all target points in all directions with respect to time.It can be seen that targets No. 1, 2, 3 and 4 exhibited higher lateral displacements since they were attached to the building near the roof elevation, whereas targets No. 5, 6 and 7 were attached near the raft elevation.Regarding the vertical displacements, the maximum value was observed for targets No. 1 and 5 (the northeast corner), while target No. 4 seemed to give the lowest vertical displacement.That is why the survey observations confirmed that the building was tilting towards the northeast corner.

The Original Site Investigation Program
Earlier in 2009, the soil stratification at the site was explored through an extensive site investigation program, including three boreholes of depths ranging from 15.0 to 20.0 m.Standard penetration tests were performed when encountering granular soils.In the case of cohesive layers, Shelby tube sampler was used to obtain undisturbed samples which were tested using the pocket penetrometer and unconfined compression tests.Figure 5(a) presents a schematic cross-section of the site soil profile which generally consists of three main soil layers as follows: (1) stiff silty clay from the ground surface to a depth of 11 m; (2) a layer of medium-dense sand with traces of silt from a depth of 11 m to 16 m; and (3) a layer of medium-dense sand from a depth of 16 m to 20 m.The groundwater table was located at a depth of about 4.5 m below the ground surface.Hence, the soil type below the bottom level of the raft, stiff silty clay followed by medium dense sand, was supposed to offer considerable bearing capacity.Consequently, a surface raft foundation system was adopted initially to support the loads of the 13-storey building.

The Additional Site Investigation Program
In August 2012, after the building had tilted, the soil stratification at the site was explored again by conducting two boreholes with depths of 20.0 m near the building at points A and B (see Fig. 3).Furthermore, three extensometers were attached to the raft at the locations shown in Fig. 3 to measure any further vertical displacements.A series of consolidation tests were conducted on the recovered undisturbed soft soil samples to help the project team predict the rate and magnitude of settlement in the soil.An 8.0-m deep layer of soft clay was encountered at a depth of 7.0 m below the ground surface at point A near the northeast corner of the building.The depth of this layer was found to decrease to 5.0 m at point B near the northwest corner.The soil profile under the rest  of the building was found to be similar to that of the original site investigation program in Sect. 3 Retrofitting Foundation System

Preliminary Analysis
A software package was used to develop a 3D finite element model for the tilted building.From this model, the estimated total load of the tower columns was 76,800 kN considering live load, dead load and floor covering.The stresses acting on all the structural elements were deemed acceptable under the action of vertical loads as well as the effect of the building tilt.This finding agreed with the fact that all beams, slabs and columns had been found in perfect condition at the site.
In addition, no critical eccentricity between the centroid of the total tower load and the centroid of the foundations was found.The eccentricity was so small.Hence, it was neglected Fig. 4 Target points movements with respect to time a in x direction b in y direction c in z direction afterward in the geotechnical analysis, in which the net contact stress acting on the entire area of the tower (572 m 2 ) was found to be uniform and equal to 133.7 kPa.
The original geotechnical design utilized a 572 m 2 surface raft at a foundation level of 4.0 m below the ground surface, depending on the net allowable bearing capacity of 145 kPa provided by the original site investigation program (see Sect. 2.3.1).Unfortunately, a relatively deep layer of soft clay, as observed later under points A and B, was the reason behind the high differential settlement leading to the building tilt.Tilt was expected to increase over time unless a suitable retrofitting system was conducted.

Discussion of Available Proposed Solutions
In the repair approach, enhancing the stiffness of the soilfoundation system, especially at the northeast zone of the building, represented a great demand to stop the tilt and resist the portion of additional structural loads exceeding the raft capacity.All the available proposed strengthening solutions are listed below: 1. Taking down a number of the upper floors to lessen the actual vertical applied loads to be lower than the vertical load capacity of the foundation.This solution was deeply encouraged by the local authorities but was rejected by the building owner.2. Soil grouting adjacent to the north and east building borders.3. Installing a number of CFA piles along the outside northern and eastern borders, followed by installing an upper new pile cap footing to connect the piles with the original surface raft.4. Taking down all masonry brick walls and replacing them with other lighter partition materials.Floor covering would be done using light material as well. 5. Underpinning the raft with micropiles.
Considering the presence of weak soil layers beneath the existing raft, micropiling the raft seemed to be the most appropriate repair technique that has the advantage of causing neither soil vibration nor disturbance to existing buildings.

