Rayleigh Wave Amplitude

[WARose]

Lately I've been reading a lot on Rayleigh waves. (I've had a bunch of [prediction of] ground vibration problems I've been dealing with.) One thing I've discovered from text to text is the equation for particle displacements (from Rayleigh waves), are typically derived independent of the amount of force causing it. (It is done (typically) to demonstrate the variation of displacement with depth.)

The derived equation(s) for a Poisson's ratio of 0.25 (in a elastic half-space) in one text I have (and I have seen it elsewhere) is:

U(z)= -exp[-0.8475(zN)] + 0.5773 exp[-0.3933(zN)]

W(z)= 0.8475 exp[-0.8475(zN)] - 1.4679 exp[-0.3933(zN)]

Where:

z=depth into medium
N=Wave Number
exp= natural log
U(z)= Horiz. component (as a function of z)
W(z)= Vert. component (as a function of z)

The one time I have seen these equations set up to give numbers caused by an exciting force.....the equation(s) are similar. I.e. the exponents are the same but the coefficients are different......and the overall equation is multiplied by a P/G. (Where P= a line load and G= shear modulus.)

But so far, I've only come across one of these equations.....can anyone recommend more examples of this (in some text)? Perhaps one derived for a point load (rather than a line load)? Any example is welcome. Thanks.

 

[dik]

Does the attached help?

Dik

 

[WARose]

Not really (as far as I can tell)....it's not really geared for the type of excitation I was talking about. (I appreciate the slides though.)

 

[WARose]

Found it......and embarrassingly enough, it was in a text I already had: 'Vibration of Soils and Foundations', by: Richart, Woods, & Hall. (See p. 87, eq. 3-84 & 85.)

Basically the equation in the OP would have to be multiplied (to obtain real results) by the source amplitude and the wave number (i.e. 2*3.14/wavelength). The afore mentioned text provides the info that allows you to derive this equation for any Poisson’s ratio.

 

[Ron]

WARose....that's the "bible" for building vibrations. The only thing that comes close is Dowding's textbook.

Keep in mind that Rayleigh waves are generally surface horizontal waves and have little vertical influence.

 

[WARose]

Keep in mind that Rayleigh waves are generally surface horizontal waves and have little vertical influence.

Depends on the excitation at the source (as well as some other parameters). For a loading primarily inducing vertical vibrations (i.e. vertically vibrating equipment), the largest component of displacement will be vertical (with some horizontal displacements). Vice versa when the loading is horizontal. (See 'Dynamics of Bases and Foundations', by: Barkan (1962), p. 341, 347-348.)