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Serrano and Olalla. [10] developed a theoretical model for determining the shaft resistance of piles embedded in rock based on the. Hoek and Brown failure ...
ARMA 11-293

Large-scale two-dimensional laboratory load tests of rock-socketed piles in synthetic rock-masses Wainshtein, I. ADI Limited, 7071 Bayers Road, Suite 2002, Halifax, NS, B3L 2C2, Canada

Hatzor, Y.H. Department of Geological and Environmental Sciences, Ben Gurion University of the Negev, Beer – Sheva, 84105, Israel Copyright 2011 ARMA, American Rock Mechanics Association This paper was prepared for presentation at the 45th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, June 26–29, 2011. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: Rock-socketed piles are a common foundation solution to transfer heavy loads from structures to the underlying rock mass. Their total capacity is largely governed by a skin friction mechanism (shaft resistance) developed at the rock-pile interface. The prediction of shaft resistance is a complex engineering problem and a traditional method to experimentally evaluate it is by in-situ load tests. Rock mass quality has a great influence on the shaft resistance, however the mechanisms and details of such influence are poorly understood since the rock mass quality is usually not defined during these load test programs. This paper presents a laboratory attempt to study the influence of two significant rock mass characteristics (joint orientation and infilling material) on the shaft resistance by a series of large-scale two-dimensional load tests. The tests were performed in four differently configured synthetic rock masses composed of concrete. The test results revealed that diagonal orientation of joint sets caused an approximately 150% reduction in shaft resistance when compared to what was measured in horizontal-vertical joint oriented rock masses. The soft and weak infilling material caused a dramatic reduction in shaft resistance, by an order of magnitude, when compared with clean and tight joints. Finally, the test results were evaluated using the micromechanical approach developed by researchers at Monash University.

1. INTRODUCTION 1.1. General Rock-socketed piles are a common foundation solution to transfer high and concentrated loads from heavy structures to underlying rock mass. Their total axial capacity consists of two major components: end bearing load (base resistance) and side friction load (shaft resistance) in the rock. Although the base resistance component may significantly contribute to a total pile capacity, it is usually not taken into account in design calculations mainly because of two reasons. The inclusion of base resistance component requires the pier bottom to be clean of debris and this technically may be difficult and expensive to achieve. In addition, the shaft resistance is normally mobilized much earlier and at considerably smaller pile movements than that of the base. As a result, the shaft resistance at the rock-pile interface is usually considered as the major or the only component in total capacity estimation process. For this case, an estimate of the ultimate socket-shaft resistance (fsu) is required in order to evaluate the total capacity of the rock-socketed pile. In the absence of analytical

solutions, most of the methods used to estimate shaft resistance in rocks are largely based on empirical rules, which usually relate to uniaxial compressive strength (qu) of the weakest component in the pile-rock interface. These rules are historically derived from pile design in clays, and for the rock masses are generally expressed as:

f su = α ⋅ quβ

(1)

where α and β are curve fitting parameters to match measured data, the value of which varies among various authors. The shaft resistance may also be empirically expressed by means of an adhesion factor αq defined as:

αq =

f su ⇒ α q = α ⋅ quβ −1 qu

(2)

Recent studies have shown that shaft resistance is influenced not only by the intact strength of the weakest component along the interface, but also by borehole roughness, characteristics of the rock-mass (i.e. deformation modulus, Poisson’s ratio, structure and shear strength of discontinuities), pile diameter, initial

normal stress on the interface prior to loading, and construction practice. Consequently, pile capacity estimates using the above-mentioned empirical methods are limited, and could be improved. Since most factors influencing shaft resistance are related to rock mass properties, including these factors in design procedures could improve estimation methods.

