Characterization of a cemented sand with the pulse-velocity method.

Abstract: The effect of variation in cement content, initial water content, void ratio, and curing time on wave velocity (low-strain property) and unconfined compressive strength (large-strain property) of a cemented sand is examined in this paper. The measured pulse velocity is compared with predictions made using empirical and analytical models, which are mostly based on the published results of resonant column tests. All specimens are made by mixing silica sand and gypsum cement (2.5-20% by weight) and tested under atmospheric pressure. The wave velocity reaches a maximum at optimum water content, and it is mostly affected by the number of cemented contacts; whereas compressive strength is governed not only by the number of contacts but also by the strength of contacts. Experimental relationships are developed for wave velocity and unconfined compressive strength as functions of cement content and void ratio. Available empirical models underpredict the wave velocity (60% on average), likely because of the effect of microfractures induced by confinement during the testing. Wave velocity is found to be a good indicator of cement content and unconfined compressive strength for the conditions of this study.

Key words: wave velocity, low-strain stiffness, cemented sands, elastic moduli, unconfined compressive strength.

Resume : On examine dans cet article l'effet de la variation dans la teneur en ciment, la teneur en eau initiale, le rapport de vide, et le temps de murissement sur la vitesse des ondes (propriete a faible deformation) et la resistance en compression simple (propriete a grande deformation) d'un sable-ciment. La vitesse d'impulsion mesuree est comparee avec les predictions faites au moyen de modeles analytique et empirique qui sont pour la plupart bases sur les resultats d'essais de colonne de resonnance publies. Tous les specimens ont ete fabriques en melangeant du sable de silice et du ciment de gypse (2,5 % a 20 % en poids) et testes a la pression atmospherique. La vitesse des ondes atteint un maximum a la teneur en eau optimale, et est affectee surtout par le nombre de contacts de ciment; alors que la resistance en compression est regie non seulement par le nombre de contacts, mais aussi par la resistance des contacts. On developpe des relations experimentales entre la vitesse des ondes et la resistance en compression simple en fonction de la teneur en ciment et du rapport de vide. Les modeles empiriques disponibles sous-estiment la vitesse des ondes (de 60 % en moyenne), probablement a cause de l'effet des microfractures induites par le confinement durant les essais. On trouve que la vitesse des ondes est un bon indicateur de la teneur en ciment et de la resistance en compression simple pour les conditions de cette etude.

Mots cles : vitesse des ondes, rigidite a faible contraintes, sables-ciment, modules d'elasticite, resistance en compression simple.

[Traduit par la Redaction]

Introduction

There are numerous situations in geotechnical engineering where naturally or artificially cemented soils are encountered. Thus, it is important to understand the effect of cementation on the static and dynamic properties of soils. Naturally cemented soils are formed by the deposition of cementing agents like silicates, carbonates, and calcite cement at the contacts of soil particles. Artificially cemented soils are mostly used for stabilization to increase the strength and stiffness or to reduce the liquefaction potential of earth structures.

Common laboratory methods to measure the dynamic properties of soils are resonant column, cyclic triaxial, and wave propagation methods. Wave velocity measurements provide information about the low-strain stiffness of the medium, however, for engineering design, the strength of the medium is required (large-strain property). Wave velocity can be measured in situ with seismic reflection or refraction, spectral analysis of surface waves (SASW), and seismic crosshole or downhole methods.

Pulse-velocity testing is the most commonly used method for assessing the quality of concrete and for relating wave velocity with strength (ASTM 2002b; Popovics and Rose 1994). In this method, pulses emitted by a transmitter travel through the material and are detected by a receiver, placed on opposite faces of the test object. The travel time of the first arriving pulse is precisely measured and recorded with electronic equipment. Wave velocity is simply computed as distance over time. The recorded signal can be transformed to study the Fourier spectrum.

The resonant column device has been used extensively to determine the dynamic properties of cemented sands (Acar and El-Tahir 1986; Saxena et al. 1988; Chang and Woods 1992; Baig et al. 1997; Fernandez and Santamarina 2001). Mathematical models have also been developed to predict the wave velocity in cemented sands (Chang et al. 1990; Fernandez and Santamarina 2001). However, there is a significant variability in the predicted wave velocities depending on the model used. Most of these studies are based on resonant column results; and they measured the simultaneous effects of confinement and cementation on wave velocity.

