Assessment of an alternative to deep foundations in compressible clays: the structural cell foundation

Abstract

The new type of deep foundation for buildings on saturated, compressible-low strength clayey soil deposits, branded structural cell essentially consists of a rigid concrete top slab, structurally connected to reinforced concrete peripheral walls (diaphragms) that enclose the natural soil. Accordingly, as the initial volume of the confined soft clays within the lateral stiff diaphragms will remain constant upon loading, the hollowed structural cell will be “transformed” into a very large cross-section pillar of unit weight slightly higher than that of the natural soft clayey soil. This type of foundation seems to be a highly competitive alternative to the friction pile-box foundations (widely used in Mexico City clays), due to its economic and environmental advantages. Economies result, for example, from the absence of huge excavations hence sparing the need of earth retaining structures. Further savings result from appreciably smaller concrete volumes required for building the structural cell than the friction pile-box foundation; moreover, the construction time of the former is much shorter than that of the latter. Regarding the impact to the environment, less air contamination follows from the fact that both traffic jams and soil excavation lessen appreciably. Considering these facts and others regarding scheduling, it was decided to replace 48-friction pile-box foundations specified in the master plan project by this new type of foundation. The overall behavior of these cell foundations over a five-year period is fared from close visual observations and their leveling during the first three years after their construction.

Keywords

deep foundations / bearing capacity / resistant moment / structural cell / 3D numerical modeling

Introduction

This paper addresses the design concepts of a deep structural cell foundation and the behavior of three out of the 48 of this type of foundation built along the elevated sectors of the Mexico City Metro Line-12. A rigid concrete top slab, structurally connected to reinforced concrete peripheral walls (diaphragms) integrates a structural cell. It is conceptually similar to a closed diaphragm wall and skirted foundation proposed by a number of researcher some years back [¹–⁶], but its purpose is somewhat different. It is widely acknowledged that the volume of saturated clays confined within concrete walls will remain constant and hence they will conform a stiff core coupled to the peripheral walls “transforming” the cell into a very large cross-section pillar of unit weight slightly higher than that of the soil it encloses [¹].

The purpose of deep structural cells is to increase the safety factors of foundations in low strength and highly compressible clays. This is achieved because the cell-enclosed soil system has an enlarged tip area that reduces significantly the soil contact pressure. Consequently, long-term consolidation settlements due to building loading will be smaller and in the case of Mexico City, a high percentage of them most likely will occur during the construction stages given the existence of micro fissure nets. Furthermore, as will be shown later, the ground subsidence caused by water withdrawal from the aquifers will not cause differential settlements between the surrounding soil and the cell-enclosed soil because the original soil deposit stress state is hardly modified. Hence, the structural cell deep foundation will nearly follow the neighboring surrounding soil subsidence.

As far as the authors are aware of, closed diaphragm walls were first used in Japan and can be considered as a spin of the diaphragm walls proposed earlier in Europe. Rectangular closed diaphragm walls have been used in the past as bridge foundations with very good results [¹,⁷,⁸]. Similarly, close diaphragms branded skirted foundations have been used to improve the bearing capacity of offshore foundations [²–⁵]. In practice, diaphragm walls are suitable for both temporary and permanent applications [⁹–¹³]. Other types of foundations for compressible soil deposits that have been proposed by a number of investigators are barrettes [¹⁴–¹⁶] and caissons [¹⁷,¹⁸]. An advantage of this type of foundations is that in addition to improve the foundation vertical bearing capacity, they are able of taking more effectible both earthquake and ocean wave-induced loadings. It is worthwhile to mention that new material developments [¹⁹] improve the behavior of diaphragms subjected to vibration loading.

Although there has been many research studies on the behavior of closed diaphragm walls [2–5,6,18], the current state of knowledge regarding the complex phenomena involved is limited and the forecasting of their overall behavior is still a bit uncertain. Therefore, it is the authors’ wish that the case history and analyses included in this paper propel further investigations so additional light is shed on the physics of this problem.

