Volume 11

Issue 2

##### Civil Engineering

JOURNAL OF

POLISH

AGRICULTURAL

UNIVERSITIES

Available Online: http://www.ejpau.media.pl/volume11/issue2/art-20.html

**
THE USE OF SEISMIC TESTS FOR DETERMINATION OF SHEAR MODULUS IN COHESIVE SOILS
**

Katarzyna Markowska-Lech, Mariusz Lech, Marek Bajda, Alojzy Szymański*
Department of Geotechnical Engineering,
Warsaw University of Life Sciences - SGGW, Poland*

The paper presents the methods and devices used in measurements of shear wave velocity to estimate the initial shear modulus in overconsolidated cohesive soil. Both shear wave velocity and initial shear modulus depends on many factors, especially mean effective stress and void ratio. This paper presents in details the results obtained from the SCPTU and the bender elements tests. Tests were carried out on overconsolidated cohesive soils from Warsaw. Finally the paper presents original relationship between the shear modulus, mean effective stress and void ratio.

**Key words:**
shear wave, shear modulus, bender elements, SCPTU, cohesive soils.

**INTRODUCTION**

The shear modulus G_{0} at very small strain (initial shear modulus) is widely considered to be a fundamental soil stiffness property. It is important in practical geotechnical solutions, especially in earthquake engineering and the prediction of soil structure interaction [8,13,14,16]. Hardin & Black [4] identified major factors which contribute to the actual value of the shear modulus such as vertical effective stress, void ratio, OCR, soil fabric, temperature and degree of saturation. It is known that the initial shear modulus of soil at induced strain levels (less than 0.0001%) is possible to obtain from shear wave velocity according to the following equation:

(1) |

where:

G_{0} – shear modulus,

ρ – bulk density,

V_{s} – velocity of shear waves for linear, elastic and isotropic medium.

Recently, most developing techniques which are represented by combination of standard geotechnical tests with geophysical module (shear wave velocity measurement) have been used both in the laboratory end in the field. Representation of such hybrid (field/lab) method is shown in Fig. 1 [15]. Field techniques, besides seismic cone and seismic flat dilatometer, include crosshole and downhole tests in the classical geophysical version and as well as SASW method. Laboratory tests in turn, are represented by resonant column, torsional shear and triaxial tests with local strain measurement and bender elements. Such configurations diminish disadvantages of each group of tests and considerable enhances optimization of data collection [19]. This paper presents the results obtained from the bender elements and the SCPTU tests.

Hardin & Blanford [5] suggested calculation of the initial shear modulus from equation (2). Originally this formula was proposed for sands but it also applies to clayey soils:

(2) |

where:

S_{ij} – non-dimensional material constant reflecting the soil’s fabric,

F(e) – void ratio function,

OCR – overconsolidation ratio,

k – empirical function dependent on the plasticity index of the clay, k=0 when PI<40 and k=1 when PI>40; pr – references stress, pr=1 kPa; ni, nj – empirical stress exponents.

Jamiolkowski et al. [6] evaluated the constants for a number of clays using a void ratio function as follows:

(3) |

where:

x = -1.3 for clays [8] and assuming that n_{i}≈n_{j} they showed that k=0.

Additionally assuming isotropic stress condition, equation (2) is simplified to:

(4) |

where:

σ_{m} – mean effective stress.

Factors, which the most affecting soil stiffness, are vertical effective stress and void ratio. In this paper influence of soil overconsolidation is not to be taking into account.

Fig. 1. Field and laboratory methods for determining shear modulus [15] |

**LABORATORY AND FIELD TEST**

The laboratory tests were carried out on undisturbed clay samples included: general index tests for classification and characterization of the clay – density, grain size distribution and measurement of shear wave velocity at very small strain. The samples were undisturbed natural lacustrine deposits of Pliocene (Tertiary) developed as clays retrieved by means of Shelby sampler from depths between 12 and 22.5 meters under ground surface at the site in Warsaw, Poland. The tested overconsolidated stiff clay samples (OCR – 2 – 6 from DMT tests) were characterized as follows: water content from 20 to 36.8%, liquid limit from 56 to 88%, plastic limit from 20 to 32%, plasticity index from 32.2 to 60.6%, the clay content from 31 to 81%. Its’ physical and mechanical properties are presented in Table 1 and Fig. 2–3.