1.2. Previous attempts to integrate rock mass quality into foundation design schemes Since the early eighties researchers have attempted to upgrade the empirical relationships in order to quantify the influence of rock mass quality on shaft resistance. Williams at el. [1], based on a series of laboratory and field tests on Melbourne mudstone, concluded that the shaft resistance is influenced (among other factors) by the rock mass deformation modulus. While the intact rock modulus (ER) is typically considered as a function of rock strength, the rock mass deformation modulus (EM) is also critically controlled by rock mass discontinuities. Williams proposed to apply a reduction factor, labeled here as MMF (Mass Modulus Factor), on the existing empirical rules in order to account for the effect of rock-mass discontinuities on modulus reduction. Consequently, the upgraded empirical relationships to estimate the ultimate socket-shaft resistance were reformulated as follows: β −1

α q = MMF ⋅ α ⋅ qu

(3)

The accepted way to evaluate MMF is through its empirical relationship with moduli ratio (EM/ER). Published trends for these relationships are plotted in Figure 1.

considerable research effort [2-7] has been made in past few decades to empirically establish RQD - Moduli ratio relationship. The integration of MMF (evaluated based on RQD) into the empirical design procedures remains one of the most popular and widely used methods to account for rock mass quality influence on shaft resistance. However, this method has the following drawbacks that prevent it being fully reliable. The existing RQD - Moduli ratio empirical relationships are quite wide scattered and could yield very different results for the same RQD values. The empirical design procedures and particularly α and β factors (Eq. (1)) are usually derived from large databases of in-situ load tests performed in varied rock mass conditions. Use of this same data therefore may create distortion, since MMF as per definition should be applied on empirical design procedure developed for the intact rock only. Lastly, rock mass deformation modulus and consequently shaft resistance generally decrease with decreasing RQD. However, at the same time, lowering RQD, reflecting higher intensity of rock mass discontinuity, typically results in higher borehole roughness, and consequently may increase the shaft resistance [8]. Therefore, RQD exact relationship to shaft resistance still remains unclear. Recently a few attempts [9-11] have been made to develop new approaches incorporating rock mass quality to estimate the ultimate shaft resistance. All of them were derived based on the Hoek-Brown failure criterion for rock mass [12], which is expressed as:

 σ  σ 1 = σ 3 + σ ci  mb 3 + s   σ ci 

a

(3)

MMF 1

Rowe and Armitage, 1986

0.9

Williams and Pells, 1981 0.8

(Roughened Socket)

O'Neill and Reese, 1999

0.7

0.6 Williams and Pells, 1981 (Normal Roughness) 0.5

E m/E r

0.4 0

0.2

0.4

0.6

0.8

1

Fig. 1. Mass Modulus Factor (MMF) versus Moduli ratio.

Since rock mass deformation modulus isn’t routinely obtained during the substrata investigations, many researchers suggested using empirical correlations between the Moduli ratio and RQD in order to estimate MMF. Unlike the rock mass deformation modulus, RQD is usually available from borehole data and a

where σ1, σ3 and σci are the major stress, minor stress and uniaxial compressive strength of the intact rock, respectively; mb, s and a are constants that can be obtained from the Geological Strength Index (GSI) [13] or the Rock Mass Rating (RMR) [14]. Note that unlike GSI and RMR, RQD only partially reflects the overall rock mass quality. Serrano and Olalla [10] developed a theoretical model for determining the shaft resistance of piles embedded in rock based on the Hoek and Brown failure model. They checked the model later [11] based on an international load test database, consisting of 79 cases. Due to lack of the data, RMR and GSI indexes for some of the cases were roughly assumed. After a comparison between the measured shaft resistance and what the model predicted, the researchers suggested that their theory underestimated the behavior of the shaft’s pier. Sagong et al [9] proposed a different approach to estimate the shaft resistance based on Hoek-Brown failure criterion and the borehole roughness. A comparison between side resistance measurements from

14 field tests and estimates from the proposed method were made by authors in order to evaluate the accuracy of its predictions. As in the previous case, most RMR and GSI indexes were roughly assumed based on an approximate description of the rock. The authors argued that the proposed method appears to be robust and that it showed a good correlation with the field test results. Despite that, Wainshtein [15] for example found that the simple empirical design rule in form of Eq. (1) proposed by [16] has a higher prediction capability than the method proposed by Sagong et al [9].

(iii)

Case ii configuration but with greased joint interfaces simulating the infilling material

(iv)

Fractured rock-mass with two orthogonal joint sets rotated by ±450

Although the incorporation of rock mass classification methods may be promising for developing more robust design methods, the existing methods appear not to be a significant improvement over the simple empirical rules derived from Eq. (1). The lack of field load test results that include the actual RMR and GSI measurements could be one of the possible reasons. The acquisition of measured data of the rock mass quality is the first necessary step in developing, correlation or optimization of new approaches.