General project issues

The Metro Line-12 is 28.4 km long and crosses Mexico City from the Southeast to the West. Geotechnical solutions included deep tunnels, cut and cover tunnels and elevated viaducts. The Master Plan specified that friction-pile box foundations would provide support to the columns buttressing the deck of the viaduct where deposits of compressible clays existed. In average, the excavations needed for accommodating the boxes of the piled foundations ranged between 13.0 by 11.0 m in plan and 2.5 m deep. To follow the ground subsidence of the zone each foundation included yielding friction piles. Since the elevated viaduct followed an avenue having a median strip approximately 4.0 m wide and three traffic lanes each way, it was necessary to close two traffic lanes each side of the central strip to have enough room to dig the excavation and build the ramps according to the construction logistic. This, obviously, reduced the total vehicle flow capacity of a very traffic-conflicting avenue by more than two-thirds leading to monumental traffic jams and consequently significant increases of combustion fumes emissions. Furthermore, excavations increased air-small-particles-content adding to ambient pollution. All this and further related foundation-construction activities, affected significantly the incoming revenues of neighboring commercial businesses and the avenue became somehow more dangerous for passers-by. Consequently, social unrest grew up at the working area and surrounding neighborhood.

Accordingly, to ease the time-increasing conflicting situation Romo proposed the structural cell foundation to replace the friction pile-box foundations to be built and specified in the master plan project; the general idea was introduced early this century [²⁰]. Fig. 1 shows a scheme of a structural cell, the cross section of which can be circular, square or rectangular. It is worth mentioning that the structural cell is a simplified version of a honeycomb-type configuration of closed diaphragm walls proposed as a viable foundation solution to support airways or highways on deep deposits of compressible-low strength cohesive soils [²¹]. As mentioned previously, it is reasonable to consider that saturated clays confined within the structural cell will have negligible volume changes upon loading the foundation. Consequently, the soil within the cell walls will behave as a stiff core coupled to the peripheral walls as has been from the results of many numerical studies using finite element and finite differences methods [1,6,18].

The geometrical dimensions of all structural cells mentioned herein were determined from the results of 3D finite difference [²²] analyses. All structural cells have cross sections of 6.5 by 6.5 m and the peripheral walls went down to between 12.5 m and 15.5 m, depending mainly on the soil deposit characteristics. The reduction in foundation construction area allowed the opening of one and a half lanes more for traffic in each way. Fig. 12 illustrates the widening of the avenue (from two to three lanes) in one of the zones where structural cells replaced the friction-pile foundations. Obviously, the above-mentioned advantages are even more appealing when dealing with the foundations of a linear structure such as an elevated freeway (or metro line) along a crowded, heavily transited urban avenue, making vehicle flow more fluid hence lessening traffic jams and pollution.

It is worth mentioning that the structural cell has several conspicuous advantages over the friction pile-box foundation. While the latter requires large excavations to build the foundation boxes, the former needs only a peripheral excavation to lay the cell concrete walls either cast in place or precast. Needless to say that the time, the cost and the geotechnical complex issues to carry out the tasks required to set up the foundations are much higher for the friction pile-box foundation than for the structural cell, particularly in deep-low strength-compressible clayey deposits. Furthermore, there are issues like the bottom stability of large excavations or settlements caused in the neighboring ground surface that can induce appreciable structural damages to surrounding constructions. In addition, the imperviousness of the complete box concrete walls is a most to avoid ground water seeping into the box foundation and hence increasing the foundation loading as time passes by. As to the structural cell, the concrete walls permeability or the bottom stability as well as hydrostatic water pressures on the walls are not issues of real concern.

In this paper, we present the 3D numerical analyses carried out to evaluate the bearing capacity under sustained and earthquake-like loading. As well as, the computations to evaluate the immediate and long-term settlements of a particular structural cell. Long-term (10 and 50 years) settlements caused by soil consolidation due to external loading and ground subsidence induced by water withdrawal from the aquitards underneath. Finally, comments on the overall behavior of a number of structural cells after more than five years of their construction are made.

3D Analysis of a typical structural cell foundation included in the Metro Line L-12

Numerical model characteristics

The length (L) and width (B) of the top slab and the cell walls depth (H) of the structural cell analyzed are L= 6.5 m, B= 6.5 m and H= 13.8 m. The thicknesses of the cover slab (t_s) and walls (t_w) are t_s= 1.7 m and t_w= 0.6 m, and that of the compacted fill (see Fig. 3) placed over the concrete cap is 1.2 m. The numerical model, shown in Fig. 2, has the following dimensions: length= 80.0 m, width= 80.0 m and depth= 34.0 m.

The vertical lateral boundaries of the numerical model were at a 5.6B distance away from the cover slab edges, and all nodal points on the model lateral boundaries were restricted to move horizontally. A fixed bottom horizontal boundary was set up near 2.5B away from the wall tips of the cell. The outer wall-soil contacts were considered smooth (interface elements were included) to allow relative movements between the walls and the soil, and the stiffness and strength of the soil near the walls were assumed to be 80% of those of the surrounding soil to account for soil remolding upon cell construction. Soil and concrete top slab materials were modeled with eight node-lagrangian zones. Shells mimicked walls.