Table 1. Index properties of tested soil samples |

*FC – clay content (<0.002 mm) |

Fig. 2. Grain size distribution of soils tested in laboratory |

Fig. 3. Plasticity chart for soils tested in laboratory |

The triaxial tests were performed in cell which has internal linking bars what enables easy access to a specimen at each stage of its preparation, and in addition equipped with bender elements located in the top and the bottom platens. This type of cell results also in more reliable deformation characteristics obtained during consolidation and shearing stage of a test. Triaxial tests were performed on 14 undisturbed clay specimens by three stages: saturation (back pressure method), consolidation and shearing (strain controlled mode with strain rate 0.005 mm·min^{-1}). Shearing of samples was performed in isotropic stress condition, 5 samples in drained and 9 in undrained condition.

The field tests were performed at Stegny site located in the south of Warsaw in the old terrace surface of Vistula River. The subsurface stratigraphy of the site are Quaternary deposits in the form of fine and medium grained sands up to 7 m thick, underlain by overconsolidated Pliocene clays. The free ground water table is in medium sands at the depth of 3.2 m. Properties of cohesive soils from Stegny site are presented in Table 2 and Fig. 4. The tests were carried out in 4 profiles to 10m using SCPTU cone.

Table 2. Index properties of cohesive soils at the Stegny site [1] |

*FC – clay content (<0.002 mm) |

Fig. 4. Grain size distribution of soils at Stegny Site |

**BENDER ELEMENT TESTS**

The bender elements are small electro-mechanical transducers which either bend as an applied voltage is changed or generated the voltage as they bend. Bender elements were located into soil sample used in the triaxial tests. A change of voltage applied to the transmitter causes it to bend and transmit a shear wave through the sample; the arrival of the shear wave at the other end of sample is recorded as a changed of voltage by the receiver [3,7,18], Fig. 5).

Fig. 5. Bender element [3] |

Velocity of the shear wave (V_{s}) is calculated from ratio of the tip-to-tip distance between the transmitter and receiver (h) (the effective wave travel path through the sample) and the travel time (t):

(5) |

Measurements of shear wave velocity were performed at the end of each of saturation and consolidation stage during triaxial tests. To rule out incorrect measurements, in addition the travel time at the same stress condition in different frequency of input signal were made [17].

**SCPTU TESTS**

The field tests were carried out by Hyson 200kN hydraulic equipment and seismic cone produced by ISMES which is shown in Fig. 6. During the standard CPTU test the following parameters are usually measured: cone resistance, sleeve friction resistance and pore pressure [9,10]. The SCPTU cone is additionally equipped with two geophones located in the distance of 1m which permit to measure shear wave velocity in one-meter layer.

During each SCPTU test the cone penetration was stopped every 1m and from the ground surface shear wave was generated. When the impulse had arrived to the upper geophone, the oscilloscope has started and the impulse which was running to the lower geophone has been recorded. The travel time obtaining from the oscilloscope readings and the distance between geophones allow to estimate the shear wave velocity from equation (5).

Fig. 6. The ISMES seismic cone and schematic diagram of shear wave velocity measurement |

**TEST RESULTS**

The results obtained in laboratory from bender element tests are presented in figures below. Fig. 7 & 8 show relationships between shear wave velocity, mean effective stress and void ratio. Values of shear wave velocity vary from 100 to 300 m.s^{-1} in applied mean effective stress in range between 15 and 450 kPa. The increase of mean effective stress during the next stage of consolidation causes the decrease of void ratio and in result gives the increase of shear wave velocity. The largest increase of value of shear wave velocity was observed for sample NNS-7 and the smallest one for sample NNS-13. The more horizontal direction of the lines in the Fig. 7 & 8 indicates the less influence of stress changes on the shear wave velocity. Shear modulus at very small strain calculated from equation (5) in tested clays does not exceed 150MPa. Test results are shown in Fig. 9.

