1 INTRODUCTION The high compressibility and low shear strength of Mexico City lacustrine clays, together with regional subsidence due to pumping of water from the subsoil and high seismic activity, have made of this city (A soil Mechanics paradise according to K. Terzaghi) a full-scale laboratory where it has been possible to ponder the influence of many factors on foundation behavior in extreme conditions. This document presents an overall picture of the subsoil of Mexico City and of the problems encountered in excavations and foundations design and construction. The multiple geotechnical hazards and corresponding serviceability and failure limit states to be considered in design are examined. The special conditions prevailing in Mexico City led to the adoption of different types of excavation and foundation techniques in which an impressive amount of creativity was involved. These systems are briefly described herein and their respec-tive merits are evaluated.

2 THE SUBSOIL OF MEXICO CITY

The urban area of Mexico valley can be divided in three main geotechnical zones (Marsal & Mazari, 1975): Foothills (Zone I), Transition (Zone II) and Lake (Zone III). In the foothills, very compact but heterogeneous volcanic soils and lava are found. These materials contrast with the highly compressible soft soils of the Lake Zone. Generally, in between, a Transition Zone is found where clayey layers of lacustrine origin alternate with sandy alluvial deposits er-ratically distributed.

Excavations, Foundations and Geotechnical Hazards: The case of Mexico City

G. Auvinet Research Professor, Institute of Engineering, National University of Mexico, Mexico City ISSMGE Vice President for North America

gauvinetg@iingen.unam.mx

ABSTRACT: An overview of the main geotechnical hazards that must be taken into account in the design and construction of deep excavations and foundations in soft soils is presented. The paper focuses on the case of the lacustrine zone of Mexico City. The solutions commonly adopted for excavations and foundations of buildings in these very difficult soft soil conditions are examined. It is concluded that most geotechnical hazards can be dealt with by using ration-ally the geotechnical information available and performing analyses based on sound soil me-chanics principles.

Figure 1. Soil profile in the Lake Zone of Mexico City (Marsal, 1975)

In Figure 1, a typical soil profile corresponding to the Lake Zone is presented. The water ta-

ble is close to the surface. Three clayey layers are to be distinguished, denominated upper (Formación Arcillosa Superior, FAS), lower (Formación Arcillosa Inferior, FAI) and deep de-posits (Depósitos Profundos, DP). The clays of FAS are separated from FAI by a hard layer (Capa Dura, CD), a sandy clayey stratum, some 3m thick, lying at a typical depth of 30 to 35m. Generally, FAS is covered by a desiccated crust and/or an artificial fill several meters thick.

Average values of index properties for borehole Pc 28 are presented in Table I.

Table I. Typical average values of index properties in Lake Zone (Borehole Pc-28, Marsal, 1975)

PROPERTY FAS CD FAI Water content, % 270 58 191 Liquid limit wL, % 300 59 288 Plastic limit, wP, % 86 45 68 Density of solids, Ss 2.30 2.58 2.31 Initial void ratio, e0 6.17 1.36 4.53 Unconfined compressive strength, qu, kN/m2 85 24 160

The spatial variations of soil properties in the lacustrine zone have been assessed forming a

data base consisting of more than 10,000 boreholes. This data base was incorporated in a Geo-graphical Information System focused on geological and geotechnical problems. Interpolations of data have been performed using estimation and simulation geostatistical techniques (Auvinet, 2002). The present geotechnical zoning of Mexico City is presented on Fig. 2. An updated zoning will be available in 2014.

Figure 2. Geotechnical zoning of Mexico City (GDF, 2004)

Due to extraction of potable water from deep aquifers and to other factors, since the begin-

ning of the XXth century, the lacustrine zone of Mexico City has suffered a general subsidence that in some locations has exceeded 13m. Recent data show that subsidence rate tends to de-crease in certain areas. However, in newly developed urban zones such as the center of Texco-co Lake and of former lakes of Xochimilco and Chalco, in the south of the valley, the consoli-dation process is only in its first stage and the subsidence rate attains 40cm per year. There is no end in sight for this phenomenon since close to 70% of the potable water of Mexico City is directly obtained from the subsoil of the valley. Differential settlements associated to general subsidence induce soil fracturing. This is becoming a severe problem in some zones of Mexico City. Soil fracturing is also induced by other mechanisms, including hydraulic fracturing (Ovando et al., 2012).

After the 1985 earthquakes, an extensive research program was undertaken to obtain a better

knowledge of dynamic properties of Mexico City clays. Shear modulus attenuation curves were obtained and modeled and the degradation and residual strains due to cycling loading have been assessed. Important advances have also been registered in the modeling of site effects on ground motions and of soil-structure interaction in seismic conditions (Romo & Auvinet, 1992; Romo, 2002). The present and future influence of the subsidence process on the properties of Mexico City clays has been evaluated and important consequences such as a significant modifi-cation of the ground seismic response can been foreseen.

From the above, a list of the main geotechnical risks can be established for excavations or

foundations in Mexico City soft soil: - Large short-term and long term deformations of the soil induced by loading or unloading

(foundations, excavations). - Shear failure of the soil due to its low shear strength (slopes, superficial foundations) - General subsidence effects on excavations and foundations (negative skin friction, appar-

ent protruding) - Soil fracturing due to different mechanisms (affecting excavations and foundations) - Seismic site effects (affecting excavations and foundations)

3 EXCAVATIONS

Many different techniques have been and are being used for large excavations in Mexico City clays. Few open excavations with slopes are executed these days, since they can only be per-formed in large lots where interference with existing constructions is not a problem. Generally, excavations can only be made using some sort of lateral support system. a) Support elements

- Berlin Walls. Application of support systems constituted by anchored or unanchored soldier

piles and wood lagging is limited to very shallow (<3m) excavations in Mexico City. When the FAS clay is reached, risk of base failure or extrusion of soft layers at the base of the wall, be-fore the boards can be placed, becomes unacceptable.

- Sheet Piles. Wood, steel and concrete sheet piles driven in the soil before the excavation

starts have been commonly used to support excavation walls in Mexico City. Difficulties are sometimes encountered to drive the sheet piles and pre-boring may be required, especially in the Transition Zone. Seepage of water and/or intrusion of soil through joints between adjacent elements can also be a problem. Due to their flexibility, wales are used to support the concen-trated forces transmitted by the struts.

- Cast-in-place Diaphragm Walls. This technique consists of casting concrete in trenches sta-

bilized with slurry. Diaphragm walls were introduced in Mexico City for the construction of the first lines of the subway system in 1967 and have received a wide acceptance since then.