L=85cm bracing rod

2. LOAD TEST OF SHAFT MODELS

screwing rod

2.1. General In the absence of the necessary field data, lab load tests performed in a well controlled environment can be an alternative way to assess the effect of rock mass quality on shaft resistance. Many researchers [17-21] have studied different aspects of rock-socketed piles by performing lab load tests in the past few decades. In most of the cases, the load tests were performed on relatively small pile models embedded in sound natural or synthetic rock. In order to study the rock mass quality influence on axial loaded pile performance, the tests have to be done in blocky rock masses. Although the actual problem is three dimensional, the creation of a volumetric rock mass domain separated by several joint sets or obtaining a natural one is a very difficult task. For the current study, simplified two-dimensional lab load tests were conducted as a first step to provide a more comprehensive understanding of the analyzed phenomena. In this paper the particular influences of two main rock mass quality components, namely joint orientation and infilling material, on ultimate socket shaft resistance were studied.

2.2. Model Design and Construction The main testing program consisted of loading tests using a 46 cm high by 16 cm wide reinforced concrete block (pile) constructed in four differently configured synthetic rock-masses: (i) (ii)

Intact rock-mass Fractured rock-mass with two orthogonal (horizontal to vertical) joint sets (Figure 2)

10 mm thickness bracing steel plate

e Pil

UNP 260 L=85cm

Sy

h nt

UNP 260 L=90cm

ic et

R

kM oc

ass

UNP 260 L=160cm

UNP 260 L=90cm

UNP 260 L=90cm

Fig. 2. Test configuration for fractured rock-mass with two orthogonal joint sets: built up model (top) versus setup design plan (bottom).

The tested rock mass domain made of unreinforced concrete had the following dimensions: length 150 cm, height 80 cm and width 10 cm. The intact rock mass was in fact a one-piece concrete slab cast into wood formwork. The fractured rock mass consisted of separate cubic blocks 10 x 10 x 10 cm cast into stainless steel standard molds. In order to create a number of alternatively shaped blocks, PVC inserts were inserted into the molds (Figure 3). The pre-designed dismantled PVC formwork was also used to achieve the desired shape for the cast test piles. The reinforcing steel cage, comprised of four 8 mm rebars welded to a top steel plate, was placed into the formwork prior to the casting (Figure 4).

10 cm 10 cm

Fig. 3. Stainless steel molds with the PVC inserts for the cubic blocks.

16 cm

Fig. 4. PVC formwork for the pile.

All concrete components were cured for 28 days at 20°C and at 100% relative humidity. Note that the concrete strength for the synthetic rock was selected to be weaker than that of the piles, to force the failure to occur within the rock mass.

All load tests were conducted at Ben-Gurion University in an experimental apparatus comprised of a reaction frame and a single-acting hydraulic piston with normal force capacity of 1.4 MN. The piston is operated in open loop load control mode. A hydraulic control valve and a

2.3. Instrumentation Measurements of vertical displacements were made at the middle of each pile using linear variable displacement transducers (LVDT) with accuracy of ± 0.5%. Vertical displacement was also measured at the top of the pile by an additional LVDT. The load was measured using high capacity compression load cell (Vishay Tedea-Huntleigh – Model 120) placed on top of the pile with a capacity of 300 kN. Measurements of vertical displacements were also made at the top of rock mass in two different locations using two electronic digital indicator gauges with 0.001 mm resolution. Two dial indicator gauges (each division represented 0.0025 mm displacement) also monitored vertical displacement of the bottom of the supporting frame. Strain gages were installed on the bracing rods to monitor strains and calculate stresses using a stress-strain relationship. Three additional strain gages were inserted into a concrete block forming a strain gage rosette and were used occasionally to measure strains in the rock mass. During the tests, a NI data acquisition system controlled by a LabView algorithm was employed to collect the data from the strain gages, the load cell and the LVDTs. Figure 5 shows the schematic test setup and instrumentation plan. Load Frame Press Load Cell Deflectometers