Fig. 7. Shear wave velocity vs. mean effective stress |

Fig. 8. Shear wave velocity vs. void ratio |

Fig. 9. Shear modulus vs. mean effective stress |

The test results indicated possibility of estimation of the initial shear modulus in cohesive soils based on mean effective stress and void ratio. This relationship would be helpful to estimate the shear modulus at very small strain without shear wave velocity measurement according to the following equation:

(6) |

The correlation between values calculated from relationship (6) and results of laboratory tests is about 84%, mean relative error is 8%. Similarly, relationship between the shear modulus, mean effective stress and void ratio can be expressed in the following form:

(7) |

In this case, the correlation is as good as in the equation (6) – 84%, but mean relative error is twice greater (16%). Therefore, for tested soils it seems to be better estimate shear wave velocity from equation (6) and then find the shear modulus from equation (1) than estimate shear modulus directly from equation (7) [11,12].

The shear wave velocity and shear modulus obtained from in situ tests carried out in Stegny site are shown in Fig. 10. Values of shear wave velocity in cohesive soils vary from 150 to 200 m.s^{-1}. On the depth of about 4 m it is a significant difference between values of shear wave velocity due to effect of soil type changes and influence of ground water table. Similarly to the laboratory tests the initial shear modulus calculated from relationship (5), is smaller than 150MPa [2].

Fig. 10. Result of SCPTU tests in Stegny site |

**CONCLUSIONS**

On the basis of the experimental results which have been shown in this paper it is possible to draw the following conclusions:

the mean effective stress and void ratio have a visible influence on the shear wave velocity in tested soils,

there are a linear relationships between mean effective stress and shear wave velocity at very small strain for tested soils,

values of shear wave velocity from in situ and laboratory tests are similar (a little higher values from bender element tests),

a good correlation obtained for equations (6) and (7) allow estimating the initial shear modulus according to the proposed empirical formulae.

Although a good correlation between shear wave velocity and mean effective stress and void ratio was obtained in tested soil, it is necessary to continue the investigation to examine influence of stress history to shear modulus, especially in heavily overconsolidated cohesive soil.

**REFERENCES**

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_{o}w gruntach spoistych [The use of in situ tests for estimation of shear modulus G_{0}in cohesive soils]. Scientific Review Engineering and Environmental Sciences, No XII, 2(27), 48-55 [in Polish].Brignoli E., Gotti M., Stokoe K.H.II., 1996. Measurement of shear waves in laboratory specimens by means of piezoelectric transducers, ASTM Geotechnical Testing Journal, 19(4) 384-397.

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^{st}Conference of Comete of Civil and Water Engineering Polish Academy of Sciences and PZITB, 12-17.IX.2005, Krynica, 4, 65-72 [in Polish].Viggiani G., 1995. Panelist discussion: Recent advances in the interpretation of bender element tests. Pre-failure Deformation of Geomaterials, Shibuya, Mitachi&Miura (eds), Balkema, Rotterdam, 2, 1099-1104.

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Accepted for print: 6.05.2008

Katarzyna Markowska-Lech

Department of Geotechnical Engineering,

Warsaw University of Life Sciences - SGGW, Poland

Nowoursynowska 166, 02-787 Warsaw, Poland

Phone: (022) 59 35 227

email: katarzyna_markowska@sggw.pl

Mariusz Lech

Department of Geotechnical Engineering,

Warsaw University of Life Sciences - SGGW, Poland

Nowoursynowska 166, 02-787 Warsaw, Poland

Phone: (022) 59 35 207

email: mariusz_lech@sggw.pl

Marek Bajda

Department of Geotechnical Engineering,

Warsaw University of Life Sciences - SGGW, Poland

Nowoursynowska 166, 02-787 Warsaw, Poland

Phone: (022) 59 35 216

email: marek_bajda@sggw.pl

Alojzy Szymański

Department of Geotechnical Engineering,

Warsaw University of Life Sciences - SGGW, Poland

Nowoursynowska Str. 159, 02-776 Warsaw, Poland

Phone: + 48 22 59 35401

email: alojzy_szymanski@sggw.pl

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.