- Precast Walls placed in Slurry Stabilized Trenches. This is an alternative to diaphragm

walls that is increasingly popular. Precast wall elements are placed in a trench stabilized with bentonite cement grout. The main advantages of this technique are the quality of the wall sur-face and its lesser final thickness as compared to diaphragm walls. Its main limitation is the maximum weight of the precast elements that can be handled. b) Excavation and Bracing Techniques

- Central core method. This technique consists of driving vertical support elements such as steel or concrete sheet piles along the outer limit of the construction area and excavating only the central part of this area, leaving a peripheral berm in place. The central part of the substruc-ture is then built and used to support the struts that are progressively placed against the sheet piles, while short stretches of the berm are removed. The rest of the substructure can then be built. This technique is generally limited to wide excavations no deeper than 6m due to berm stability problems. It can also be used with diaphragm walls.

- Wall-to-wall bracing. Wall-to-wall bracing is used when the existing horizontal space is not

sufficient to use the central nucleus method and for very deep excavations. The bracing struc-ture consists generally of tubular struts. In some instances, cast-in-place transversal walls have been used as supporting structure. Those walls are then partially or totally demolished during excavation and substructure construction (Ponce, 1985).

- Anchors. Prestressed anchors are not used in the Lake Zone due to the low strength of the

soft clay. On the other hand, they have been quite useful in the Transition and Foothills Zones where walls can be tied back in firm soils. The main advantage of this technique is that the sub-structure can be constructed free of obstacles. However, legal aspects concerning anchors in-vading the subsoil of contiguous lots are still a problem and have been a cause of serious con-flicts.

- Use of the substructure as a bracing system. In a limited number of cases, the substructure

itself has been used as a support system. This requires driving sheet piles or casting walls in

trenches before the excavation starts and performing underground excavation while the sub-structure is being built from the ground down.

Other techniques, such as driving precast substructures by inducing failure of the soil at the

base of the peripheral wall from within, have been tested but were only partially successful due to the high sensitivity of Mexico City clay (Marsal, 1959).

For deep excavations in soft clays, and especially for tunnel shafts, some special techniques

have also been developed. These include the flotation (Auvinet et al., 2010) and the prefabri-cated rings methods (Zemva, 2011).

c) Groundwater considerations for deep excavations

In saturated soft clays like those found in Mexico City, the water table subsides spontaneous-ly as the soil is excavated due to negative pore pressures induced by unloading. Dewatering is thus required only to maintain this condition and to control the flow of water, mainly through pervious lenses, towards the excavation. It may also be necessary to eliminate uplift pressures in sand layers close to the bottom of the excavation. Dewatering contributes to avoid effective stress changes within the soil that cause volumetric expansions and have an unfavorable effect on soil strength. It can also be used to give a favorable orientation to seepage forces within the soil in order to improve the working conditions and the stability of the excavation.

Extraction of water should however be reduced to a minimum in order to avoid consolida-

tion-induced settlements of the surrounding area. In impervious clays, flow nets cannot be used to design pumping systems since the flow condition is generally not a steady one. These sys-tems are thus designed on an empirical basis, using local experience. They generally consist of a series of wells of small diameter with jet-eductor pumps. Even for large excavations, the vol-ume of water extracted rarely exceeds a few liters/s. d) Analysis and design of deep excavations

Much of the experience in matter of deep excavations in the soft soils of the Mexico City valley has been incorporated in the guidelines and requirements included in Mexico City Build-ing Code and Complementary Norms for Design and Construction of Foundations (2004).

According to these documents, two types of limit states must be considered: - Failure Limit States: collapse of slopes and/or supported or unsupported walls, failure of

the foundation of contiguous constructions, failure of the bottom of the excavation due to shear stresses or to water pressure in pervious layers located below the excavation depth.

- Service Limit States: short and long term vertical and horizontal movements induced by un-

loading in the excavated area and its surroundings. A minimum uniform vertical surcharge of 15kPa in the area surrounding the excavation must

be considered in the stability analysis. From the point of view of Failure Limit States for design of deep excavations, the main con-

siderations are the following: - Slopes Stability of excavation slopes must be verified using limit analyses considering kinematically

admissible potential failure surfaces. Cracking of soil induced by unloading must be taken into account and attention must also be paid to failure mechanisms involving extrusion of very soft thin layers (Reséndiz and Zonana, 1969). Time has also been shown to be an important factor in

the stability of slopes as cohesion tends to decrease (Alberro, 1987). The resisting forces or moments considered in the analyses must, in general, be reduced multiplying them by a re-sistance factor of 0.6; however, a factor of 0.7 is considered acceptable when failure cannot af-fect public facilities or contiguous constructions.

- Failure of bottom of excavation induced by uplift pressure. When an excavation is performed in the upper clay layer, where some pervious horizontal

lenses are interbedded, it is essential to check that the water pressure in these lenses cannot in-duce uplift failure of the bottom of the excavation. The minimum thickness of impervious mate-rial above any lens should be:

h > (w/m)hw (1) where: h thickness of impervious layer hw water pressure in lens (meters of water) w unit weight of water m unit weight of impervious material When this condition cannot be satisfied with an ample safety margin (safety factor larger

than 2, to allow for cracks in the clay), water pressure in critical lenses must be abated by pumping from vertical wells. This has become a common practice in Mexico City.

- Stability of supported walls. In braced excavations, the main points to check are the stability of the bottom, the stability of

a mass of soil including the support elements and the structural capacity of struts.

Base shear failure is especially critical for deep excavations. The following condition must be checked:

RcuCv FNcqFp (2)

where: cu undrained shear strength of the soil below the level of the bottom of the excavation Nc Skempton's bearing capacity factor, a function of the dimensions of the excavation

(Skempton, 1951) pv vertical total stress in the soil at excavation depth qFc superficial lateral loads affected by a load factor FR resistance factor equal to 0.5 when public services or contiguous constructions can be

affected and to 0.7 when such a risk does not exist. Analyses by the characteristic lines method have shown that safety against base failure can

be significantly improved (up to 44%) by preloading of struts (Alberro, 1987). For an accurate evaluation of this risk and estimation of induced movements, step-by-step finite element model-ing of the excavation and bracing, assuming that the soil presents an elasto-plastic behavior, has been used (Romo et al , 1992; Rodríguez, 1998).

Thrust on struts can be estimated from measurements that were performed on actual struc-

tures (Rodríguez, 1969; Alberro, 1970). Pressure diagrams similar to those proposed for clays by Peck (1969) are commonly used for design. However, it is always considered that for exca-vations performed below the water level, the resultant thrust on braces should be at least equal to the hydrostatic pressure.

