Analysis of shear strength of armourstone based on 1 m 3 direct shear tests

Coastal Engineering 341 Analysis of shear strength of armourstone based on 1 m 3 direct shear tests J. Estaire & C. Olalla Laboratorio de Geotecnia (CEDEX, Mº de Fomento) Madrid, Spain Abstract In this paper an analysis of the shear strength of armourstone is made based on the results obtained in 16 direct shear tests made in a 1 m 3 box, belonging to CEDEX, in which 68 probes were broken. The tests were performed with seven types of armourstone coming from different quarries and with different characteristics. The material was placed in the shear box by simple dropping, in some tests, and with light mechanical compaction in other ones. The vertical stresses used in the tests varied from 50 to 800 kpa. The results of the tests were analysed with three different criteria: using the Mohr-Coulomb strength model, with and without cohesion and using parabolic fitting curves. Keywords: shear strength, armourstone, shear test. 1 Introduction Armourstone, as construction material, has a relevant role in the design of coastal structures, such as breakwaters, and of foundation structures such as the ones used in the foundation of caissons. A good design of these structures requires the knowledge of the mechanical properties of the armourstone. The difficulty comes from the great size of the grains or pieces of these materials, which need both test equipment of great dimensions and heavy weight samples. Equipment that fulfils the requirements to perform tests to determine armourstone shear strength is the direct shear test with box of great dimensions, as the one belonging to CEDEX. Due to this difficulty, the aim of this paper is to collect all the results obtained in the direct shear test of 1 m 3, since its construction, performed with

342 Coastal Engineering armourstone. The interpretation of the tests makes it possible to have a clear and wide idea of the mechanical characteristics of the armourstone. 2 Test equipment All the tests were performed in a direct shear box of 1 x 1 x 1m 3 of capacity, belonging to the Laboratorio de Geotecnia (CEDEX). The maximum vertical load that can be imposed to the sample is 1000 kn. The maximum horizontal displacement of the tests box is 25 cm. The horizontal load, with a maximum of 1000 kn, can be imposed at a constant speed, ranging from 0.5 to 45 mm/min. Figure 1 shows a photograph of the equipment used in the tests. Figure 1: Equipment used in the tests. 3 Tests performed In this equipment, 16 direct shear tests were performed, in which 68 probes were broken. The tests were performed with seven types of armourstone coming from different quarries and with different characteristics. The material was placed in the shear box by simple pouring, in some tests, and with light mechanical compaction in other ones. The vertical stresses used in the tests varied from 50 to 800 kpa. The principal data of the tests are summarized in Table 1.

Coastal Engineering 343 Table 1: Principal data of the tests. Material Number of tests No samples Vertical stress (kpa) Preparation M-1 T-1 5 100-200-400-600- Pouring 800 M-2 T-2, T-3, T-4, 20 100-300-500 700 Pouring T-5, T-6 200-400-600-800 M-3 T-7 9 100-200-300-400- Pouring 500-600-700-800 M-4 T-8 4 50-100-150-300 Pouring M-5 T-9, T-10 8 50-100-200-400 Pouring M-6 T-11 2 100-200 Pouring M-7 T-12 4 50-100-200-400 Pouring M-2 T-13, T-14, 16 100-300-500 700 Compaction T-15, T-16 200-400-600-800 Total 16 68 From 50 to 800 - The rocks used in the tests can be identified, in a great number, as limestone. The uniaxial compressive strength of the intact rock pieces ranged from 45 to 75 MPa, with an average value of about 60 MPa. This value corresponds to a strong rock according to ISRM classification (Brown [1]). The density of the material, once placed in the shear box, ranged from 16.5 to 19.0 kn/m 3 with an average value of 17.5 kn/m 3, for the tests performed with poured armourstone. In the case of compacted armourstone tests, density was between 19.0 and 20.8 kn/m 3, being the average value of 20 kn/m 3. The increment in density, obtained with the compaction, is nearly 15%. 4 Test results 4.1 Interpretation using the Mohr-Coulomb strength model The first way to interpret the test results at failure is by using the Mohr-Coulomb model, under associative plasticity theory. Each test is interpreted only using the samples broken in such test. Furthermore, this method of interpretation has been made taking into account two alternatives: assuming an apparent cohesion and without that cohesion, what implies to suppose a purely frictional behaviour. The results obtained with these two alternatives, identified as Hypothesis 1 and 2, respectively, are collected in Table 2, for the tests with poured armourstone, and in Table 3, for the ones prepared with compacted armourstone. All these values have been represented in Figure 2 to make their interpretation easier. The analysis of the results makes it possible to highlight the following experimental aspects:

