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264 C O R R E S P O N D E N C E

I.00 I I I0.85 090 0.95 I.00

0.99

I35 Ib/cu.125 lb/cue135 Ib/cu.125 Ib/cu.

fc)t

ft

>ft135 lb/m ft

#J=3s

+=40

+=4s0

RELATIVE WATER LEVEL m

+ Minor sloughing o b s e r v e d n o pIO- I5 fc of panel walls

Fig . 1 . P lo t o f r eq u i r ed s lu r r y d en s i ty v srelative water leve l

densities of 125 and 135 Ib/cu. ft (2.05 to 2.16 Tonne+. m). The measured slurry densitiesand the ratio m for each panel tested have been plotted on Fig. 1.The results of these tests support Morgenstern and Amir-Tahmassebs observation that theslurry density is increased due to suspended soil particles ; for the particular case mud densitieswere increased from 3.5% to 12%. These results do not support the suggestion that hydro-static forces alone explain the trench stability. Yours faithfully,C.B.A . E n g in ee r in g L td .

4 5 4 5 M a in S t r ee t ,Vancou ver 10 , B.C.,

18 April, 1966.

D. J. BAZETT and J. W. GADSBY

The Secretary,The Institution of Civil Engineers,DE AR SI R,

GROUND-WATER FLOW STUDIES By RES ISTANCE NETWORK

As a result of the recently published paper on the use of resistance networks for studyinggroundwater problems (Giotechnique 16 : 1: 53-75) the Authors have found that many users ofresistance networks are unaware of the inadequacy of a finite difference network in repre-senting regions in which a rapid change in head occurs. In the Paper the rapid change in the

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266 CORRESPONDENCEeffective well radius to the mesh interval at the well. Thus in the problem considered above,the effective well radius is 2043 ft compared with the correct well radius of 264 ft. The effectis even more marked with larger mesh spacings ; for a mesh interval of 1000 ft the actual wellmodelled by the network has a radius of 208 ft.

(2 (b)Fig. 2. Replacement of standard resistances by radial resistances

However, by a simple modification to the network, an adequate representation of a wellcan be achieved. Fig 2(a) illustrates that a single resistance in a square or rectangular net-work represents the total flow through the shaded area in one direction only. If radial flow isto be modelled satisfactorily the resistor must represent the radial flow through the shadedportion of Fig. 2(b). To model this radial flow the resistance should have a value,R radial = :Rlog, F, . . . . . . . .7r ( 1

where R s the standard resistor for a square network of mesh length a, and rw is the radius ofthe well.Thus for the numerical problem discussed above the four resistors connected to the noderepresenting the well should take the value,R radial2.266 R.

When these resistors are connected in the circuit, the piezometric head at a distance of 100 ftfrom the centre of the well is 53.1 ft which compares well with the analytical value of 53.3 ft.The concept of connecting a radial network to a square network as illustrated in Fig. 2(b)cannot be justified rigorously. However, several other possible approaches have beenadopted to calculate the resistance to be connected to the well, and each has led to an equationsimilar to (1).Finally it must be stressed that many previous investigators have used resistance networkssuccessfully for well problems without introducing this correction. They have not beenseriously troubled by the inadequacy of the standard network because they have imposed theconditions of correct discharge from the well, rather than specifying the well water level. Ifthe correct discharge is enforced, the correct flow through the aquifer is obtained and thepiezometric head takes approximately the correct value at all points apart from the wellitself.Therefore it is not essential to make this correction every time that a well is represented ona resistance network. For example when a large area is to be modelled with the dischargefrom the wells specified, only minor errors will arise if the correction is ignored, but if a study is

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BOOK REVIEW 267concerned with the design of a complete water abstraction unit, then the well water level is ofprimary importance, and it is essential that the correction of equation (1) is made.Yours faithfully,K. R. RUSHTON

R. HERBERTDepartment of Civil Engineering,The University,Birmingham, 15.18 March, 1966.

Foundation En&ineerinB, Vol . 2BOOK REVIEW

(in German) by K. SzechySpringer, Vienna, 1965, 759 pp.

In the review of the first volume of this book (Geoteclzlziqzte,3 :3 :263) the future secondvolume was announced. This has now been published in two separate parts.The first part of Volume 2 covers the subject of excavations. The design and constructionof strutted excavations, sheet pile walls, cofferdams and soil stabilized slopes are discussed indetail both from the theoretical and practical points of view. Of particular interest is thetreatment of recently developed construction methods which have not so far been readilyavailable in book form. The section on control of ground water in excavations covers theproblem of drainage, of ground water lowering with many practical examples.The second part of the present volume treats the design and construction on different typesof foundations. An extensive section on the design of spread foundations precedes the treat-ment of the design and construction of piled foundations, including the results of the mostrecent investigations of this difficult subject. The section on caissons, foundation stabilizingand machine foundations is followed by numerous references of the rapidly growing literatureon foundation engineering.The present volume is well illustrated by clear diagrams and many interesting photographsfrom the authors wide experience and contains a variety of numerical examples of methods offoundation designs.This work forms an important contribution to foundation engineering and can be warmlyrecommended to students and practising engineers as an authoritative text and reference bookon the subject.

G.G.M.

PUBLICATIONS RECEIVEDThe following publications have been placed in the Institution Library.

Earth and rock--U damsEstabilidad de presas de tierra y escollera. (Stability of earth and rock-fill dams).V. Escario. Laboratorio de1 Transporte y Mechanica de1 Suelo. Monografia, numero 1.(In Spanish).

Computer programmesSlope stability reference manual. English Electric-Leo-Marconi Computers Ltd.