Proposed Micropiling System
A total number of 200 micropiles of 20 cm in diameter, 17 m in length and a design geotechnical allowable capacity of 250 kN were considered adequate to satisfy the repair objectives.

Micropiles Length and Design Capacity
The philosophy of micropile design consists of two main aspects which are as follows: the structural design and the geotechnical design.The used steel reinforcement is the main governing factor in controlling the structural compression capacity since the reinforcement ratio can reach more than 15% of the micropile cross-sectional area [20].For the current case study, the available reinforcement was high tensile steel tube with an inner/outer diameter of 76/89 mm and a yield stress of 3600 kg/cm 2 (5.4% of area cross-section).A structural capacity of 520 kN was estimated using the relationship proposed by FHWA [35] as When considering the geotechnical design, the two main governing factors are the grouting method and the embedded bond length in the bearing layer.The vertical capacity of a micropile can reach ultimate values in excess of 365 kN per meter of bond length in dense granular soils [35].Micropiles are classified according to the method of grouting into four categories which are as follows: Type A, Type B, Type C and Type D [35].For the current case study, Type B micropiles were adopted, where a high injection pressure was used in pouring the grout into the holes.The advantage of using pressurized grout in the construction process of micropiles is to densify the surrounding coarse-grained soil [27].With taking a factor of safety of 2.5 and assuming an embedded bond length in the sand layer of 6.0 m, a geotechnical capacity of 250 kN was estimated using the relationship proposed by FHWA [35] as where P G-allowable = micropile allowable geotechnical capacity; α bond = grout-to-ground ultimate bond strength; F.S. = factor of safety (2 to 3); D b = diameter of the drill hole; and L b = bond length.

Micropiles Number and Arrangement
Figure 6 presents the layout of the existing raft after being underpinned with micropiles.Micropiles' number was estimated, and their arrangement was specified according to the following approach: 1.As explained earlier, the structure analysis showed that the net contact soil stress due to the entire building loading was uniform and equal to 133.7 kPa. 2. The contact soil stress, which results from the own weight of the raft and the live load on the basement floor, was estimated to be 39.1 kPa.Hence, the total contact soil stress was 172.8 kPa. 3. Considering the principle of floating foundation, it was found that a structure causing stresses of 66 kPa (the weight of excavated soil) should cause zero settlement.4. The micropiling system was deemed to resist additional stresses exceeding 66 kPa.That's why the micropiles were supposed to carry a total stress of 106.8 kPa (172.8-66).
123 5.An adequate number of micropiles were concentrated under the critical areas of loading with an intermediate spacing which generally ranged between 0.65 and 1.00 m, such that they resist at least 106.8 133.7 ≈ 80% of the column load.Some loading areas were not micropiled since they were far from the weak northeast zone.
It is worth noting that some design practitioners tend to model the foundation system on elastic supports, using the growing research in new optimization algorithms for designing the coefficients and locations of elastic springs [36,37].

Installation Process of Micropiles
Each micropile was drilled using a hollow stem auger and bentonite as a drilling fluid.Once the desired design depth was achieved, grout was poured through the hollow stem under pressure to fully replace the drilling fluid.After extracting the hollow stem, a steel tube with inner/outer diameter of 76/89 mm was inserted.Finally, a micropile steel head plate (25 cm × 25 cm) was installed.The drilling technique of micropiles allowed the project team to explore the soil profile under various parts of the building, which appeared to be consistent with the performed soil investigation programs.An additional micropile cap of 400 mm thickness was constructed at each column's location to connect the micropiles with the column and the existing raft.A network of shear connectors was used for this purpose.Figure 7 shows Fig. 7 Cross section of the micropiled raft a cross section of the new foundation system, including the micropiles, additional and existing rafts and columns.