344 Coastal Engineering Table 2: Strength values (Poured armourstone). Test Hypothesis 1 (with cohesion) Hypoth. 2 (without cohesion) c (kpa) φ (º) R 2 c (kpa) φ (º) R 2 T-1 54 44 0.99 0 47 0.98 T-2 115 43 0.98 0 48 0.93 T-3 59 43 0.99 0 46 0.98 T-4 11 44 0.99 0 45 0.99 T-5 21 46 0.99 0 47 0.99 T-6 88 44 0.99 0 48 0.97 T-7 60 43 0.99 0 46 0.97 T-8 23 49 0.99 0 52 0.98 T-9 40 42 0.99 0 46 0.95 T-10 30 42 0.99 0 45 0.98 T-11 48 38 0.99 0 47 0.85 T-12 27 37 0.99 0 41 0.97 Average 50 43 0.99 0 46 0.96 Maximum 115 49 0.99 0 52 0.99 Minimum 11 37 0.98 0 45 0.85 Table 3: Strength values (Compacted armourstone). Test Hypothesis 1 (with cohesion) Hypoth. 2 (without cohesion) c (kpa) φ (º) R 2 c (kpa) φ (º) R 2 T-13 103 48 0.99 0 52 0.96 T-14 98 48 0.99 0 52 0.96 T-15 95 48 0.99 0 52 0.95 T-16 138 40 0.98 0 47 0.90 Average 108 46 0.99 0 51 0.94 Maximum 138 48 0.99 0 52 0.96 Minimum 95 40 0.98 0 47 0.90 Both interpretations, considering and not the existence of apparent cohesion, have quite high values of the coefficient of regression, superior to 0.95. The average values of cohesion and friction angle obtained from the results are: c=50 kpa; φ=43º for the tests performed with poured material and c=108 kpa; φ=46º for the ones corresponding to compacted material. The interpretation of the results assuming a purely frictional behaviour gives a friction angle of 46º, for the tests with poured material, and 51º, for the ones with compacted material. The comparison of the results indicates the beneficial effect of compaction on the strength of armourstone, both in terms of cohesion and friction angle.

Coastal Engineering 345 Angle of friction (º) 55 52.5 50 47.5 45 42.5 40 37.5 35 Poured Arm. Poured Arm. (c=0) Compacted Arm. Compacted Arm.(c=0) 0 25 50 75 100 125 150 Cohesion (kpa) Figure 2: Strength values (Mohr-Coulomb model). The second way of interpretation is to analyse the test results in a global way, as if the 68 samples had been broken in a unique test. The results obtained in such a way have been summarized in Table 4. Figures 3 and 4 show all the test results and the curves representative of Mohr envelope lines obtained when it is made a global interpretation of the tests prepared with poured and compacted armourstone, respectively. Table 4: Strength values (Global interpretation). Armourstone Hypothesis 1 (with cohesion) Hypoth. 2 (without cohesion) c (kpa) φ (º) R 2 c (kpa) φ (º) R 2 Poured 39 45 0.98 0 46.5 0.98 Compacted 110 45.5 0.96 0 50.5 0.91 The results obtained with the global interpretation of the test values are quite similar to the ones obtained previously, so the same comments can be made. A third way to interpret the test results is to calculate the angle of friction of each sample, when considering absence of cohesion. The results obtained with this way of interpretation are collected in Table 5 and represented in Figure 5. The analysis of the results makes it possible to state the following: The values obtained for secant angle of friction for compacted armourstone are, for all the vertical stress, greater than the ones corresponding to poured armourstone.