- Stability of trenches for diaphragm walls. Stability of trenches used for diaphragm walls can be verified by a number of limit analysis

methods (Nash, 1963; Alberro and Auvinet, 1984). For the impervious clays of Mexico City, it has been shown that plain water or water mixed with local clay can be used instead of bentonite slurry to stabilize the trenches (Santoyo et al., 1987). Formal reliability analyses (Arias, 1997) suggest that the critical stability factors are the level of the slurry in the trench and the magni-tude of the lateral vertical surcharge in the surrounding area. It must also be taken into account that soil fracturing is a common problem during the construction of trenches. This phenomenon can generally avoided by controlling the level of the slurry within the excavation.

- Stability of contiguous building foundations Attention must be given to possible damage or failure of foundation of contiguous buildings.

Conversely, superficial footings must always be designed taking into account the eventuality of an excavation being opened in contiguous lots. Accordingly, for footings close to lot limits, a low resistance factor, of the order of 0.3, must be considered.

From the point of view of Service Limit States, the following aspects are particularly rele-

vant: - Short and long-term movements associated to unloading Very large short-term vertical soil movements induced by unloading have been registered in

excavations performed in Mexico City soft clay (Cuevas, 1936). These movements can be suc-cessfully predicted using the theory of elasticity (Alberro, 1970). The short-term modulus to be used for Mexico City clay in this type of calculation is typically around 5MN/m2 and Poisson's ratio is close to 0.5. Vertical movements of several decimeters can be expected in the bottom of large excavations. In order to reduce the impact of such movements on the foundation structure, it has been found convenient to divide the excavation in small areas, following a symmetrical sequence. The corresponding parts of the foundation structure are built immediately in order to ballast the excavated areas and to reduce overall unloading and differential movements.

When the excavation remains open during a significant period, expansions associated to vol-

umetric changes can also become very important, especially if drainage is inadequate and water can flow freely towards the excavation.

Permanent unloading of the soil for structures such as underground parkings, or subway cut

and cover tunnel, lead to additional long-term vertical movements due to interference with re-gional subsidence. The subsoil of unloaded areas becomes preconsolidated and less susceptible to this phenomenon. Progressively, these structures tend to protrude, sometimes by several me-ters, above the surrounding ground (Díaz Cobo, 1977).

- Settlement of the ground around the excavation. The short-term settlement of the surrounding area induced by excavation depends mainly of

the movements of the bracing system. Preloading of struts close to their design load has been a common and efficient practice to control these movements.

For deep excavations in Mexico City clays, elasto-plastic finite element analyses have been

performed in order to check and extend the results presented by Mana and Clough (1981), O'Rourke (1981) and Hashash and Whittle (1996) regarding soil movements near braced exca-vations. The soil thrust/struts reaction ratio was singled out as the main factor that controls the magnitude and path of the soil movement (Rodríguez, 1998).

4 FOUNDATIONS

4.1 General design considerations

Foundations of buildings in the lacustrine zone of Mexico City have to be designed taking into account the high compressibility and low shear strength of the thick soft clays layers of the sub-soil. Design must also consider, among other factors, the general subsidence induced by pump-ing of potable water from the deep strata, the fracturing of the soil frequently observed in some areas, and the site effects that induce a strong amplification of the seismic waves that periodi-cally affect Mexico Valley subsoil.

As specified by Federal District (Mexico City) Building Code (G.D.F., 2004), foundations

must present an adequate safety against a large number of limit states that can be divided as fol-lows:

a) Failure limit states: flotation, plastic local or general displacement of the soil below the foundation and structural failure of footings, slabs, piles, drilled shafts or other foundation ele-ments.

b) Serviceability limit states: vertical average movement, settlement or emersion with respect to the surrounding ground, average tilting and shear deformation induced in the structure.

Security against these different limit states must be guaranteed for different load combina-

tions including extreme and average static loading but also for accidental conditions including wind and seismic actions:

a) Permanent loading plus variable loads with average intensity. This combination should be

used to compute long-term soil deformation and to evaluate the excavation required for load compensation.

b) Permanent loading plus the most critical variable loads with maximum intensity plus other variable loads with instantaneous intensity. This combination should be used to assess failure limit states.

c) Permanent loading plus variable loads with instantaneous intensity plus accidental loads (earthquake or wind). This combination should be used to evaluate failure limit states and ser-viceability limit states (including transient and permanent soil deformations).

Estimating the loads entering into these combinations is far from trivial. Too often, design is

in fact based on preliminary estimations of the permanent, live and accidental loads. Even when a careful final review of the actual loads is made, design loads retain generally a large random component.

For Mexico City buildings, the coefficient of variation of permanent loads is approximately

constant and typically equal to 0.08. The coefficient of variation of live loads is larger and is a function of the area on which they act; yet it generally has only a small effect on the coefficient of variation of the total load. Not included in these considerations is the case of gross variations of live loads due to changes in the use of the buildings or occurrences such as flooding of the basement of compensated buildings, which further increase the uncertainty on the actions at the foundation level. All these factors make it highly commendable that a reliability analysis be performed for design of important buildings.

4.2 Main types of foundations.

The solutions adopted for foundation of buildings on soft soils in Mexico City have evolved progressively since the pre-Columbian and colonial periods due to the necessity of building in-creasingly larger, higher and heavier constructions (Fig. 3).

Figure 3 Types of foundations on soft soils in Mexico City

The most common solutions used today include footings, rafts, and box-type foundations for

relatively light constructions and precast driven point-bearing piles and, to a lesser extent, bored piles and drilled shaft for heavier buildings, especially in the transition zone. A number of special systems, including friction piles, have also been used. In many cases, the choice be-tween these different solutions is not obvious and their functional and economical advantages and inconveniences have to be carefully compared. In all cases, the selected foundation must meet the safety requirements imposed by the building code.

It must be recognized that, with some notable exceptions (Zeevaert, 1973), foundation design

in Mexico City before the macro-earthquakes of 1985 was almost exclusively aimed at control-ling the magnitude of total and differential settlements or the apparent emersion of foundations in static conditions. The lessons learned during the 1985 earthquake made it necessary to re-view the traditional foundation systems taking systematically into account the seismic factor.

4.2.1 Superficial and compensated foundations Foundation on masonry footings or general raft, sometimes with short wood piles, was the first system tested by the founders of the city, with very little success at that, as attested by the spec-tacular problems registered in the foundation of the “Templo Mayor”, the main pyramid of the Aztecs, and of many heavy colonial temples such as the Metropolitan Cathedral and the Vera Cruz, Profesa, Santísima and Loreto churches, to name only a few. The large settlements of the Bellas Artes theatre, built in 1910 are also famous. It is now accepted that superficial founda-tions on footings or superficial mats are only acceptable for light constructions occupying a rel-atively small area. It must be taken into account that a uniform loading of only 20kPa applied on a large area of the lake zone can be expected to induce a total settlement close to 1m with differential settlements of about 50cm. Moreover, these foundations are vulnerable to move-ments induced by adjacent buildings.