Verification of Single Micropile Capacity
In order to confirm the micropile's actual geotechnical capacity, a vertical static micropile load test as per the Egyptian Geotechnical Code of Practice No. 202/4-2001 [38] was conducted on one of the micropiles near the southwest building corner by using a test load of 375 kN which caused a maximum settlement of 1.25 mm.The test results analysis predicted the allowable static load to be 684 kN, representing the average value obtained from modified Chin's and Brinch Hansen's methods that are usually used to analyze pile load tests [39].

Description of the Model
A 3D finite-element model was utilized to carry out a phased analysis that simulated the construction sequence of the above-mentioned case history.The assessment of the foundation system under combined loading conditions was conducted by using PLAXIS 3D.To minimize the impact of the model boundaries on the analysis results, the horizontal and vertical boundaries were kept at 180 m and 90 m, respectively.The consolidation and pore pressure changes were accounted for in the model in order to predict the variation of settlements, differential settlements, lateral displacements and load-sharing ratios with time.Vertical side boundaries with normal in x-direction were fixed in x-direction only, whereas vertical side boundaries with normal in y-direction were fixed in y-direction only.The bottom side boundary was fixed in all directions, while the top side boundary was free.In addition, since a full 3D model is simulated in the FEA, all side boundaries were opened for water drainage.The 3D 10node tetrahedral elements were used to model the soil layers which were simulated using the Hardening Soil (HS) constitutive model.Micropiles were modeled as embedded beam elements, whereas interface elements were used to simulate the interaction between the micropile or the raft and the adjacent soil through the strength reduction factor (R int ).PLAXIS 3D offers an option to consider the effect of adjacent soil layers on the micropile skin resistance by relating the local skin resistance to the soil layer strength properties (cohesion and friction angle) through the interface strength reduction factor, R int .The raft was modeled as a plate element with the plan dimensions shown in Fig. 8.The raft's center of mass was positioned at the center of the model.Based on the results of mesh sensitivity analysis, an appropriate size of the elements was adopted to ensure the high accuracy of the results.In addition, denser mesh was used at locations where highstress concentration was expected (e.g., raft base, micropile base and micropile side surface).

Analysis Outline and Applied Loads
In order to examine the applicability and the level of improvement obtained in the field due to the installation of micropiles, the numerical model was utilized to investigate two main scenarios for loading the foundation system.First scenario: applying vertical loads only or combined loading on the raft, assuming it was not micropiled during its life span.Second scenario: applying vertical loads only or combined loading on the raft along with underpinning it with micropiles 22 months after the raft construction, which simulates what happened for real.
Table 2 presents the construction stages that the analysis went through and applied tower loads with time.As shown in Table 2, it can be seen that the total vertical load was about 83,805 kN and was reached 31 months after the raft construction.As discussed before in Sect.3.3.2, the principle of floating foundation was adopted, and the soil at the excavation base was assumed not to undergo any vertical settlement until the structure's weight reached the weight of the soil removed.Therefore, only the load in excess of the weight of the soil removed was applied (i.e., the net load), and the excavation stage was not simulated in the analysis; the raft was introduced directly on the model top-side boundary.The net load was applied as concentrated loads on the raft, and as stated before in sub-Sect.3.3.2, it was estimated to be about 80% of the columns' total loads.Moreover, the own weight of the whole building was estimated to be about 37.1% of the total columns' total loads, whereas wall loads were estimated to be about 15.9% of the total columns' total loads.In addition to live loads coming from the tower columns, the raft was also loaded with a stress of 5 kPa representing the live load in the basement.
Regarding the lateral load, it was applied at the center of the raft in four directions which are as follows: + ve direction of X-axis, -ve direction of X-axis, + ve direction of Y -axis and -ve direction of Y -axis.The lateral load value of 11,000 kN was estimated according to the guidelines of the simplified equivalent static method for seismic analysis provided by the Egyptian Code for Calculating Loads and Forces in Structural Work and Masonry ECP-201 [40].Moreover, the value of 11,000 kN was 11.1% of the total weight of the building, including the raft's own weight.This was consistent with the fact that the lateral load can be 10-15% of the vertical load in the case of onshore structures [19][20][21]41].