346 Coastal Engineering It is clearly seen in the figure the non-linear character of the shear strength of armourstone. The secant angle of friction gets smaller for greater vertical stress. The values of the secant angle of friction ranges from about 55º to 45º, for low and high vertical stress, respectively, in the case of poured armourstone. For compacted armourstone, the values range from 60º to 50º, that is to say, about 5º more than poured armourstone. Shear Stress (kpa) 1000 900 800 700 600 500 400 300 200 100 0 Sample preparation: pouring Hyp.2 Hyp.1 Int.1 : τ = 39 + 0,9893.σ ; R 2 =0,98 Int.2 : τ = 1,0626.σ ; R 2 =0,98 T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 T-11 T-12 0 200 400 600 800 1000 Normal Stress (kpa) Figure 3: Intrinsic strength lines (poured armourstone). Shear Stress (kpa) 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 Sample preparation: compaction T-13 T-14 T-15 T-16 Hyp.2 Hyp.1 Int.1 : τ = 112 + 1,0203.σ ; R 2 =0,96 Int.2 : τ = 1,2173.σ ; R 2 =0,91 0 200 400 600 800 1000 Normal Stress (kpa) Figure 4: Intrinsic strength lines (compacted armourstone).

Coastal Engineering 347 Table 5: Secant angles of friction. Vertical stress Number of samples Average φ (º) (kpa) Poured Arm. Comp. Arm Poured Arm. Comp. Arm 50 4-55 - 100 9 2 52 63.5 200 9 2 50 56 300 4 2 48.5 54 400 8 2 47 52 500 3 2 46 54 600 6 2 47 51 700 3 2 45.5 50 800 5 2 46 47.5 65.0 62.5 60.0 Angle of friction (º) 57.5 55.0 52.5 50.0 47.5 45.0 42.5 40.0 Poured Arm. Compacted Arm. 0 200 400 600 800 1000 Normal Stress (kpa) Figure 5: Secant angle of friction. 4.2 Interpretation using non linear failure criteria The global interpretation of the test results as coming from a unique test can be also made using parabolic expressions, such as τ = a σ b. The expressions obtained, represented in Figure 6, are the following: Poured armourstone: τ = 2.4 σ 0.87 ; (τ and σ in kpa) R 2 =0.99. Compacted armourstone: τ = 6.05 σ 0.75 ; (τ and σ in kpa) R 2 =0.98.

348 Coastal Engineering Shear Stress (kpa) 1000 Sample preparation: pouring 900 800 700 600 500 400 300 200 Parabolic Curve: τ = 2,3947.σ 0,8713 ; R 2 =0,9884 100 Test Results Parabolic Curve 0 0 100 200 300 400 500 600 700 800 900 1000 Normal Stress (kpa) 1000 900 Sample preparation: compaction 800 Shear Stress (kpa) 700 600 500 400 300 200 100 0 Parabolic Curve: τ = 6,0323.σ 0,7488 ; R 2 =0,9793 Test results Parabolic Curve 0 100 200 300 400 500 600 700 800 900 1000 Normal Stress (kpa) Figure 6: Parabolic curves (compacted and poured armourstone). The principal aspects that can be highlighted from the previous results are: The regression coefficients of these parabolic curves are even higher to the ones corresponding to the linear curves, which indicates a non-linear strength behaviour at failure of these materials. The curve corresponding to the compacted armourstone is less linear than the one corresponding to the poured armourstone, as indicated by the lower value of the exponent. 5 Comparison of results In this section the results obtained with the different interpretations are compared with values published in literature. I) The classical plot of Leps [2], showing the angle of shearing strength as a function of effective normal stress, is shown in Figure 7, with the values deduced in this paper for the test performed with poured armourstone. It can be seen that the results obtained are in the upper part of the range defined by Leps.