Some of the problems faced when using superficial foundations can be managed recurring to compensated or “floating” foundation. The well-known compensated foundation technique consists of designing the foundation, generally a box-type structure, in such a way that the mass of excavated soil will be comparable to the mass of the building (Cuevas, 1936). Theoretically, if both weights are equal, the soil below the foundation is not submitted to any stress increment and no significant settlement should develop. When the weight of the soil is smaller than the weight of the building, the foundation is partially compensated; in the opposite case, it is over-compensated.

In practice, even perfectly compensated foundations undergo absolute and differential verti-

cal movements due to soil elastic deformation, soil disturbance during construction and static soil-structure interaction thereafter. Furthermore, constructing this type of foundation is not straightforward since a deep excavation in soft soil is generally required with the associated problems of earth slopes or support systems stability and to bottom expansion or failure (Auvinet & Romo, 1998). Water tightness of the foundation is also a critical factor for compen-sated foundations; in many cases, this type of foundation must be equipped with a permanent pumping system to control infiltrations.

a) Settlements and soil deformation The methods for estimating absolute and differential settlements of shallow or partially com-

pensated foundations in static conditions have not progressed much during the last years. The standard procedure consists of determining the vertical stress increments induced in the soil by the construction using elasticity theory and estimating the corresponding strains from one-dimensional laboratory consolidation tests. Results obtained by this widely used method are slightly on the conservative side but can be considered as adequate at least to detect the pos-sibility of grossly excessive settlements. Stress increments are now easily determined using computers instead of traditional tools such as Newmark's chart. The development of closed so-lutions for stresses induced by linearly loaded polygonal areas (Rossa & Auvinet, 1992) has al-so been helpful.

In highly compressible soils, the computed settlements are of course extremely sensitive to

uncertainties on load magnitude and eccentricity. Mexico City Building Code specifies that to-tal settlement of foundations should not exceed 30cm (first criterion) and, for concrete struc-tures, differential settlement per unit length between any two points should be less than 0.004 (second criterion). Accepting that the maximum allowable settlements constitute a critical threshold, and that the combination of permanent plus mean live loads is a random variable, the reliability of typical buildings on compensated foundations was computed by Auvinet and Ros-sa (1991). A very low reliability index was obtained, especially regarding the second criterion. Reliability decreases with the magnitude of the compensation (weight of soil excavated). If a load factor of 1.1 is introduced in the compensation calculation, reliability improves only slightly for the second criterion. Accepting a differential settlement twice as large (0.008, third criterion), as was proposed by some engineers, does not increase significantly the reliability ei-ther. Introducing load eccentricities in two perpendicular directions as additional independent random variables leads to a further decrease of reliability. It can thus be concluded that com-pensation, theoretically an ideal solution, can in fact be unreliable, especially when loads are not known with precision.

It must also be stressed that overcompensated foundations tend to present upward move-

ments due to elastic strains and volumetric expansion of the unloaded soil. On the other hand, the unloaded soil below an overcompensated foundation moves into the recompression range of the compressibility curve while the soil in the surroundings remains on the virgin branch. As a consequence, the preconsolidated soil below the foundation is less affected by the regional sub-sidence process than the soil located in the surrounding area, and an apparent protruding of the

foundation is observed. This has led to spectacular emersion (more than 1m) of some light structures such as underground parking lots and underpasses in the city.

b) Bearing capacity The bearing capacity of shallow and compensated foundations under static vertical loads is

rarely critical, since the design is generally governed by soil deformation. Moreover, it can be estimated with good accuracy using for example the well-known Skempton formula. Verifica-tion of the bearing capacity of a particular foundation can thus be made checking the following inequality:

vRcci pFcNAFQ / (3) where A area of the foundation c soil cohesion (undrained shear strength) NC Skempton coefficient pv vertical stress within soil at foundation depth Fc load factor, as specified by building code FR strength reduction factor, idem Methods for estimating bearing capacity under seismic conditions are not so satisfactory. As

a matter of fact, the present state of practice consists of comparing the maximum load on the foundation, estimated assuming rigid, elastic or visco-elastic behavior of the soil, to the static bearing capacity. The effect of the earthquake is represented by an overturning moment and a base shear force at the foundation depth. These mechanical elements are in turn considered equivalent to an inclined resultant force with a certain eccentricity, e. Eccentricity is generally taken into account by substituting the actual width B of the foundation by a reduced equivalent width equal to B-2e (Meyerhof criterion). Accepting that static bearing capacity is representa-tive for seismic conditions is implicitly equivalent to accepting a compensation of effects, namely, the increase of the soil strength in dynamic conditions on one hand (between 20 and 40% for Mexico City clay according to Jaime et al., 1988) and, on the other hand, its decrease as a result of cyclic loading when the deviator cyclic stress exceeds a critical threshold of about 0.85c. The partial mobilization of the shear strength of the soil by the seismic waves and the in-ertia forces in the foundation soil that can contribute to failure, have been neglected in the most recent versions of Mexico City building code. The reduction suggested by Terzaghi for sensi-tive soils is not taken into account either.

Much research is needed on this problem, which happened to be relevant during the 1985

Mexico earthquake. As a matter of fact, the bearing capacity should be evaluated in two differ-ent conditions: during the earthquake, when dynamic effects are present, and immediately af-terwards, when the pore pressure induced by the shaking may have reduced the available soil strength.

The bearing capacity problem under eccentric loading has been reexamined recently (Auvinet et al., 1996) using the plastic flow theory. Considering parameters N (vertical load), T (base shear), M (overturning moment) and Fx (inertia force within the potentially sliding soil mass), the cinematically admissible mechanism that leads to the best inferior limit of the bear-ing capacity is determined. The results are presented in a normalized form in terms of the vec-tor:

c

BF

cB

M

Bc

T

Bc

NF x

2 (4)

where B is the width of the foundation and c is the undrained shear strength of the soil. In the

space of normalized variables, a domain is defined where the behavior of the foundation is ex-pected to be satisfactory. The overturning moment can be divided in a normal force N and a load eccentricity e, so the results can also be presented in the space of normalized (N, T, e, Fx).

It can be established that for N/Bc < 2.5 ands a safety factor larger than 2 under central loading, the effect of the inertia forces can be neglected. On the contrary, for low safety factors, these forces induce a drastic reduction of the bearing capacity. Moreover, the results indicate that, in certain conditions, the B-2e criterion for eccentricity, generally considered as overconservative, can actually be unsafe. Within the limitations of the present methods, it can be shown that bear-ing capacity in seismic conditions is principally a problem for slender structures. Auvinet and Rossa (1991) have shown that, for Mexico City conditions and considering the local seismic coefficient as a random variable, the reliability index regarding possible overturning rapidly de-creases to unacceptably low values when the slenderness ratio of the structure increases.