Model Configuration and Parametric Study
The described case study was simulated through a 3D model, in which 200 micropiles were connected to the raft, as shown in Fig. 8.The spacing between the micropiles generally ranged between 0.65 and 1.00 m.Table 3 displays the input parameters of the micropiles and the raft used in the FEA.The micropile modulus of elasticity was estimated in the study as an average weighted modulus using the relationship proposed by FHWA [35] as 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.
The soil profile was modeled by defining several boreholes that simulated the site's actual soil conditions (see Sect. 2.3).PLAXIS 3D offers the option to automatically interpolate between multiple defined boreholes, making it possible to define soil layers of non-uniform thickness as well as layers that locally have a zero thickness [42].The detailed program for the parametric study is presented in Table 4.

Soil Parameters
The Hardening Soil model was chosen for simulating the behavior of the soil in the FE analyses.Table 5 summarizes the input parameters used in the FEM for different soil layers.The angle of internal friction (φ ) and the cohesion (C ) of all soil layers were obtained previously in the site investigation programs performed in 2009 and 2012.As for sandy soils, due to the absence of falling head permeability tests in the geotechnical investigation programs, the permeability coefficient was reasonably assumed to be consistent with the commonly accepted knowledge of sands' permeability.Additionally, secant stiffness (E ref 50 ), tangent stiffness for oedometer loading (E ref oed ) and unloading/reloading stiffness (E ref ur ) were obtained using the equations by Teo et al. [43]:  As for clayey soils, E ref 50 was obtained using the range proposed by Bowles [44] who stated that the modulus of elasticity of normally consolidated clay ranges from 200 to 500 C. The permeability coefficient and E ref oed were obtained using the results of the consolidation tests performed in the additional site investigation program in 2012.
The impact of the pressurized grouting method in the Type B micropiles construction could be considered in the numerical modeling.R int was taken at 0.95 to simulate the rough surface condition of installed micropiles [14,20,27].Moreover, some previous studies recommended using an increased value of the lateral earth pressure coefficient at rest (K s ) to simulate the high confining pressure of the surrounding soil expected due to placing grout under high pressure [20,26,27,45].

Validation of the Model
The developed numerical model was validated through four stages to ensure the reliability and accuracy of the current FE analysis.In the first stage, back-analysis was conducted in PLAXIS 3D to simulate the field axial compression test performed on one of the underpinning micropiles, as described in Sect.3.3.4.Since only low settlement levels were reached in the field test, the load-settlement curve was extrapolated using the hyperbolic method adopted by several previous studies and proved to be effective for micropiles [46,47].The hyperbolic curve is defined below:  where P = applied load; = micropile settlement; a and m = curve fitting parameters.
In the second stage, the results of the full-scale field lateral loading test of a single Type A micropile by Kyung and Lee [14] were compared with those obtained from the FEA.The 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 whose properties are described in Table 6.Since the Type A gravity grouting technique was used in the micropile construction, R int was assumed to be 0.7.The value of E mp was estimated at 85*10 6 kN/m 2 using Eq. 1.The high stiffness of the micropile was due to the large portion of steel area due to placing a 65 mm diameter steel rod and a permanent steel casing.Figure 9(a-b) shows the variation of the load versus displacement for the first two validation studies, which emphasizes the existence of a good match between numerical and field results.
In the third stage, although the target foundation considered in this study is the micropiled raft, a case study of piled rafts was selected for the third validation study as it was difficult to find a real-life case that addressed the time-dependent settlement of micropiled rafts.The selected piled raft foundation is in Messe-Torhaus in Frankfurt [48].It is comprised of two identical separate rafts 10 m apart, and each raft is 17.5 m by 24.5 m in plan and 2.5 m thick.A rectangular group of 6 by 7 floating piles, which are 0.9 m in diameter and 20 m in length, is utilized to support each raft.The modulus of concrete is 23500 MPa and 34,000 MPa for the piles and the raft, respectively.The subsoil consists of sand and gravel up to 5.0 m below the ground surface, followed by the Frankfurt   6 and 7 present the basic geotechnical properties of soil layers at Frankfurt.A uniform load of 466.5 kPa was applied over a period of eight months and then held constant, to simulate the actual loads being applied to the piled rafts as the building was constructed [48].Shown in Fig. 10 is the time-dependent settlement of the raft at an extensometer located close to the raft center.It can be seen that the predicted displacements are quite close to the measured displacements of the raft [49].
As for the fourth stage, the readings of the three extensometers, which were attached to the raft case study of the current study, were compared to the numerical predicted measurements.Since the extensometers were utilized in a tight period for about 2.0 months after the end of the stage of construction of building floors, the comparison was in terms of relative displacements taking place during the two-month period of the stage of brick masonry work.As shown in Table 8, it can be seen that the predicted relative displacements are quite close to the relative measured ones.