Coastal Engineering 349 II) The interpretation using parabolic expressions has been performed by several authors. De Mello [3], when interpreted tests performed by Marsal [4], obtained values of the exponent (b) of the parabolic expressions between 0.81 and 0.88. In a similar way, Matsumoto and Wanatabe [5] fitted 49 triaxial tests and obtained values of b which ranged from 0.77 to 0.97 with an average value of 0.85. All these values are in good agreement with the one obtained in this paper. Furthermore, Charles and Watts [6] suggested to use a value about 0.75 for the parameter b, to be used when armourstone is compacted. This value is the same as the one deduced from the test results performed for this paper. Figure 7: Shearing strength of armourstone (Leps [2]). III) Hoeg et al [7] performed seven field tests on embankments that were brought to complete breaching. Their interpretation of the results indicate that the angle of shearing resistance of competent and compacted rockfill is higher than conventionally assumed in slope stability analyses as given in Leps s [2]. Although no concrete value of the friction angle to define the shear strength is indicated, this conclusion is the same as obtained with the results of this paper. 6 Summary and conclusions 16 shear direct tests, in which 68 samples were tested, were performed using the 1 m 3 direct shear box belonging to CEDEX. Seven different armourstone were tested, making the samples by pouring and compaction. The values of Mohr-Coulomb strength criterion that best represent the test results, taking into account all the interpretations, are summarized in Table 6.

350 Coastal Engineering Table 6: Strength parameters. Armourstone With Cohesion Without Cohesion c(kpa) φ (kpa) c (kpa) φ (kpa) Poured 45 44 0 46 Compacted 110 45 0 51 It has been confirmed the non-linear character of the strength of armourstone, as the secant friction angle gets smaller when normal stress increases its value. The values of the secant angle of friction ranges from about 55º to 45º, for low and high vertical stress, respectively, in the case of poured armourstone. For compacted armourstone, the values range from 60º to 50º, that is to say, about 5º more than poured armourstone. It has been checked that the best fit is got by using parabolic expressions (τ = a. σ b ; in kpa). The values of parameters a and b are 2.4 and 0.85 for poured armourstone and 6.05 and 0.75 for compacted armourstone. Acknowledgement The authors of the paper wish to acknowledge the people who performed the test (Clemente Arias, José L. Gómez and José L. Toledo) for their enthusiastic dedication and effort. References [1] Brown E.T. (Ed). Rock Characterization, Testing and Monitoring ISRM Suggested Methods. Pergamon, Oxford, pp.171-183,1981. [2] Leps, T.M. Review of shearing strength of rockfill. J. Soil Mech.ans Found. Div. ASCE, Vol. 96, No. SM4, pp. 1159-1170, 1970. [3] De Mello, V. Reflections on Design Conditions of Practical Significance to Embankment Dams. 17th Rankine Lecture. Geotechnique, Vol. 27, No. 3, pp. 281-354, 1977. [4] Marsal, R.J. Mechanical Properties of Rockfill. Embankment Dam Engineering. Casagrande Volume. J. Wiley & Sons, 1973. [5] Matsumoto, N. & Wanatabe, K. The Shear Strength of Rockfill Materials. Tsuchi-to-Kiso. ISSMFE. 35, No. 12, 1987, (in Japanese). [6] Charles, J.A. & Watts, K.S. The Influence of Confining Pressure on the Shear Strength of Compacted Rockfill. Geotechnique, Vol. 30, No. 4, pp. 353-367, 1980. [7] Hoeg, K., Lovoll, A. & Vaskinn, K.A.. Stability and breaching of embankment dams: filed tests on 6 m high dams. The International Journal on Hydropower & Dams, Vol. 11, Issue 1, pp. 88-92, 2004.