LVDT sensor

Vishay Tedea-Huntleigh - Model 120 (Load Capacity 30 ton)

bracing rod strain gauges

0 5 3 W L 0 5 2 6 0 A 2 C y a h s i V

For the current study, a micromechanical approach developed by researchers at Monash University [22-26] was adopted to analytically simulate the pile behavior during the tests and to interpret the results. The approach is based on a theoretical model and is generally able to predict the full load–displacement behavior. The basic model assumptions, such as unbonded rough rock-pile interfaces or applying an initial normal stress, were used as guidelines for preparation and performance of the tests. The roughness of the rock-pile interfaces included regular 4 mm high triangular asperities selected based on socket roughness heights proposed by Seidel et al. [27]. Note that a void space was always left under the pile bottom to ensure that only the shaft resistance was mobilized during the tests.

manually operated hydraulic regulator controlled the pressure supplied by the hydraulic pump to the piston during the tests. A vertical load was applied to the pile models in approximately 5 to 10 kN increments up to the failure. Each increment was held for approximately 1 min to allow taking instrument readings. A specially designed and built supporting frame, made of welded steel beams, was placed into the loading frame to hold the synthetic rock masses during testing. Note that the fractured rock masses were constructed in the supporting frame like Lego blocks. All rock masses had been confined laterally by the bracing plates, stressed by studs, to simulate the initial lateral stress conditions prior to loading.

bracing rod

Pile Synthetic Rock Mass

void

Fig. 5. Test setup and instrumentation plan.

2.4. Properties of materials for models The engineering properties of the concrete for both the piles and the synthetic rock mass were determined from uniaxial and triaxial compression tests using a stiff, hydraulic, closed-loop servo controlled load frame with a maximum axial force of 1.4 MN (Terra-Tek model FX-S-33090). Details of the testing procedures can be found in [28]. The average values for the concrete of the piles were compressive strength, σc = 33 MPa; elastic tangent modulus, E = 15.62 GPa; and Poisson's ratio, ν = 0.22. The corresponding average values for the synthetic rock mass concrete were respectively: 9.6 MPa, 4.27 GPa and 0.23. An internal friction angle of 420 and cohesion of 7.2 MPa were calculated for the concrete of the piles using the Coulomb-Mohr failure criterion. The corresponding values for the synthetic rock mass concrete were respectively 390 and 2.3 MPa.

compressed column made of “n” single blocks consists of two major components: a deformation within the blocks (Hooke's law) and a deformation at the interfaces, and it can be formulated as follows:

∆lblock system =

(n − 1) ⋅ σ n + kn

φ, deg.

Stiffness, MPa/mm 18

60

50

12

40

9

30

6

20

3

kn

10

ks

φ

f

0

0 0

1

2

σn, MPa

3

4

5

Fig. 6. Direct shear test results of concrete-concrete interface.

Additional series of uniaxial compression tests were performed on columns composed of three single concrete blocks using a manual, hydraulic, mini-load frame (SBEL model PLT-75). The main purpose of the tests was to determine the normal stiffness of greased and ungreased concrete-concrete interfaces and to compare the results of the latter with those measured in the direct shear test. The deformation of axially

1



concrete

 ⋅ l  (4) 

where l is a length of a single block and kn is a normal stiffness of a concrete-concrete interface For the compression tests, Eq. (4) has the normal stiffness as the only unknown and can be solved by changing the subject of the formula. Figure 7 shows the test results in σn - kn space. k n, MPa/mm 18 16

Uniaxial Compressive Test

Three Blocks + Grease Direct Shear Test

14 12 10 8 6 4 2

σn, MPa

0 0.0

15

 σn

∑  E

Three Blocks

The shear strength and stiffness of the smooth concreteconcrete interface were obtained at Ben-Gurion University using a hydraulic, close loop servo-controlled direct shear system (TerraTek model DS – 4250). Seven segments direct shear test was performed on the interface under a constant shear displacement rate of 0.025 mm/s and under an imposed constant normal stress ranged from 0.39 MPa to 4 MPa. Figure 6 shows a variation of the obtained interface stiffness (Kn for normal and Ks for tangential) and friction angle with the applied normal stress (σn).

n

1.0

2.0

3.0

4.0

Fig. 7. Normal stiffness of concrete – concrete interface obtained from the direct shear test and the uniaxial compression tests performed on columns composed of three single concrete blocks.