Analysis of Results
The improvement level achieved after micropiling the existing raft was checked under the action of vertical loads only and then under the action of combined loading.The effect of consolidation on results was discussed.

Settlement Criteria (Vertical Loads Only)
Figure 11 (a and b) provides the settlement profile 271 months after the raft construction for both unmicropiled and micropiled raft cases.It is evident from the figures how much the soil conditions played a significant role in obtaining a critical rotation for the unmicropiled raft.In contrast, micropiling the raft managed to lower the obtained rotation effectively.Moreover, the outermost northeast corner exhibited the highest settlement, whereas the outermost southwest corner exhibited the least.Figure 12 presents the time-dependent settlement of the outermost northeast corner, the most critical part of the raft.The case of the unmicropiled raft underwent a maximum vertical displacement of 20.48 cm, 65.79 cm and 89.23 cm at the northeast corner, 22 months, 31 months and 271 months after the raft construction, respectively.After all vertical loads had been applied, this corner underwent a 23.44 cm consolidation settlement under sustained vertical loads from the 31st month to the 271st month.However, micropiling the raft after the stage of (Brick masonry work) caused a colossal decline in the maximum final vertical displacement which was observed to be only 23.26 cm instead of 89.23 cm.In other words, the underpinning process, done when the maximum vertical settlement was 20.48 cm, eradicated almost 96% of the subsequent vertical displacement, compared to the case of the absence of micropiles.
The raft rotation can be calculated using Eq. 8.
Rotation = Settlement of outermost northeast corner − Settlement of outermost southwest corner Distance between the two corners (8) Shown in Fig. 13 is the variation of the raft rotation with time.The case of the unmicropiled raft underwent a rotation of 0.004289, 0.01599 and 0.02266, 22 months, 31 months and 271 months after the raft construction, respectively.After all vertical loads had been applied, the raft underwent a 0.00667 rotation under sustained vertical loads from the 31st month to the 271st month.However, micropiling the raft after the stage of (Brick masonry work) caused a colossal decline in the final rotation which was observed to be only 0.00455 instead of 0.02266.In other words, the underpinning process, done when the rotation was 0.004289, eradicated almost 98.6% of the subsequent rotation that would have happened in the case of the absence of micropiles.In order to assess comprehensively the improvement level achieved after micropiling the existing raft from the 22nd month, the reduction ratios of the observed rotations and maximum settlements were determined and plotted in Fig. 14.The micropiles reduced the final raft rotation and maximum settlement by 79.9% and 73.9%, respectively.It can be seen from the figure that the reduction ratios rose dramatically during the period of applying the live loads from the 22nd to the 31st month, and then the rate of increase decreased continuously under sustained vertical loads from the 31st to the 271st month.This is attributed to the fact that the unmicropiled raft exhibited a vertical settlement which rose dramatically during applying the live loads from the 22nd to the 31st month, compared to the period from the Fig. 14 Variation of reduction ratio in rotation and settlement with time 31st to the 271st month.Moreover, a higher reduction ratio would have been gained in the case study under investigation if the micropiles had been installed earlier.Therefore, if a building is observed or expected to tilt, it is recommended to underpin the raft as fast as possible to gain the most benefit from the installed micropiles with regard to the early control of the raft settlements.