During the 1985 earthquake, for a small number of superficial and partially compensated

foundations, punching of the soil and tilting of the building were observed (Auvinet & Mendo-za, 1986). This type of behavior could be traced to excessive contact pressures at the foundation level in static conditions, loading eccentricity, and infiltration of water in the substructure. Some cases of structural collapses of the substructure were also observed showing that design-ers wishing to use compensated foundation tend to structurally underdesign the substructure to gain some weight. It was also obvious that compensation is a poor solution for slender build-ings submitted to large overturning moments since it may lead to an unstable equilibrium.

4.2.2 Foundation on point-bearing piles.

Precast or cast-in-place end-bearing piles embedded in a deep hard stratum are an apparently obvious solution for foundations on soft soils. Moreover, this solution has proven to be more reliable than other types of foundation in seismic conditions in Mexico City. However, founda-tions on point-bearing piles may present some serious problems and their design faces many difficulties. The bearing capacity of the hard layer in which the piles rest is a first source of un-certainty. The shortcomings of classical analytical methods for evaluating this capacity have long been recognized. Most of them assume rigid-plastic behavior of the soil ignoring the es-sential role of soil deformability. Bearing capacity estimations thus tend to be based principally on in situ tests (cone penetration test, pressuremeter) or on loading tests. Heterogeneity of these hard strata is difficult to assess and may originate tilting of buildings with such a foundation. Another source of uncertainty is the scale factor that should be considered when piles of large diameter are used, to take into account soil deformability, curvature of Mohr envelope for high confining pressures, and progressive failure. Some of the scale factors proposed in the literature (Meyerhof, 1983) lead to unrealistically low bearing capacities.

In consolidating subsoil, negative skin friction develops on the pile shaft, reducing its net

bearing capacity (Auvinet & Hanell, 1981). Moreover, an apparent protruding of the structure is generally observed and damage can be induced in adjacent constructions supported by other types of foundation. Consolidation has also the effect of separating the slab of the substructure from the soil. In that condition, the head of the piles is no longer confined and can be structural-ly vulnerable to the combined effect of overturning moment and base shear (Auvinet & Mendo-za, 1986).

As recognized in Mexico City building code, when estimating the forces induced in piles by

negative skin friction, the following elements should be taken into account:

1) The shear stress developed on the shaft of a pile cannot be larger that the limit soil shear strength determined in CU triaxial tests under a confining pressure representative of the conditions of the soil in situ.

2) This limit shear stress can only be reached when the soil attains the corresponding re-quired shear deformation.

3) The axial force developed in a pile due to skin friction within a pile group cannot be larger than the weight of the soil located within the tributary area of the pile.

4) The unloading stresses induced by the skin friction within the soil cannot be larger than those that are sufficient to stop the consolidation process that originates the skin fric-tion in the first place.

Curiously, many of the methods available to assess negative skin friction do not consider all

of the above conditions, especially the last one. It seems that the best way to take into account all of these factors is by using numerical (finite element) modeling (Auvinet & Rodríguez, 2002; Rodriguez, 2011).

As mentioned above, foundations on point-bearing piles presented generally an acceptable

behavior during the 1985 earthquake. However, some cases of structural damages in the upper part of the piles were detected. They were attributed to load concentration in the perimeter of the structure due to the overturning moment and to the base shear.

3.2.3 Special deep foundation systems

Objective Special deep foundation systems have been developed with the principal aim of avoiding

both excessive settlement and apparent emersion associated to consolidation of the upper clay formation. Some systems also allow controlling the load transmitted to each pile.

Foundation systems The different systems all have in common the inclusion in the piles of a “fuse” (an element

presenting large deformations when a critical load is exceeded) allowing the construction to fol-low the regional subsidence. In Table I, the principal systems have been regrouped according to the position of this fuse (in the upper or lower part of the pile, or both). The type of fuse used is characteristic of each system.

Table 1 Principal types of special foundations.

Type Fuse in lower part

Fuse in upper part

Friction piles X Piles with penetrating point X P3 piles X Telescopic piles X Negative skin friction piles X Control piles X Overlapping piles X X

Another solution, not included in the above table, consists of using piles placed within a flex-

ible case (Tamez in Sedesol, 1992). These piles are designed to avoid overloading of point bearing piles by negative skin friction.

a) Friction piles

Friction piles are generally used to transfer stresses induced by shallow or partially compen-

sated foundations to deeper, less compressible layers of the subsoil, and to reduce settlements. Not so often, they constitute the main foundation system and the stability of the structure is made dependent on the bearing capacity of the piles. A clear distinction must be established be-tween these two types of design (Fig. 5; Auvinet & Mendoza, 1987)

WT

a) TYPE I

U

FN

NEUTRAL LEVEL

FP

C P

W + FN = FP + C P + U

WT

b) TYPE II

Q L + U

FP

C P

W = Q L + FP + C P + U

W W

Figure 5. Friction piles

Type I: Design in terms of bearing capacity In this first type of design, the number and dimensions of the piles are selected with the aim

of guaranteeing that they will be able to support the load from the structure under static as well as dynamic conditions, with a safety factor generally larger than 1.5. In areas affected by re-gional subsidence, this type of friction pile is submitted to complex loading conditions (Fig 5a). It has been shown (Reséndiz & Auvinet, 1973) that negative skin friction can develop on the upper part of the piles while positive friction develops in the lower part. A "neutral" level can then be defined where no relative displacement occurs between soil and piles. The position of the neutral level can be approximately determined by a simple equilibrium equation (Reséndiz & Auvinet, 1973):

W + FN = FP + Cp + U (5)

where: W weight of the construction U water uplift pressure on the substructure (if any) Cp end-bearing capacity of piles FN negative skin friction on the upper part of the piles FP positive skin friction on the lower part of the piles

When the neutral level is in a low position (large number of piles or high strength of the low-er layers), negative skin friction may induce significant compression in the piles. Moreover, with time, the head of the piles can be expected to protrude due to the consolidation of the sur-rounding soil located between the surface and the neutral level. When this design philosophy is adopted, the bearing capacity of piles must be estimated taking into account the possibility of group behavior. When the density of piles is high, soil friction available on the perimeter of the pile group plus its base capacity can in effect be smaller than the sum of the capacities of indi-vidual piles.