2.5. Load Test Results Eight successful load tests in total were conducted during the research program: four tests in fractured rockmass with two orthogonal (horizontal to vertical) joint sets (num. 1 – 4), two tests in fractured rock-mass with two orthogonal joint sets rotated by ±450 (num. 5 and 6), one test in intact rock mass (num.7) and one test in fractured rock-mass with two orthogonal (horizontal to vertical) greased joint sets (num. 8). The magnitude of the mobilized shaft resistance at failure ranged from 2727 kPa for the intact rock mass to 105 kPa for the fractured rock mass with greased joint sets. Figure 8 shows the results of all load tests in widely accepted t-z curve form. Note that no significant difference between the readings from the LVDTs monitoring a vertical displacement at the middle and at the top of the pile was noticed. That means that the piles reacted as a stiff body during the tests.

t, kPa 3000

Tests 1-4 (90-0 joint orientation)

INTACT ROCK

Tests 5,6 (45-45 joint orientation) Test 7 (Intact Synthetic Rock) Test 8 (90-0 joint orientation + grease)

2500

2000

FRACTURED

1500

ROCK

1000

the rock mass. This lateral stress was evaluated based on an average of the forces acted in the stressed studs prior to and during the tests. The initial normal stress in the intact rock mass, the fractured rock-mass with horizontal to vertical joint sets and with the joint sets rotated by ±450 was estimated respectively as 450 kPa, 230 kPa and 85 kPa. The corresponding values of the average normal stress at the failure were estimated respectively as 1080 kPa, 550 kPa and 195 kPa. In all cases the average normal stress at the failure increased at least 2.3 times over its initial value. Note that the fractured rock mass with the greased joint sets wasn't almost stressed by the studs in order to avoid the significant grease squeezing through the joints prior to the pile loading.

3. TEST RESULTS ANALYSIS 500

3.1. General analysis z,mm 0 0

5

10

15

20

Fig. 8. The summary of the lab load test results in t-z form.

Figure 9 shows the typical failure pattern at the pile-rock interface observed in the fractured rock-mass with two orthogonal (horizontal to vertical) joint sets.

Data from the load tests were reviewed for comparison with the predictions of the empirical methods for rock socketed pile design, searching for potential trends between the shaft resistance and the rock mass quality. Since the current experiments were performed in relatively large-sized synthetic rock masses, the rock mass quality could be directly quantified by means of rock mass classification systems without need to consider an aspect of size effect. The most widely applied rock mass classification methods RMR, GSI and Q-system [29] were employed to characterize a quality of the synthetic rock. Since the shaft resistance was measured in both fractured and intact synthetic rock masses, a ratio between the two, which is in fact Mass Modulus Factor, was also calculated. Table 1 summarizes values of average adhesion factor, rock mass classification indexes and MMF for each lab load test configuration. Table 1. The summary of the adhesion factor, the rock mass quality rating and MMF for each test configuration αq

Fig. 9. The typical failure pattern at the pile-rock interface.

As would be expected, the asperities have been sheared at the rock side of the interface and stayed almost completely intact at the pile’s side. In general, the interface failure gradually changed from almost completely asperities shearing with no visually observed interface dilation (in the intact rock mass) to sliding along the dilated interface, with no asperities shearing (in the fractured rock mass with greased joint sets). The normal stress at the rock-pile interface was assumed to be uniform and equal to the average lateral stress at

1. Intact Synthetic Rock 2. Fractured rock-mass with horizontal to vertical joint sets 3. Case 2 configuration but with greased joint interfaces 4. Fractured rock-mass with two orthogonal joint sets rotated by ±450

RMR

GSI

Q

MMF

0.277

87

82

800

1.00

0.130

55

50

50

0.47

0.011

30

25

3.1

0.04

0.086

40

35

50

0.31

A graphic relationship between the synthetic rock mass quality indexes and the adhesion factors is plotted in Figure 10, along with the adhesion factor's boundaries suggested by [15] based on data from a large international in situ load tests catalogue. 1

10

100

0.40 GSI

Upper Bound of

αq

1000

Q

from in situ load test catalogue

MMF 1 R owe and Armitage, 1986 0.9 0.8

Williams and Pells, 1981 (Roughened Socket)

0.7

O'Neill and Reese, 1999

0.6

RMR

0.5

Q

0.30

Williams and Pells, 1981

0.4

αq

0.20

(Normal Roughness)

0.3 0.2

0.10

Lab. Loading Tests

0.1 Lower Bound of

αq

from in situ load test catalogue

0.00

GSI or RMR 0

20

40

60

80

100

Fig. 10. The graphic relationship between the rock mass quality indexes and the adhesion factor.