Evaluation of the Lateral Response (Combined Loading)
Figure 15(a and b) presents the variation of the lateral performance of the unmicropiled raft and the micropiled raft, respectively, such that the lateral load was applied just after applying all vertical loads.It can be seen that the highest values of lateral displacement were obtained for the cases of + ve direction of both X-axis and Y -axis.This can be attributed to the weakness of the passive resisting soil at the northeast zone of the building.The lateral load-displacement curves for the -ve direction of both X-axis and Y -axis are nearly linear.The same variation of results was seen for other cases in which the lateral load was applied at 18, 38, 143 and 240 months after applying all vertical loads.Figure 16(a and b) shows the variation of the maximum obtained lateral displacement of the rafts with the time at which the lateral load was applied.It can be found that the maximum lateral displacement decreased with time for about 143 months of consolidation, after which the decrease was not significant.For the unmicropiled raft, there was a reduction in the maximum lateral displacement of 23.2%, 18.73%, 15.9% and 10% for the cases of the + ve direction of Y-axis and X-axis and -ve direction of X-axis and Y -axis, respectively, at the 143rd month compared to 0 months.As for the micropiled raft, there was a reduction in the maximum lateral displacement of 5.8%, 2.9%, 1.6% and 2.8% for the cases of the + ve direction of Y -axis and X-axis and -ve direction of X-axis and Y -axis, respectively, at the 143rd month compared to 0 months.It can be observed that the reduction percentages were higher in the case of the unmicropiled raft than those of the micropiled raft.In other words, the consolidation process under a steady level of vertical loading caused an enhancement in the lateral behavior of the rafts, but the enhancement rate decreased with time towards the end of the consolidation process.The improvement of lateral behavior with time may be explained as shown in Fig. 17.It is well known that consolidation of cohesive soils allows the dissipation of the excess pore pressure induced due to applying vertical loads.Suppose, just after applying all vertical loads, a resisting soil element with effective vertical stress of σ 1 .The dissipation of excess pore pressure will engender an increase in the effective vertical stress up to σ 2 , with a value of shear stress q which remains constant due to the steadiness of the applied vertical loads.Applying the lateral load, afterwards, will cause an increase in the shear stress.However, in order to reach the failure line, the soil element with σ 2 and q will have to cut a longer stress path than in the case of σ 1 and q.That is why a consolidated element will need a higher lateral load than a non-consolidated one to yield.This explanation emphasizes the importance of investigating the stress paths of the soil elements resisting a lateral load after being loaded vertically.Similar findings were reported by Liu et al. [50] who stated that the lateral behavior of a single pile in a normally consolidated clay was ameliorated by applying a vertical load on condition that the excess pore pressure was allowed to dissipate.
In order to assess comprehensively the improvement level achieved after micropiling the existing raft, the reduction ratios of the observed lateral displacements were determined and plotted in Fig. 18.When the lateral load was applied just after all vertical loads had been applied, the reduction ratios were 44%, 31%, 26% and 26% for the cases of the + ve direction of Y -axis and X-axis and -ve direction of Y -axis and X-axis, respectively.It can be seen from the figure that the reduction ratios decreased with time for about 143 months of consolidation, after which the decrease was not significant.