For piles working in the conditions indicated in Fig. 5a, settlements cannot be calculated by

ill-adapted methods such as the "2/3 rule". Depending on the position of the neutral level, the foundation can in fact present either settlement or emersion. Details of a more realistic method for estimating foundations movements adapted to these conditions were presented by Reséndiz and Auvinet (1973) and are now implemented in software commonly used by designers in Mex-

ico City. A comparison between the results obtained using this analytical model and those given by 2D and 3D numerical models has been presented by Rodríguez (2011)

Type II Design in terms of soil deformation In this case, only a limited number of piles are used with the principal objective of reducing

the settlements of a partially compensated foundation in static conditions while avoiding pro-truding (compensated foundations with friction piles; Zeevaert, 1973). Since the number of piles is low, the neutral level generally coincides with the piles cap (Fig 5b). In that case, posi-tive friction is mobilized along the full length of the piles, and the piles are in permanent failure state, which justifies the name of “creep piles” that they were given by some authors (Hansbo, 1984). In that case, the equilibrium equation is written:

W = Q + FP + Cp + U (6)

where Q is the effective contact pressure at the interface of soil and slab. Problems similar to those discussed for compensated foundations may occur. Reliability is

low against excessive settlements in static conditions (Auvinet & Rossa, 1991). Without any doubt, the foundations of this type were those that suffered most damages during the 1985 earthquake: 13% of all buildings between 5 and 15 stories, most of them on compensated foun-dation with friction piles, experimented settlement, tilting and, in one case, total failure.

“Creep piles” piles cannot be expected to absorb cyclic loading during earthquakes, since

soil-pile adherence is already fully mobilized, and can even decrease due to clay remoulding as cyclic shear stresses develop at the interface between soil and pile. Full scale experiments per-formed by Jaime et al. (1991) have shown that piles fail when the combination of sustained plus cyclic loading exceeds the static bearing capacity during more than ten cycles. When the total loading exceeds this value by more than 20%, the subsequent sustained bearing capacity decreases to a value as low as 50% of the static capacity, while a penetration of the pile of 10 cm or more is observed.

In the laboratory, direct shear tests of the soil concrete interface have also been performed

(Ovando, 1995). The results show that static friction can decrease significantly after cyclic loading.

When this type of design is adopted, it should then be clear that it is commendable to ignore

the contribution of the piles to the global bearing capacity. The bearing capacity to be consid-ered under seismic conditions should merely the capacity of the soil to take the slab contact pressure. The presence of the piles should only be taken into account in the static settlement es-timation

A number of proposals aiming at increasing the efficiency of friction piles by modifying the

shape of their cross-section (triangular, H, etc.) have been presented. Jaime et al. (1991) have shown that this is generally not achieved. Among the research work aiming at improving fric-tion piles, the attempts to develop high adherence electro-metallic piles using electrosmotic treatment should also be mentioned (Tamez, 1964)

To improve further the understanding of the behavior of friction piles, a foundation of this

type has been instrumented (Mendoza, 2002). Most of the above considerations about Type II foundations have been confirmed.

b) Pile with penetrating point.

This type of pile (Reséndiz, 1964) was conceived to increase the bearing-capacity of friction

piles with a controlled contribution of the point. The diameter of the point is smaller than the rest of the pile in order to facilitate penetration in the hard layer under the combined effect of

loading and negative skin friction and to avoid emersion. The point can be made of reinforced concrete (Reséndiz, 1964; Ellstein, 1980) or steel (Reséndiz et al., 1968). In the latter case, the bearing capacity of the pile can be better controlled by using a point with a pre-established fail-ure load. Flexibility of the point constitutes however a problem during installation of piles.

c) Negative skin friction piles

Those are simply point-bearing piles that penetrate freely through the foundation slab (Cor-

rea, 1961). They can contribute to reduce significantly the settlements due to negative skin fric-tion that develops on the shaft of the piles under the combined effect of the structural load and the consolidation of the clay layer. Finite element modeling of this type of piles has been pre-sented (Rodríguez, 2001). Spacing of the piles appears to be the most significant design param-eter.

d) Control piles The so-called “control piles” are similar to the previous ones but they are equipped in their

upper part with a mechanism that controls the load received by each pile. Each pile can also be unloaded by removing the mechanism in order to correct any tilting of the building. Those sys-tems have sometimes been installed during the life of the structure as part of an underpinning process (González Flores, 1964, 1981; Auvinet, 1989). The different available control mecha-nisms have been reviewed by different authors (Martínez Mier, 1975; Correa, 1980; Aguilar, 1990; Rico, 1991). In Table 2 a list of the best known systems is presented.

En seismic conditions some of these special systems can be vulnerable and suffer damage go-

ing from simple deformations to total collapse. Lack of maintenance can also be a problem. Several proposals have been made to improve the design of control piles (Aguilar & Rojas,

1990). Overturning of the loading frame can be avoided using a new type of anchors. The mechanism can also be transformed to absorb traction forces.

Table 2 Principal types of control mechanisms for piles.

Mechanism Reference

Loading frame with deformable wood cubes González Flores, 1948; Salazar Resines, 1978 Loading frame with jack and automatic relief

valve A, Pilatovsky, cited by J.J. Correa, 1980

Metallic tensors P. González, 1957, cited by Aguilar, 1990 Metallic cap Aguilar, 1960, cited by Aguilar, 1990 Loading frame with flat hydraulic jacks W. Streu, 1963, cited by J.J. Correa, 1980 and

Aguilar 1990 Sand confined within a capsule J. Creixell and J.J. Correa C., 1975, cited by

Aguilar, 1990 Energy dissipater M. Aguirre, 1981; D. Reséndiz, 1976 Mechanical system of self control M.A. Jiménez, 1980 Mobil wedge P. Girault, 1986, cited by Aguilar, 1991 Communicating hydraulic jacks F. Zamora Millán, cited by A. Rico A., 1991 Constant friction cell E. Támez, 1988 Cell with teeth for transmission of tensions A. Rico A., 1991

e) Telescopic piles

These are tubular piles with a piston-like cylindrical point lying on the hard layer (Correa,

1969). The tubular portion of the pile is partly filled with sand. When sand reaches a certain level, an arching effect develops and both parts of the piles work as a unit. If necessary, sand can be removed to free the point and avoid emersion of the foundation.

Figure 6. Control pile

f) Overlapping piles

This type of foundation (Girault, 1964, 1980) includes conventional friction piles (A Piles)

together with negative skin friction piles (B piles) lying on the hard layer. This arrangement re-duces the increment of stresses in the soil and the corresponding settlements. Emersion is also prevented.

4.2.3 A new popular foundation system: stiff inclusions.

For housing projects consisting of low buildings for which earthquake is not a critical aspect , stiff inclusions are now being widely used to control settlements. An ISSMGE TC36 interna-tional workshop “Stiff inclusions in difficult soft soil conditions” was organized (May 11-12th 2006) on this subject in Mexico City (TC36, 2006). This solution is economically attractive in many situations.