Constitutive model and material parameters

The constitutive soil model is elasto-plastic material having a Mohr-Coulomb failure criterion, for both short and long periods (this model has proven to yield consistently accurate results for the clays of Mexico City when used in finite element analyses [²³]). The analyses were performed in terms of total stresses for the former condition, and in terms of effective stresses for the latter condition. Tables 1, 2 and 3 include the soil parameters for short-term, including parameters for pseudo-static analyses, and long-term conditions, respectively, considered. The soil parameters included in these tables were obtained from laboratory tests performed on samples retrieved from the site where the structural cell selected for its study was to be founded, and complemented with properties of normally consolidated or slightly over-consolidated Mexico City clay samples obtained from nearby borings. Henceforth, the soil material properties considered are representative of the foundation site.

The concrete structural elements (walls and top slab) and the compacted fill material were assumed to have a linear-elastic behavior; the 28-day concrete compressive strength (f´c) of the cover slab was 35 MN/m² and that of the concrete walls, 25 MN/m². Concrete Younǵs modulus was estimated from E= 14,000 (f’c)^0.5 and its unit weight was considered equal to 24 kN/m³. The elastic parameters of the compacted fill material, structural cell walls and concrete cover slab used in the analyses are included in Table 4.

Loading system upon the concrete structural cell

The analyses to evaluate the bearing capacity of the structural cell considered a loading system that included lateral (H), vertical (V) and overturning moment (M), see Fig. 3. Table 5 specifies the magnitudes of the acting loads according to the particular analysis direction. These loads conform to the 2004 Construction Code requirements [²⁴], which specifies that the magnitudes of the overturning moments applied be 100% (30%) in the across (along) directions and then 100% (30%) in the along (across) directions, keeping constant the vertical loading. Herein the results yielded by the analyses considering the former loading condition, which resulted the most critical, are only included.

Numerical results

Vertical sustained loading

The vertical load (9,141.6 kN) applied directly on the top concrete slab, see Fig. 3(a), produced a maximum uniform elastic settlement near to 1.3 cm. Fig. 4(a) shows the corresponding settlement contours computed throughout the vertical section along the symmetry plane and Fig. 4(b) the settlement configuration of the top slab.

It is worth noticing that the settlement contours shown in Fig. 4(a) indicate that the soil enclosed within the structural cell settles as a block, indicating that it moves downwards coupled with the structural cell. Hence, the hypothesis that considers that the enclosed soil within the cell follows in a coupled fashion the cell displacements is satisfied. According to Fig. 4(a), there exists a very small maximum differential vertical displacement of around 4.0 mm, between the elevations of the cell center and of the wall tip foundation, which could be due to round off errors. Of course, the dome formed at the bottom of the cell due to these small differential settlements is for all practical purposes negligible.

The undrained vertical bearing capacity of the structural cell foundation defined from the collapse curve shown in Fig. 5(b) for 30% of the normalized vertical displacement (2D_max /B; D_max= top slab maximum settlement; B= top slab width) is 865 kPa. The procedure for reaching the collapse curve, was applying smaller vertical load increments as the load-displacement curve, Fig. 5(b), became flatter. The displacement velocity contours depicted in Fig. 5(a) correspond to the 30% of the normalized settlement (collapse point).

Here it is important to emphasize that the process followed to obtain the collapse curve q_u-2D_max /B includes the influences of the lateral, q_L, and the tip, q_T, resistances plus the overload at foundation depth, q₀= g_mH (g_m is the unit weight of soil and H is the foundation depth). The lateral resistance is the friction force developed along the external sides of the cell walls-soil contacts (once this is exceeded the lateral friction is assumed to drop to zero and relative movements at the wall-soil interface can follow); the tip resistance is the vertical bearing capacity of the cell-soil system.

To fulfill the project requirements regarding tolerable displacements and stability, the collapse load (ultimate bearing capacity) was defined when the normalized settlement 2D_max /B was equal to 10%. According to Fig. 5(b) the ultimate bearing capacity was q_u = 793 kPa. Considering the vertical loading imposed and the bearing capacity computed numerically as mentioned above, the resulting safety factor SF= q_u / q = (793.0 / 273.4) = 2.90 is high enough to be considered admissible.