Evaluation of the Vertical Load-Sharing Ratio
According to the design approach used when calculating the number of micropiles to be installed in the investigated case study, it was assumed that the micropiles would carry 80% of the columns' total load, as described in Sect.3.3.2.There is a need to calculate the vertical load-sharing ratio between the micropiles and the raft to evaluate it with respect to the above-mentioned assumption.
The vertical load-sharing ratio (α v ) can be defined as the proportion of the vertical load taken by the micropiles to the total applied vertical load, whereas the additional vertical load-sharing ratio (α v ) can be defined as the proportion of the vertical load taken by the micropiles to the proportion of vertical loads applied after installing the micropiles.Figure 19 shows the variation of α v and α v with respect to time during 123 Fig. 15 Lateral load-displacement response just after applying all vertical loads a unmicropiled raft b micropiled raft Fig. 16 Maximum obtained lateral displacement at different times a unmicropiled raft b micropiled raft Fig. 17 Diagram the effect of pore pressure dissipation on a soil element the consolidation process happening after applying all vertical loads.It can be observed that the dissipation of excess pore pressure caused a moderate increase in α v from 37.4% at 0 months to 47.8% at 240 months, while α v surged from 132.7% to 169.7%, but the rate of increase was decreasing with time.Similar findings of the increase of vertical loadsharing ratios with the consolidation process were reported by El Kamash et al., Watcharasawe et al. and Hooper [24,51,52].Watcharasawe et al. [51] reported that the load taken by piles can increase by up to 12% due to the consolidation effect, while Hooper [52] stated that the piles' load increased by 6% for a piled raft on London clay.
The observed results emphasize that the 200 micropiles carried only about (37.4 to 47.8%) of the applied load during a life span of 20 years, which indicates that the raft carried a significant proportion of the applied load.This could be attributed to the fact that the raft was heavily loaded with 71.8% of the total vertical loads before the micropiling process.Still, the raft needs a relatively long time to transfer the loads to the micropiles.El Kamash et al. [9] reported that the more the raft is loaded before installing the micropiles, the less the loading ratio will be.In addition, not all the loading areas were underpinned with micropiles; several columns near the southwest corner were left without underpinning.Thus, the loads of these areas were transferred directly to the soil.Furthermore, it can be said that assuming that the micropiles will carry all the loads exceeding the excavated soil weight was already too conservative, as it leads to a high unpractical load sharing ratio.Design practitioners are encouraged to assume that the strengthening micropiles will resist loads that exceed the allowable capacity of soil instead.

Evaluation of the Lateral Load-Sharing Ratio
The lateral load-sharing ratio (α h ) can be defined as the proportion of the lateral load taken by the micropiles to the total applied lateral load.Figure 20 presents the variation of α h with respect to the time at which the lateral load was applied.Comparing all the four directions, it can be seen that the micropiles carry (57.4-76.6%) of the lateral load.The highest values of α h were obtained for the cases of + ve direction of both Y -axis and X-axis, with α h of about 76.6% and 75.2%, respectively, at 240 months.
For every single direction, the lateral load-sharing ratio seemed to be slightly affected by the time at which the lateral load was applied.For the + ve direction of both Y -axis and X-axis, there was a slight increase in α h of not more than 3.5% from 0 to 38 months, after which α h remains almost constant.As for the -ve direction of both Y -axis and X-axis, the variation of α h with the time was minimal as it remained almost constant after an initial very little decrease.These results emphasize that the value of α h and its variation with time is not identical in the four directions.This may be caused by the fluctuation of the soil profile and the depth of different soils in the site.Moreover, the micropiles are not uniformly distributed under the entire area of the raft; more micropiles were installed near the northeast corner than the opposite corner.