First, as can be seen in Figure 10 the adhesion factors measured during the lab load tests are within the acceptable range of values and that may indicate a reliability of the obtained results. The plotted trends clearly show that the rock mass quality has a significant influence on the mobilized shaft resistance at failure. In general, the observed decrease in shaft resistance caused by the joint sets and the infilling material corresponds well with the rock mass quality decreasing classified by RMR, GSI and Q-system methods. However, the decrease in the shaft resistance caused by rotation of the horizontal to vertical oriented joints by 450 could be properly reflected only by RMR and GSI methods since they include an adjustment for a joint set orientation with regards to foundations. Thus, these two methods may be preferable over the Q-system method in searching and establishing a potential rock mass quality shaft resistance relationship. The test results also indicate that the adhesion factor measured in the synthetic intact rock is higher, at least two times, that which was measured in the blocky rock masses. This number may make an interesting parallel with simple rules of thumb such as a reduction of proposed shaft resistances by 50% where the rock is extremely jointed [30]. Fractured rock mass of lab load tests with an average joint space of 10 cm can be considered in a certain sense as an extremely jointed one. Note that the 50% reduction mentioned above is in fact the Mass Modulus Factor and appears to be its known lower bound according to the published trends (Figure 2). These trends and that obtained from the lab load tests are plotted in Mass Modulus Factor – Moduli ratio space in Figure 11.

(This study)

E m/E r

0 0

0.2

0.4

0.6

0.8

1

Fig. 11. Published MMF - Moduli ratio trends and the trend obtained from the lab load tests.

Note that the fractured rock mass deformation modulus required to estimate the Moduli ratio was evaluated based on an analysis presented in Section 3.2. As can be seen in Figure 11 the obtained relationship is mostly below the range studied by others and needs to be verified by real field data. However the close proximity of the obtained in two-dimensional domain trend to the published ones around the Mass Modulus Factor of 0.5 may be a first preliminary verification of the test results. Furthermore, the closest agreement to the obtained trend is the one that was proposed by Williams and Pells [31] for the roughened socket that in fact can be the most appropriate trend to compare with, considering the roughness of the tested rock-pile interfaces. It also can be interesting to compare the currently obtained peak shaft resistance with those predicted by two previously mentioned empirical methods: Serrano and Olalla [10] and Sagong et al [9]. Figure 12 presents the obtained and the predicted peak shaft resistance. Note that the lab load test results may not be fully comparable with the empirical method predictions since the tests were conducted in the two-dimensional domain. However, as can be seen in Figure 12, the Serrano and Olalla method [10] keeps underestimating the peak shaft resistance as they previously had noted [11] based on real field data. Sagong et al [9] method seems to overestimate the peak shaft resistance and that tendency increases with an increase in rock mass quality.

decrease in the rock mass deformation modulus. Note that the initial normal stress that varied between the tested configurations may also be partly responsible for the variation in the measured shaft resistances. However, according to [32] the peak shaft resistance is not particularly sensitive to such variations in initial normal stress.

fsu, kPa (measured)

5000

4000 +50%

Since the rock mass deformation modulus and the rock mass quality are intuitively and empirically interrelated, the influence of the latter on the shaft resistance appears to be mainly expressed through the different lateral resistance supplied by the rock mass, as would be expected, and the challenge is to quantify that influence properly.

3000

1 : 1 2000 -50%

1000

3.2. Analytical modeling and analysis

Sagong et al., 2007 Serrano and Olalla, 2004

0

fsu, kPa (estimated)

0

1000

2000

3000

4000

5000

Fig. 12. The currently obtained and the empirically predicted ultimate shaft resistance.