This study uses the pulse-velocity method to evaluate the effects of cementation on wave velocity and unconfined compressive strength without applying confinement. A total of 153 specimens with different cement and water contents are tested under atmospheric pressure. The test specimens are prepared using gypsum cement. The effects of cement content, initial water content, void ratio, cement type, and curing time on wave velocity are studied. The measured wave velocities are compared with the predictions of mathematical and empirical models available in the literature. The relationship between wave velocity and compressive strength is also studied.

Low-strain stiffness models for cemented sands

Several researchers have studied the low-strain properties of cemented sands (elastic moduli and attenuation), mostly with the resonant column device (Acar and El-Tahir 1986; Saxena et al. 1988; Chang et al. 1990; Chang and Woods 1992; Dvorkin and Nur 1996; Fernandez and Santamarina 2001). These studies show that wave velocity of cemented sands is mainly affected by cement content, confining pressure, and void ratio. A summary of the models and the parameters used in these studies is given in Tables 1 and 2. The equations summarized in Table 1 are numbered using the letter T as prefix to avoid confusion with the equations presented in the text. For comparison purposes, the increase in the ratio [G.sub.c]/[G.sub.sand] for the same increase in cement content ([DELTA]cc = 7.5%, i.e., from cc = 2.5% to cc = 10%) is given for all the models in Table 2.

General equations

This section summarizes basic equations from the literature and some derived by the authors for the analysis of the experimental results.

Compressional waves (P-waves) propagate at different velocities in an infinite medium or in a rod. When the wavelength is equal to or greater than the diameter of the rod, the velocity of the compressional wave is called the longitudinal wave velocity ([V.sub.L], called wave velocity in this study) and is given as a function of the Young's modulus (E) and mass density ([rho]) of the rod by

[1] [V.sub.L] = [square root of (E/[rho])]

In an infinite medium, the lateral deformation of the elements is constrained; thus the velocity of compressional waves ([V.sub.P]) depends on the constraint modulus (M) as

[2] [V.sub.P] = [square root of (M/[rho])]

The ratio [V.sub.P]/[V.sub.L] can be described as a function of Poisson's ratio (v), and is given by

[3] [V.sub.P]/[V.sub.L] = [square root of ((1 - v)/(1 + v)(1 - 2v))]

The P-wave velocity ([V.sub.P]) can be computed from the shear modulus (G) by

[4] [V.sub.P] = [square root of (2(1 - v)G/(1 - 2v)[rho])]

Therefore for an elastic medium, wave velocity depends on the elastic constants and mass density of the medium. Additionally, from the micromechanics point of view, wave velocity depends on the characteristics of the contacts and the average number of contacts per particle (coordination number, n). Coordination number varies almost linearly with void ratio (Chang et al. 1990; Field 1963, Chang and Woods 1992; Cascante and Santamarina 1996).

For the analysis of wave velocity, it is important to compute the void ratios of the sand matrix (e) and the cemented sand after curing ([e.sub.m]). The void ratios e and [e.sub.m] are related to the initial mass density of the sand-cement-water mixture ([[rho].sub.I]), the mass density of the cemented sand after curing ([[rho].sub.c]), and the degree of cement saturation ([S.sub.c]) by the following equations, which were derived in this study from basic phase relationships:

[5] [[rho].sub.I] = (1 + [[omega].sub.I])(1 + cc)/(1 + e)[G.sub.s][[rho].sub.w]

[6] [[rho].sub.c] = [1 + cc(1 + [[omega].sub.o])][[rho].sub.co]/(1 + [e.sub.m][[[rho].sub.co]/[[rhos].sub.sp] + cc(1 + [[omega].sub.o)]

[7] [S.sub.c] = cc [[rho].sub.sp](1 + [[omega].sub.o])/e[[rho].sub.co]

[8] e = [e.sub.m]/[1 - [S.sub.c]([e.sub.m] + 1)]

where [[omega].sub.I] is the initial water content of the sand-cement mix

(cement not cured), [[omega].sub.o] is the water content of cured cement (hydration water), and …