Summary and Conclusions
The present study deals with a real-life case study of micropiling the raft of a residential tower that tilted due to the existence of a deep soft clay layer under the northeast zone of the building.The micropiling process was discussed in detail, which can be helpful to engineers dealing with similar cases of tilted buildings.In addition to describing the field measurements and micropile installation process, the paper also presents the adopted design approach for determining the number, depth and location of the micropiles.
A series of 3D finite element analyses were then performed to simulate the case study and evaluate the time-dependent performance of the raft under combined vertical and lateral loading with and without the consideration of the micropiles.The consolidation and pore pressure change were accounted for in the model.The main conclusions drawn are listed below: (1) Micropiling the raft was an efficient solution to stop the continuous rise of the raft's total settlements and rotation.The micropiles reduced the final raft rotation and maximum settlement by 79.9% and 73.9%, respectively.A higher reduction ratio would have been gained if the micropiles had been installed earlier.
(2) The micropiles contributed to reducing the lateral displacements of the raft when being loaded laterally compared to the case of unmicropiled raft.When the lateral load was applied just after all vertical loads had been applied, the reduction ratios were 44%, 31%, 26% and 26% for the cases of the + ve direction of Y -axis and X-axis and -ve direction of Y -axis and X-axis, respectively.
(3) The consolidation process under a steady level of vertical loading positively impacts the performance of the micropiled and unmicropiled rafts against upcoming lateral loads and causes a reduction in the lateral displacement.The reduction ratios in the observed lateral displacements were higher in the case of the unmicropiled raft than those of the micropiled raft.(4) Knowing that the investigated raft was loaded with 71.8% of the total vertical loads before the micropiling process, the micropiles carried 37.4% of the loads once the raft was loaded with 100%.Then, after a life span of 20 years, the micropiles carried 47.8% of the load.(5) During a life span of 20 years, the vertical load-sharing ratio increased with time by 10.4% due to the consolidation process, but the increase was at a decreasing rate.(6) Comparing all the four directions, the micropiles carried (57.4-76.6%) of the lateral load.In general, the lateral load sharing ratio variation with the time at which the lateral load was applied was minimal.(7) From the economic and practical points of view, assuming that the micropiles will carry all the loads exceeding the excavated soil weight was too conservative in the investigated case study.Design practitioners are encouraged to assume that the strengthening micropiles will resist loads that exceed the allowable capacity of soil instead.
These conclusions were drawn in accordance with the studied case study, where a non-uniform distribution of endbearing micropiles was used to underpin a rotated raft of a tilted building.Moreover, it is recommended to widely investigate the stress paths of the soil elements resisting a lateral load after being loaded vertically with and without the consideration of consolidation since these stress paths can show the effect of the vertical load on the lateral response.

Fig. 2
Fig. 2 Layout of the building

Fig. 3
Fig. 3 Plan location of monitoring targets and additional boreholes 2.3.1.Figures5(b) and 4(c) present schematic cross sections of the site's soil profiles at points A and B, respectively.The soil includes a stiff silty clay layer up to a depth of 7.0 m and 10.0 m at points A and B, respectively.Then, a soft clay layer extends to a depth of 15.0 m.Below this, medium-dense sand was observed.The groundwater table was found at a depth of 4.50 m below the ground surface.Additionally, it was observed that the raft exhibited vertical settlements of about 56 mm, 22.1 mm and 11 mm at the location of extensometers No. 1, 2 and 3, respectively, during a period of about 2.0 months from August 2012 to October 2012, which confirmed that the building was tilting towards the northeast corner with a high rate.

Fig. 5
Fig. 5 Soil profile a beneath the raft b under point A c under point B. q un , unconfined compressive strength; ∅, internal friction angle; C, cohesion; C c , compression index; e o , initial voids ratio; k, coefficient of permeability; D r , relative density

Fig. 8
Fig. 8 3D FEM used in the analyses and mesh pattern

Fig. 9
Fig. 9 Comparison of numerical model results with field load tests a Type B vertically loaded micropile b Type A laterally loaded micropile

Fig. 10
Fig. 10 Comparison of numerical model results with field results for time-dependent settlement at the center of the Messe-Torhaus raft

Fig. 11 Fig. 12
Fig. 11 Settlement profile of the raft in the FEA 271 months after the raft construction

Fig. 13
Fig. 13 Time-dependent rotation for both cases of unmicropiled and micropiled rafts

Fig. 18 Fig. 19 Fig. 20
Fig. 18 Variation of reduction ratio in maximum lateral displacement with time

Table 1
Monitoring survey measurements over time (dimensions in m)

Table 3
Input parameters of micropiled raft used in FEM

Table 4
Parametric study

Table 5
Input parameters of soil layers used in FEM r = relative density of sand; E ref oed = tangent stiffness for oedometer loading; E ref ur = unloading/reloading stiffness.

Table 6
Input soil parameters at Gongju and Frankfurt used in FEA

Table 7
Variation of Frankfurt clay modulus with depth

Table 8
Comparison of results obtained from the numerical model and the extensometers