As can be seen from the test results, the rotation of horizontal to vertical joint sets by 450 caused to the shaft resistance to decrease in approximately 150%. We propose the following rationale for this observation: rotating the joints introduces additional degrees of freedom such that the rock blocks are free to move along the joint surfaces. Consequently, the response of the rock mass to external loading becomes softer in this jointing configuration, leading ultimately, to a decreased shaft resistance. The infilling material due to its high compressibility caused, in the same manner, the softening of the rock mass reaction and reduced the shaft resistance dramatically, by an order of magnitude, when compared with clean and tight joints. In general, the micromechanical approach developed at Monash University (that the lab load tests were adjusted to) assumes that the preferred mechanism for a failure at the pile–rock interface is initially by slip rather than shear through the intact rock or concrete [32]. As the pile undergoes axial displacement due to imposed load, the socket roughness forces dilation and increasing both the normal and the shear stresses at the interface up to the point of the failure. That dilation will be resisted by the surrounding rock mass. The mobilized shaft resistance will be mainly a function of both the asperities shear strength and the lateral resistance supplied by the surrounding rock. Since the asperities strength of the tested interfaces was similar for all rock mass configurations, the different lateral resistance, or in other words the different rock mass deformation modulus, was the main reason for the variation in the measured shaft resistance. Consequently, the softening of the rock mass reaction mentioned previously relates directly to the

In order to make a further analysis of the lab load test results, the analytical simulations were conducted using the ROCKET 2.1 program [33]. ROCKET is based on the micromechanical approach developed at Monash University and designed to compute a side shear resistance of rock socketed piles and the shear response of direct shear tests of unbonded rough joints under constant normal stiffness (CNS) conditions. As mentioned previously, the rock surrounding the pile laterally resists dilation at the rock-pile interface and that resistance can be modelled as a spring with a constant stiffness. In general, that stiffness can be calculated from the rock mass elastic parameters and for the current twodimensional plane stress lab load test configurations can be roughly assumed as follows:

k n = Em l

(5)

where l is a length of the rock mass domain on each side of the pile. The two-dimensional module of ROCKET, simulating direct shear tests, was employed for the analysis of the test results. For this case, ROCKET input data include the following parameters: elastic modulus, Poisson’s ratio and Mohr - Coulomb parameters of an intact rock; initial normal stress and constant normal stiffness imposed during the tests. That stiffness is in fact the only unknown input parameter to properly simulate the lab load tests in the fractured rock masses since their elastic modulus required for Eq. (5) is unknown. However, for the lab load test simulation in the intact rock, the elastic modulus of the concrete can be used to evaluate the constant normal stiffness. To verify the validity of the micromechanical approach developed at Monash University, ROCKET simulation analysis has been carried out using the lab load test results in the intact rock. The comparison between the test results and the prediction of ROCKET are shown in t-z form in Figure 13.

t, kPa

t, kPa 3000

1600

Intact Synthetic Rock

Test 7

90-0 joint orientation Test # 4 ROCKET

ROCKET

2400

1200

1800

800

1200

400

600

0

z, mm 0

z, mm 0 0

5

10

15

20

Fig. 13. The comparison between the test results in the intact rock and the prediction of ROCKET.

5

The constant normal stiffness values obtained from the calibration were converted to the rock mass deformation moduli using Eq. (5). That yielded the following deformation modulus values: 360 MPa for the fractured rock-mass with horizontal to vertical joint sets, 200 MPa for the rock mass with the joint sets rotated by ±450 and 10 MPa for the rock mass with the greased joint sets. An analytic solution proposed by Wei and Hudson [34] to estimate a rock mass deformation modulus can be very helpful to interpret and better understand the obtained values. The solution was developed for a twodimensional rock mass with two orthogonal joint sets and is expressed as:

1 1 cos 4 ϖ cos 2 ϖ ⋅ sin 2 ϖ = + + + Em Er kn1 ⋅ s1 ks1 ⋅ s1 +

sin ϖ cos ϖ ⋅ sin ϖ + k n 2 ⋅ s2 k s 2 ⋅ s2 4

2

2

15

20

Fig. 14. The calibration of ROCKET using the lab load test performed in the fractured rock-mass with two orthogonal (horizontal to vertical) joint sets. t, kPa 1200

It can be seen that there is a reasonable agreement between the test results and ROCKET prediction. The residual rock-pile interface behavior predicted by ROCKET appears to be stiffer than the measured one. For the rest of the test configurations, the calibration of ROCKET has been performed in order to estimate the constant normal stiffness required to achieve the closest agreement with the lab load test results. The calibration results are shown in t-z form in Figures 14, 15 and 16.