5 CONCLUSION

Design and construction of foundations in Mexico City soft soils constitute a difficult chal-lenge. Mexican geotechnical engineers have developed a number of original solutions to solve this problem. This never-ending research received a new impulse after the 1985 earthquake and is still very active nowadays. Using sound soil mechanics principles has been reiterately proven to be the best way to deal with the numerous geotechnical hazards encountered in Mexico val-ley.

6 REFERENCES AND BIBLIOGRAPHY

Aguilar, J.M. & Rojas, E., 1990, Importantes mejoras en los dispositivos de control de pilotes (Important improvements to control piles mechanisms), Proceedings, XVth Soil Mechanics National Meeting, San Luis Potosí, Mexico.

Aguirre, M. , 1981, Dispositivo para controlar hundimientos de estructuras piloteadas (A device for controlling settlement of piled foundations), Internal Publication No 439, Institute of En-gineering, UNAM, Mexico, D.F.

Ang, H.S. & Tang, W.H., 1984, Probability Concepts in Engineering Planning and Design. De-cision, Risk and Reliability, Wiley & Sons, Inc.

Auvinet, G. & Hanell, J.J., 1981, Negative skin friction on piles in Mexico City clay, Proc. Xth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Swe-den, Vol.2

Auvinet, G. & Mendoza, M., 1986, Comportamiento de diversos tipos de cimentaciones en la zona lacustre de la Ciudad de México durante el sismo del 19 de Septiembre de 1985 (Beha-vior of different types of foundations during the September 19th 1985 earthquake), Proceedi-ngs, Symposium "Los sismos de 1985; casos de mecánica de suelos (The 1985 earthquakes; soil mechanics case histories)", Sociedad Mexicana de Mecánica de Suelos, pp. 227-240, México, D.F.

Auvinet, G. & Mendoza, M., 1987, Consideraciones respecto al diseño de cimentaciones sobre pilotes de fricción (Some considerations on design of friction piles), Proceedings, VIIth Na-tional Meeting of Seismic Engineering, November 19-21, Querétaro, Mexico.

Auvinet, G. & Gutiérrez, E., 1989, Instrumentación de un edificio en proceso de recimentación (Instrumentation of an underpinned foundation), Proceedings, Symposium on underpinning, Sociedad Mexicana de Mecánica de Suelos, pp. 137-148, Mexico.

Auvinet, G., & Rossa, O., 1991, Reliability of Foundations on Soft Soils, Proceedings, Sixth In-ternational Conference on Applications of Statistics and Probability in Civil Engineering, CERRA-ICASP-6, June, pp. 768-775, Mexico, D.F.

Auvinet, G., 2002, Uncertainty in Geotechnical Engineering/Incertidumbre en Geotecnia, Six-teenth Nabor Carrillo Lecture/Decimosexta Conferencia Nabor Carrillo. Publicación espe-cial (Libro bilingüe English/Español) de la Sociedad Mexicana de Mecánica de Suelos, Mé-xico, 131p. , ISBN: 968-5350 10-8

Auvinet, G. & Rodríguez, J.F., 2002, Modeling of Friction Piles in Consolidating Soils, ASCE Geotechnical Special Publication N° 116, USA, ISBN 0-7844-0601-4.

Auvinet, G., Pecker, A. & Salençon, J., 1996, “Seismic bearing capacity of shallow foundations in Mexico City during the 1985 Michoacan Earthquake”, Proceedings, Eleventh World Con-ference on Earthquake Engineering, (CDROM), Acapulco, Mexico, July.

Auvinet, G. & Romo M.P., 1998, Deep excavations in Mexico City soft clay, Invited presenta-tion, ASCE's 1998 National Convention, Boston, Massachusetts, USA. Geotechnical Special Publication N0 86, Big Digs around the World, pp. 211-229.

Auvinet, G., Rodríguez, J.F. & Rángel, J.L., 2010, Construction of tunnel shafts in Mexico City soft clays by the flotation method, Acta Geotechnica, Volume 5, Number 1 / April, pp. 63-68, DOI: 10.1007/s11440-010-0115-2, Springer Berlin/Heidelberg. ISSN 1861-1125 (Print) 1861-1133 (Online), IDS number 665QS.

Correa, J.J., 1961, The application of negative friction piles to reduction of settlement, Proceed-ings, Fifth International Conference on Soil Mechanics and Foundation Engineering, Paris, France

Correa, J.J., 1969, A telescopic type of pile for subsidence conditions, Proc. Specialty session on negative skin friction and settlements of piled foundations, VIIth International Conference on Soil Mechanics and Foundation Engineering, Mexico, D.F.

Correa, J.J., 1980, Estado actual del conocimiento sobre pilotes de control (Present knowledge on control piles), Proceedings, Meeting of Consultant-Constructors of deep foundations, Mexican Society of Soil Mechanics, Mexico, D.F.

Cuevas, J.A., 1936, The floating foundation of the new building for the National Lottery of Mexico: an actual size study of the deformations of a flocculent structured deep soil, Pro-ceedings, First International Conference on Soil Mechanics and Foundation Engineering, Harvard, Mass., USA

Ellstein, A., 1980, El pilote penetrante o P3 (Penetrating pile P3), Proceedings, Meeting of Consultant-Constructors of deep foundations, Mexican Society of Soil Mechanics, Mexico, D.F.

Girault, P., 1964, A new type of pile foundation, Proceedings, Conference on Deep Founda-tions, Mexican Society of Soil Mechanics, Vol. 1, Mexico, D.F.

Girault, P., 1964, “Discussion”, Proc. Conf. on Deep Foundations, Mexican Society of Soil Mech., Vol. 1, Mexico, D.F.

Girault, P., 1980, Pilotes entrelazados, Teoría y funcionamiento (Overlapping piles, Theory and mechanism), Proceedings, Meeting of Consultant-Constructors of deep foundations, Mexi-can Society of Soil Mechanics, Mexico, D.F.

Gobierno del Distrito Federal (GDF), 2004, Reglamento de Construcciones para el Distrito Fe-deral (Mexico City building code), Gaceta Oficial del Distrito Federal, January 29th, Mexi-co.

Gobierno del Distrito Federal (GDF), 2004, Normas técnicas para diseño y construcción de ci-mentaciones (Complementary technical norms for design and construction of foundations), Gaceta Oficial del Distrito Federal, Décima Cuarta Época, October 6th 2004, Vol. I, No 103 bis, Mexico.

