**Bearing capacity of embedded piles in rocks considering their contribution to friction **

* Universidad Central Marta Abreu de Las Villas, Villa Clara. CUBA

**ABSTRACT**

This article has the objective to show a study of different existing theories that consider the friction contribution of embedded piles in rock. It initially summarizes the adopted criteria for such theories and the coefficient ranges considered for the application of their basic expressions. The results of these theoretical analyses were applied in the solution of the foundations of a hotel, and its marine, built on the beach in the city of Varadero, Cuba. The study area presented a high geologic and engineering complexity, with highly variable stratification characteristics together with distinct soil and rock properties, where the presence of a calcareous stratum stands out in the deposit. The calcareous layer is found in a variable depth within the strata and has a quality ranging from very poor to good, where all the pile tips were founded. In order to obtain the bearing capacities from the designed piles, it was necessary to take into account their friction contribution within the rock, which was done by validating the existing theories through the execution of in situ pile load tests, combined with the use of theoretical models. This exercise allowed the establishment of practical coefficient values that were required by the theories in such particular site conditions. It was finally possible to yield design solutions for the deep foundations of this case history, which comprised over 2000 driven piles..

**Keywords: **Piles in rock, bearing capacities, friction contribution, in situ pile load tests

**1. Introduction**

As known classical theories of Soil and Foundation Mechanics state, when a pile manages to become embedded in rock at least one time its diameter, that pile will work with support only at the tip and its friction contribution will not be taken into account, on the basis that the displacements at the tip of the pile will be negligible and thus pile-rock friction will not be generated. The above statement is true when the piles rest on high quality rocks. However, for cases where the piles are supported by low quality rocks, where they can be embedded in rock several times their diameter, the above statement is not true, and it is necessary to take the friction contribution within the rock into account when determining the ultimate bearing capacity of the pile.

In international literature, there are several works studying this issue, including among the most recent: Serrano (2008), Perez Carballo (2010) and Olmo (2011). All these studies agree that there are two groups of theories to establish ultimate resistance to friction in piles in rock T_{ult}

• Theories that consider the T_{ult} as a linear function of the compressive strength of rock R_{c}

• Theories that consider the T_{ult} as a quadratic function of the compressive strength of rock R_{c}

In this research, all these theories were studied, establishing basic expressions and intervals of the coefficients proposed therein. This study was necessary to apply to the solution of the foundations over piles in a hotel on the beach in Varadero, Cuba. The engineering geological conditions of the area were very complex and variable, together with the existing soil and rock properties. This can be simplified in a stratification consisting of a series of soft soils, with variable thickness of fill, peat, silt and other very loose soils, none of which contribute to the bearing capacity of the piles, and a stratum of calcarenite, which appears at different depths and with very variable quality, from good to very poor. There, the piles achieve embedded length (EL) from only 1.5 times its diameter to more than 14 times its diameter, depending on the quality of the rock.

To determine the bearing capacity of piles, determinations for existing models, including the analyzed theories that consider the friction contribution within the rock where necessary, were combined with in situ pile load tests, which served to calibrate the models and set the interval at which coefficients taken into account in the conditions for the case study could vary. A very good engineering calibration of the models was achieved, and from it the resistant capabilities of the piles, for various conditions of support, were established. This allowed for a significant reduction in the length of piles, resulting in cost savings for construction.

**2. Characterization of the engineering geology of the study area**

In order to characterize the engineering geological conditions of the study area, which was necessary for the determination of the bearing capacity of the piles, several in situ studies were carried out by the companies CeoCuba (2008) and ENIA (2010, 2011). This research included surveys, description of strata, geophysical studies, and laboratory studies in order to obtain the main physical and mechanical properties of soils and rocks.

The following types of soil and rocks, of varying thickness, positions, and engineering properties, were found in the general zone:

• Till stratum, always on the surface but with different capacities

• Peat stratum, with low thickness

• Silt strum, with low thickness

Stratum composed of a combination of various loose soils, which may or may not be present in different

• areas of the building

• Calcarenite stratum, which is present at very variable depths and qualities, from good from very poor

Figure 1 shows two photos of these soils during sample collection in the field, where the fill characteristics and especially the different qualities of calcarenite, with variable RQD values, can be observed.

**Figure 1.** Photos of the fill samples and calcarenite collected during exploration

For the purposes of this study, stratification can be simplified to two zones, the first of which is composed of fill, peat, silt, and other loose soils that may or may not be present, which is formed by soft soils that do not contribute to the bearing capacity of piles. The second zone is composed of calcarenite, with different thickness and quality, which is what actually contributes to the tip and friction, accordingly.

As previously mentioned, the quality of calcarenite is very variable, and can be grouped, based on the study of all the geological engineering research done, into 3 groups:

• Good quality calcarenite, with an average value of R_{c}=9000 kPa

• Poor quality calcarenite, with an average value of R_{c}=1650 kPa

• Very poor quality calcarenite, with a value of R_{c}=1000 kPa

The tested piles were always embedded, with different EL embedded lengths, in calcarenite, with one of the above qualities. The result was when it was embedded in poor or very poor quality calcarenite, it was necessary to consider the contribution to friction, whereas when it was embedded in good quality calcarenite, only the contribution in the tip was taken into consideration.

**3. Analysis of different theories to take into account the contribution to friction of embedded piles in rock**

As was outlined in the introduction of the article, in international literature, there are several works studying this issue, including among the most recent: Serrano (2008), Perez Carballo (2010) and Olmo (2011). All these studies agree that there are two groups of theories to establish ultimate resistance to friction in piles in rock T_{ul}

• Theories that consider the T_{ult} as a linear function of the compressive strength of rock R_{c.}

The general expression posed by this theory to obtain the ultimate friction resistance of pile in rock is defined by Formula 1.

**(1)**

According to Pérez Carballo (2010), the expressions proposed by the main authors are those that are shown in the following formulas:

• Thorne**(2)**

• Poulos y Davis**(3)**

• Australian Code**(4)**

• Hooley y Lefroy **(5)**

• Spanish Technical Code **(6)**

The general expression posed by this theory to obtain the ultimate friction resistance of pile in rock is defined by Formula 7.

**(7) **

All the authors of these studies agree that k=0.5, so what varies in each one is the range of values of a that were considered. According to Pérez Carballo (2010), the expressions proposed by the main authors are those that are shown in the following formulas:

• Rosenber y Journaux **(8)**

• Hovarth y Hovarth **(9)**

• Fleming **(10)**

• Hooley y Lefroy **(11)**

• Manual de la AASHO* * **(12)**

• Carubba **(13)**

All previous theories can be expressed by Formula 7, considering the following variation intervals for variables *k and α*.

If K=1 then a takes the values of a = 0.05~0.4

If K=0.5 then a takes the values of a = 0.10~0.45

**4. Determination of bearing capacity of piles.**

The procedure for determining the bearing capacity of piles, given the complexity of the study area, is set forth in Figure 2.

**Figure 2.** Proposed methodology to determine the hearing capacity of piles