10

45-45 joint orientation Test # 5 Test # 6

1000

ROCKET

800

600

400

200

z, mm 0 0

5

10

15

20

Fig. 15. The calibration of ROCKET using the lab load test performed in the fractured rock-mass with two orthogonal joint sets rotated by ±450. t, kPa 125

90-0 joint orientation + grease Test 8 ROCKET

100

75

(6)

where kn1, kn2, ks1 and ks2 are respectfully the normal and the shear stiffness of joint sets 1 and 2, s1 and s2 are the average joint spacing of sets 1 and 2 and ϖ is the angle between the applied normal stress and the normal to the first set.

50

25

z, mm 0 0

5

10

15

20

Fig. 16. The calibration of ROCKET using the lab load test performed in the fractured rock-mass with two orthogonal (horizontal to vertical) greased joint sets.

Figure 17 presents the rock mass deformation moduli for the different test configurations obtained from the ROCKET calibration and calculated from the analytical solution of Wei and Hudson [34] (Eq. (6)). Em , MPa 400

Wei and Hudson, 1986

45-45 joint orientation 300

90-0 joint orientation

200

1:1

100

90-0 joint orientation + grease

0

E m , MPa 0

100

200

300

400

Predicted by R OCKET

Fig. 17. The rock mass deformation moduli obtained from the ROCKET calibration versus that obtained from the analytical solution of Wei and Hudson [34] .

Note that the normal and shear stiffness obtained in the direct shear test and the unconfined compressive test described in Section 2.4 were used in Eq. (6) to calculate the deformation modulus. It can be seen that there is a reasonable agreement between the deformation modulus values of the rock masses with horizontal to vertical joint sets obtained in both ways. However, softer response of the rock mass to external loading is required according to the ROCKET calibration to comply with the test results in the fractured rock mass with joint sets rotated by ±450. As mentioned previously, the joint sets rotation introduced additional degrees of freedom and allowed the rock blocks to slip independently along the joint surfaces. Such a behavior was visually observed during the tests and cannot be accommodated properly in the elastic solution of Wei and Hudson that predicted a stiffer rock mass response. Notwithstanding that limitation, the analytic solution proposed by Wei and Hudson can be effectively incorporated with ROCKET in design of rock socketed piles embedded in interlocked simply configured blocky rock masses.

4. CONCLUSIONS This paper presented the results and analysis of a large scale lab load test program performed on the twodimensional pile models embedded in the synthetic rock mass. The test results indicated that the shaft resistance measured at the synthetic intact rock is higher, at least two times, that which is measured for blocky rock masses, as would be expected. The results also revealed that diagonal orientation of joint sets at the synthetic

rock mass caused an approximately 150% reduction in shaft resistance in comparison with the shaft resistance measured with horizontal-vertical joint set orientations. Finally, it was found that when the joints were filled with soft and weak infilling material (represented here by grease) the shaft resistance was reduced dramatically, by an order of magnitude, when compared with clean and tight joints. Two empirical methods for rock socketed pile design with particular emphasis on rock mass quality characterization were reviewed based on the lab load test results. The methods’ ability to predict the shaft resistance was found to be only partly accurate and must be improved. The test results also suggested the potential behavior of Mass Modulus Factor beyond the range of Moduli ratio of less than 0.1. The prediction capabilities of ROCKET 2.1 were tested by comparison with the lab load tests results and found to be satisfactory when actual rock-mass modulus is provided. It was also found that the rock-mass modulus of the interlocked simply configured blocky rock masses could be accurately calculated by analytical approaches and therefore applying ROCKET in such rock-masses could be especially effective. Since the two-dimensional plain stress lab load tests can only partially reflect the three-dimensional nature of the studied phenomena, the experimental results can only provide a preliminary assessment of the influence of joint orientation and infilling material on ultimate shaft resistance. More field data and further research are required to verify the conclusions of this study and to establish a more robust relationship between rock mass quality and ultimate shaft resistance. Acknowledgements: We thank Chris Haberfield, Julian Seidel and Samuel G. Paikowsky for sharing their data with us in the form of reports, theses, and papers. Dr. Seidel is thanked for providing ROCKET software for this study. Tim Murphy and Brian Walker are thanked for their helpful reviews of this paper. Oren Vilnay and Michael Tsesarsky are thanked for many discussions on the load test program and the results processing.

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