Two orthogonal overturning moments

The overturning moments and inertia horizontal forces given in Table 3 correspond for a viaduct service life of 50 years and a return period earthquake of 475 years, required by the 2004 Federal District Construction Code [²⁴]. The site natural period obtained with an in-house computer program assuming vertically propagating shear waves through layered soil deposits was 2.5 s, which neglecting earthquake soil-foundation interaction and considering the 2004 Construction Code Regulations [²⁴], the design seismic coefficient was 0.40.

Short-term cell distortions

The Federal District 2004 Construction Code does not include any recommendation regarding distortions allowable for deep foundations (i.e., piles, deep boxes); it only stresses the point that great care should be exercised when carrying out the construction activities required. Accordingly, to evaluate the magnitude of potential distortions along the cell walls and rotation of the top slab, the suitable results of the 3D finite difference analyses were plotted in Fig. 6. It is interesting to point out that overlapping the overturning moments-induced movements shown in the three pictures of Fig. 6 roughly delineate the rocking-swaying coupling modes. On the left picture one can discern the rocking of the foundation around a somewhat skewed horizontal axis passing within the cell-soil system. The skewness of the virtual rotation axis is due to the action of the two orthogonal overturning moments; the pictures in the middle and on the right depict the two-direction swaying of the cell.

All calculated displacements in the three directions are very small as indicated in Fig. 6. The corresponding surface slab rotation and tilting of the cell walls are as follows: rotation of surface cover cap 0.00258; tilting of front cell walls, 0.00243 (top-tip of cell walls); tilting of lateral cell walls, 0.00198 (top-tip of cell walls). Since rotation and tilting values are very small, they will not pose any concerns as to potential damage to the concrete cell components.

Overturning moment resistance

When computing the resistance to the overturning moment, the acting vertical loading remained constant while the horizontal and moment loadings applied corresponded to the values and directions given in Table 3. Fig. 7(c) shows the cell rotations (indicated by the arrows) obtained for the case when horizontal and overturning moment (row 1 and corresponding column of Table 3) correspond with “across” direction for several stage loads (A, B, C and D). Fig. 7(c) show how the cell rotates as the overturning moment increases monotonically from stage A to D. The last load increment corresponds to the velocity displacement contours equal to 23% of the angular rotation of the cell cap slab (η = Dd / Dh, where Dd is the maximum differential settlement on the cap slab and Dh is the horizontal distance between the points where the maximum Dd develops). The velocity displacements represented by arrows in the plots of Fig. 7(c), show that the resisting moment mainly depends on passive and active pressures developed on the front and back of the cell walls, the shear strength of the shallow soil located in front of the cell and the bearing capacity of the soil located beneath the cell tip. Moreover, these plots clearly indicate that the cell rotation center shifts in accordance with the load magnitude. At failure, the cell rotation center is located at the cell mid width and some (1/2)^0.50 deep underneath the surface slab. This is piece of information is very important because most analysis consider that the overturning moment rotates around cell mid-section at its tip foundation, which differs significantly from the results shown by Fig. 7(c) for the stage D.

Considering that, the cell-soil system fails when the slab surface reaches 23% rotation, the collapse curve of Fig. 7(b) obtained from 3D finite difference analyses shows that the ultimate overturning moment (M_u) is around 122.1 MN-m. Accordingly, the safety factor (SF) against failure (hypothesized it occurs at h = 23%) SF= M_u / M = (122.1 / 69.7) = 1.75, which is admissible for dynamic loading. Considering that h=2% is the upper limit of the rotation of the surficial concrete slab for not exceeding the maximum tilting of the supporting columns then, SF= (103/69.7) = 1.63.

Consolidation settlements

Table 3 indicates the compressibility parameters used to compute the consolidation settlements. These initial compressibility values modified as a function of the effective stress state, which is time dependent as the clay deposit consolidates. Fig. 8 shows typical effective-stress variation curves of the Mexico City clay compressibility modulus, used in the analyses carried out in this study. The profile of pore water pressure existing in the site where the foundation was designed (2009) is in Fig. 9. In this figure are also included the pore pressure profiles for 10 and 50-year forecasts. A representative permeability coefficient k= 0.43 m/day for the construction site was considered to obtain the forecasted isochrones. The computed settlements for 10- and 50-year periods indicate that the ground surface across the traffic lanes remains horizontal for all practical purposes, as shown in Fig. 9. Comparing the graph corresponding to the 10-year period with the picture included in Fig. 14, one can conclude that the theoretical pavement settlements across the traffic flow conforms well enough the observed pavement surface. Hence, it may be argued that the forecasted settlements for a 50-year period, included in Fig. 10, are reliable and indicate that the pavement surface will remain for all practical purposes horizontal throughout this period.