González Flores, M., 1948, Level control in buildings by means of adjustable piling, Proc. Sec-ond International Conference on Soil Mechanics and Foundation Engineering, Rotterdam, Vol. IV, p. 152

González Flores, M., 1964, Recimentación y enderezado de una iglesia del siglo XVIII, por medio de pilotes de control en México, D.F., (Geometrical correction of a XVIIIth century church using control piles) Proceedings, Conference on Deep Foundations, Mexican Society of Soil Mechanics, Vol. 1, Mexico, D.F., pp. 343-360

González Flores, M., 1981, Raise of a side-settled XVIII Century Church in Mexico City, Proc. Xth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, pp. 101-105

Hansbo, S., 1984, Foundations on friction creep piles in soft clays, Proceedings, Int. Confer-ence on Case Histories in Geotechnical Engineering, St Louis, Mi., USA, pp. 913-922

Jaime A., Romo M.P. & Reséndiz, D., 1988, Behavior of friction piles in Mexico City clay, Journal of Geotechnical Engineering, ASCE, Vol. 116, N0 6, pp. 915-931.

Jaime, A., Rojas, E. & Legorreta, H., 1991, Pilotes de fricción hincados en arcilla blanda; respuesta bajo carga estática (Friction piles driven in soft clay: response to static loading), Internal Publication N

o 534, Institute of Engineering, UNAM, Mexico City.

Jiménez, A., 1980, Pilotes de autocontrol (Self controlling piles), Revista Obras, August, Mexi-co, D.F.

Marsal, R.J. & Mazari, M., 1975, The subsoil of Mexico City, Engineering Faculty, UNAM, Mexico, D.F.

Martínez Mier, J., 1975, Influencia del hundimiento de la ciudad de México en el comporta-miento de cimentaciones piloteadas (Influence of subsidence of Mexico City on the behavior of piled foundations), DEPFI, UNAM, Mexico City.

Mendoza, M., et al., 1996, Instrumentación y comportamiento de una cimentación mixta en la ciudad de México durante su construcción e inicio de operación (Instrumentation and beha-vior of a mixed-type foundation during construction and first operation stage), Proceedings, XVIIIth Soil Mechanics National Meeting, Mexican Society of Soil Mechanics, Vol. 1, pp 143-159, Morelia, México.

Mendoza, M., 2002, Performance of friction-piled foundation in Mexico City, Proceedings, ISSMGE TC36 workshop, May 23-24th, SMMS, Mexico City.

Meyerhof, G.G. , 1983, Scale Effects on Ultimate Pile Capacity, Journal of Geotechnical Engi-neering, ASCE, Vol. 109, 797-806

Ovando, E., 1995, Direct shear tests on Mexico City clay with reference to friction pile behav-ior, Geotechnical and Geological Engineering, 13, 1-16

Ovando E., Lermo J., Auvinet, G., and Méndez E., 2012, “Microtremors measurements to iden-tify zones of potential fissuring in the basin of Mexico”, Geofísica Internacional, 2012, 51-2: pp.143-156, México D.F.

Reséndiz, D., 1964, On a type of point bearing pile through sinking subsoil, Proceedings, Con-ference on Deep Foundations, Vol 1, 385-403, Mexico City.

Reséndiz, D., Auvinet, G. & Silva, C., 1968, Conception et comportement des fondations du Palais des Sports de la ville de Mexico en présence de frottement négatif (Design and beha-vior of Mexico City Sport Palace Foundations affected by negative skin friction), Proc. Spe-cialty Session on negative skin friction and settlements of piled structures, VIIth International Conference on Soil Mechanics and Foundation Engineering, Mexico City.

Reséndiz, D. & Auvinet, G., 1973, Analysis of pile foundations in consolidating soils, Proceed-ings, VIIIth International Conference on Soil Mechanics and Foundation Engineering, Mos-cow, USSR, Vol.2

Rico Álvarez, A., 1991, Sistemas mecanizados para pilotes (Mechanized systems for piles), Thesis, Engineering Faculty, UNAM, Mexico, D.F.

Rodríguez, J.F., 2001, Uso de inclusiones rígidas para el control de asentamientos en suelos blandos (Use of stiff inclusions for settlement control in soft soils), Master degree thesis, DEPFI, UNAM, México D.F.

Rodríguez, J.F., 2011, Modelado del comportamiento de pilotes e inclusiones sometidos a conso-lidación regional en la zona lacustre de la Ciudad de México, (Modeling of piles and inclusions submitted to regional subsidence in the lacustrine zone of Mexico City). Doctoral Thesis, Pro-grama de Maestría y Doctorado en Ingeniería Civil, Facultad de Ingeniería, UNAM, 26 de Enero, México D.F.

Romo, M.P. & Auvinet, G., 1992, Seismic behavior of foundations on cohesive soft soils, in Recent Advances in Earthquake Engineering and Structural Dynamics, edited by V. Da-vidovici, Ouest Editions, pp. 311-328, Paris, France.

Romo, M.P., 2002, Foundations in a seismic Environment, Proceedings, ISSMGE TC36 Work-shop, may 23-24th, SMMS, Mexico City.

Rossa, O. & Auvinet, G., 1992, Stresses induced by superficial and deep loading in an elastic medium, Vol. 118, No 8, August, Journal of Geotechnica1 Engineering, ASCE, pp. 1241-1246, USA.

Salazar Resines, J., 1978, Control de las cargas en la cimentación y de los asentamientos de edi-ficios mediante mecanismos en los pilotes (Loading and settlement control using mecha-nisms in piles), UNAM-UAM, México, D.F.

Sedesol-SMMS, 1992, La Catedral Metropolitana y el Sagrario de la ciudad de México (The Metropolitan cathedral and the Sagrario of Mexico City), México, D.F.

Tamez, E., 1964, Pilotes electrometálicos en las arcillas del valle de México (Electro-metallic piles in Mexico Valley clay), Proceedings, Symposium on deep foundations, Vol. 1, pp. 277-291, México, D.F.

TC36, SMMS & Institute of Engineering, 2006: Stiff inclusions in difficult soft soil conditions. Proceedings of the May 11-12th 2006 TC36 workshop. G. Auvinet, J.L. Rangel and M. Jua-rez editors. Available from Mexican Society of Soil Mechanics, now SMIG, Mexico City.

Zeevaert, L., 1973, Foundation Engineering for difficult subsoil conditions, Van Nostrand Reinhold Co., New York.

Zemva, Slobodan, 2011, Diseño y construcción de lumbreras en suelos blandos por el procedi-miento de los anillos prefabricados (Design and construction of shafts in soft soils by the prefabricated rings method), Tesis de Maestría en Ingeniería (Mecánica de Suelos), Progra-ma de Maestría y Doctorado en Ingeniería, UNAM, México D.F.