The differential settlements, shown in Fig. 11, along the superficial line that links two consecutive concrete cell foundations, which are some 20 m apart from each other, clearly indicate that the concrete cells are following the soil subsidence due to water withdrawal. Comparing these results with Fig. 14 that shows the superficial conditions of the concrete asphalt pavement, one comes to the conclusion that the computed settlements conform with the structural cell behavior observed over a 5 years period after their construction.

Accordingly, the profile forecasted for a 50-year period is reliable and therefore the pavement surface will remain for all practical purposes with the original inclination required to allow rain water draining (i.e., large swamps due to rain water will unlikely develop on the asphalt concrete surface). From these results, it could be argued that a 20 m separation between two consecutive cell foundations is advisable for the soil and hydraulic conditions prevailing in Mexico City to keep differential settlements tolerable within them.

Behavior of structural cell foundation after five years of being built

Fig. 12(a) shows the plan view of the Line-12 elevated viaduct stretch where supports have structured cells foundation. Structural cells foundations were fully loaded on early October 2010 and the Metro Line-12 operations began in June 2012. In this period, topographic leveling reported settlements of 0.01 and 0.03 meters, Fig. 12(b) includes the settlement-time curves of the three supports that had settled more up to late October, 2012 (cl-33, cl-34 and cl-35). Unfortunately, due to economic issues, levelling was suspended on November 28, 2012 hindering a unique possibility of settlement monitoring of a new type of foundation and hence gather data regarding their long time behavior. Nonetheless, close observation of the overall response of the cell foundations allowed drawing conclusions regarding their performance.

Since the soil foundation is a saturated soft clay deposit with thickness up to 26 meters, these settlement histories point out that after about five years of their construction the structural cell foundations consolidation settlements, due to overloading, have for all practical reasons have stopped. Furthermore, Fig. 12(b) seems to indicate that the structural cell foundations are following at present times the zone regional settlements. Since the topographic leveling of the cell foundations refers to a specific ground surface bench level, Fig. 12(a), the differences in lectures between the supports and all bench levels are relative settlements that do consider the regional subsidence. Accordingly, the settlement-time curves represent the differential settlement between the supports and the ground surface. Fig. 14 clearly shows the flatness of the avenue pavement surface. It is worth mentioning that long-term consolidation laboratory tests indicate that secondary consolidation-induced settlements reach values between 5% to 6% of those caused by primary consolidation, which agrees well with previous studies carried out on highly plastic clays [²⁵].

It is important to stress the fact that a number of high magnitude earthquakes (see Table 6) have shaken the elevated viaduct and no damage to the upper structure nor sudden foundation settlements have been observed, as depicted by Fig. 13. These observations indicate that the foundation-structure system has behaved properly under seismic loading.

Fig. 13 shows that as to now (June 2016) both friction pile-box foundations and structural cell foundations have had a similar behavior (i.e. no sign of distress in the columns is seen nor foundation displacements causing fissures on the central traffic strip or the asphalt concrete pavement are observed). This overall behavior stresses the fact that the structural cell is a viable alternative to the friction pile-box foundation in deep strata of soft clay. Moreover, as mentioned earlier the structural cell causes less traffic jams during its construction and obstructs less traffic lanes afterwards, as seen in Fig. 13. This picture shows that the friction pile-box foundation (background) blocks two lanes (one on each side of the median strip) and the structural cell (in the foreground) allows traffic throughout three lanes on each side of the median strip. Obviously, this affects directly the traffic flow during peak hours and reflects upon economic and environmental issues.

Conclusions

In this article, we show the good behavior of the squared-structural cell cl-31 acted upon by vertical and overturning moment loading after more than five years of its construction. We arrived at this conclusion from leveling measurements over three years, and posterior close observations till our days showing that the structural cell foundations (particularly cl-31, cl-32 and cl-33) have no sign of any distress and the asphalt concrete pavement surface neighboring the cell foundations is in good conditions. It is interesting to note that the 3D numerical analyses results show that the soil consolidation settlements due to external loading are being slowly overridden by the relative upward movement of the structural cells with respect to the surrounding soil that settles due to water pumping out of the aquifers. It seems that the cell foundation induces a negligible overcompensation (i.e., the regional settlement underneath the structural cells occurs at a similar rate than that at the near “free field”). It is worth to mention that several 7.0 and above 6.0 M_w magnitude earthquakes have hit the structure over the 5-year observation period reported in this paper, and no damage whatsoever has been reported.

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